Relevant bibliographies by topics / Einstein metric

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Einstein metric'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Einstein metric"

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Kong, De-Xing, and Jinhua Wang. "Einstein's hyperbolic geometric flow." Journal of Hyperbolic Differential Equations 11, no. 02 (2014): 249–67. http://dx.doi.org/10.1142/s0219891614500076.

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We investigate the Einstein's hyperbolic geometric flow, which provides a natural tool to deform the shape of a manifold and to understand the wave character of metrics, the wave phenomenon of the curvature for evolutionary manifolds. For an initial manifold equipped with an Einstein metric and assumed to be a totally umbilical submanifold in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric is Einstein if and only if the corresponding manifold is a totally umbilical hypersurface in the induced space-time. For an initial manifold which is equipped with an Einstein metric, assumed to be a totally umbilical submanifold with constant mean curvature in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric remains an Einstein metric, and the corresponding manifold is a totally umbilical hypersurface in the induced space-time. Moreover, the global existence and blowup phenomenon of the constructed metric is also investigated here.
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ROD GOVER, A., and F. LEITNER. "A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS." International Journal of Mathematics 20, no. 10 (2009): 1263–87. http://dx.doi.org/10.1142/s0129167x09005753.

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Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré–Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincaré metric we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman–Graham) obstruction tensor vanishes.
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GHOSH, AMALENDU. "QUASI-EINSTEIN CONTACT METRIC MANIFOLDS." Glasgow Mathematical Journal 57, no. 3 (2014): 569–77. http://dx.doi.org/10.1017/s0017089514000494.

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AbstractWe consider quasi-Einstein metrics in the framework of contact metric manifolds and prove some rigidity results. First, we show that any quasi-Einstein Sasakian metric is Einstein. Next, we prove that any complete K-contact manifold with quasi-Einstein metric is compact Einstein and Sasakian. To this end, we extend these results for (κ, μ)-spaces.
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Deng, Shaoqiang, and Jifu Li. "Some cohomogeneity one Einstein–Randers metrics on 4-manifolds." International Journal of Geometric Methods in Modern Physics 14, no. 03 (2017): 1750044. http://dx.doi.org/10.1142/s021988781750044x.

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The Page metric on [Formula: see text] is a cohomogeneity one Einstein–Riemannian metric, and is the only known cohomogeneity one Einstein–Riemannian metric on compact [Formula: see text]-manifolds. It has been a long standing problem whether there exists another cohomogeneity one Einstein–Riemannian metric on [Formula: see text]-manifolds. In this paper, we construct some examples of cohomogeneity one Einstein–Randers metrics on simply connected 4-manifolds. This shows that, although cohomogeneity one Einstein–Riemmian 4-manifolds are rare, non-Riemannian examples may exist at large.
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Hall, Stuart James, and Thomas Murphy. "Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class." Proceedings of the Edinburgh Mathematical Society 60, no. 4 (2017): 893–910. http://dx.doi.org/10.1017/s0013091516000444.

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AbstractWe develop new algorithms for approximating extremal toric Kähler metrics. We focus on an extremal metric on , which is conformal to an Einstein metric (the Chen–LeBrun–Weber metric). We compare our approximation to one given by Bunch and Donaldson and compute various geometric quantities. In particular, we demonstrate a small eigenvalue of the scalar Laplacian of the Einstein metric that gives numerical evidence that the Einstein metric is conformally unstable under Ricci flow.
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CASE, JEFFREY S. "SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS." International Journal of Mathematics 23, no. 10 (2012): 1250110. http://dx.doi.org/10.1142/s0129167x12501108.

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Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.
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Ida, Cristian, Alexandru Ionescu, and Adelina Manea. "A note on para-holomorphic Riemannian–Einstein manifolds." International Journal of Geometric Methods in Modern Physics 13, no. 09 (2016): 1650107. http://dx.doi.org/10.1142/s0219887816501073.

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The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. First, we make some general considerations about para-complex Riemannian manifolds (not necessarily para-holomorphic). Next, using a one-to-one correspondence between para-holomorphic Riemannian metrics and para-Kähler–Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-Kähler–Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a natural para-Kählerian–Norden Einstein metric.
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RǍSDEACONU, RAREŞ, and IOANA ŞUVAINA. "Smooth structures and Einstein metrics on." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 2 (2009): 409–17. http://dx.doi.org/10.1017/s0305004109002527.

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AbstractWe show that each of the topological 4-manifolds $\bcp^2\# k\overline{\bcp^2}$, for k = 5, 6, 7, 8 admits a smooth structure which has an Einstein metric of scalar curvature s > 0, a smooth structure which carries an Einstein metric with s < 0 and infinitely many non-diffeomorphic smooth structures which do not admit Einstein metrics. We also exhibit new examples of higher dimensional manifolds carrying Einstein metrics of both positive and negative scalar curvature.
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NAJAFI, B., and A. TAYEBI. "A FAMILY OF EINSTEIN RANDERS METRICS." International Journal of Geometric Methods in Modern Physics 08, no. 05 (2011): 1021–29. http://dx.doi.org/10.1142/s021988781100552x.

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We classify all Einstein Randers metric on R4 constructed from ga, the Hawking Taub–NUT metric, and a homothetic vector field W for ga in the Zermelo navigation representation. All of these Einstein Randers metrics are Ricci-flat and are not of scalar flag curvature. Finally, the moduli space of constructed Randers metrics is obtained.
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Tayebi, Akbar, and Ali Nankali. "On generalized Einstein Randers metrics." International Journal of Geometric Methods in Modern Physics 12, no. 10 (2015): 1550105. http://dx.doi.org/10.1142/s0219887815501054.

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In this paper, we study the Ricci directional curvature defined by H. Akbar-Zadeh in Finsler geometry and obtain the formula of Ricci directional curvature for Randers metrics. Let F = α + β be a Randers metric on a manifold M, where [Formula: see text] is a Riemannian metric and β = biyi is a closed 1-form on M. We prove that F is a generalized Einstein metric if and only if it is a Berwald metric.
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Dissertations / Theses on the topic "Einstein metric"

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Harst, Ulrich [Verfasser]. "Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity / Ulrich Harst." Mainz : Universitätsbibliothek Mainz, 2013. http://d-nb.info/1032940662/34.

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Champion, Daniel James. "Mobius Structures, Einstein Metrics, and Discrete Conformal Variations on Piecewise Flat Two and Three Dimensional Manifolds." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145313.

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Spherical, Euclidean, and hyperbolic simplices can be characterized by the dihedral angles on their codimension-two faces. These characterizations analyze the Gram matrix, a matrix with entries given by cosines of dihedral angles. Hyperideal hyperbolic simplices are non-compact generalizations of hyperbolic simplices wherein the vertices lie outside hyperbolic space. We extend recent characterization results to include fully general hyperideal simplices. Our analysis utilizes the Gram matrix, however we use inversive distances instead of dihedral angles to accommodate fully general hyperideal simplices.For two-dimensional triangulations, an angle structure is an assignment of three face angles to each triangle. An angle structure permits a globally consistent scaling provided the faces can be simultaneously scaled so that any two contiguous faces assign the same length to their common edge. We show that a class of symmetric Euclidean angle structures permits globally consistent scalings. We develop a notion of virtual scaling to accommodate spherical and hyperbolic triangles of differing curvatures and show that a class of symmetric spherical and hyperbolic angle structures permit globally consistent virtual scalings.The double tetrahedron is a triangulation of the three-sphere obtained by gluing two congruent tetrahedra along their boundaries. The pentachoron is a triangulation of the three-sphere obtained from the boundary of the 4-simplex. As piecewise flat manifolds, the geometries of the double tetrahedron and pentachoron are determined by edge lengths that gives rise to a notion of a metric. We study notions of Einstein metrics on the double tetrahedron and pentachoron. Our analysis utilizes Regge's Einstein-Hilbert functional, a piecewise flat analogue of the Einstein-Hilbert (or total scalar curvature) functional on Riemannian manifolds.A notion of conformal structure on a two dimensional piecewise flat manifold is given by a set of edge constants wherein edge lengths are calculated from the edge constants and vertex based parameters. A conformal variation is a smooth one parameter family of the vertex parameters. The analysis of conformal variations often involves the study of degenerating triangles, where a face angle approaches zero. We show for a conformal variation that remains weighted Delaunay, if the conformal parameters are bounded then no triangle degenerations can occur.
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Wink, Matthias. "Ricci solitons and geometric analysis." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:3aae2c5e-58aa-42da-9a1b-ec15cacafdad.

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This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. This work provides a rigorous construction thereof. A Lyapunov function is introduced to prove that the Ricci soliton metrics lie in a bounded region of an associated phase space. This also gives an alternative construction of non-compact Einstein metrics of non-positive scalar curvature due to Böhm. It is explained how the asymptotics of the Ricci flat trajectories induce Böhm's Einstein metrics on spheres and other low dimensional spaces. A numerical study suggests that all other Einstein metrics of positive scalar curvature which are induced by the generalised Hopf fibrations occur in an entirely non-linear regime of the Einstein equations. Extending the theory of cohomogeneity one steady and expanding Ricci solitons, an estimate which allows to prescribe the growth rate of the soliton potential at any given time is shown. As an application, continuous families of Ricci solitons on complex line bundles over products of Fano Kähler Einstein manifolds are constructed. This generalises work of Appleton and Stolarski. The method also applies to the Lü-Page-Pope set-up and allows to cover an optimal parameter range in the two summands case. The Ricci soliton equation on manifolds foliated by torus bundles over products of Fano Kähler Einstein manifolds is discussed. A rigidity theorem is obtained and a preserved curvature condition is discovered. The cohomogeneity one initial value problem is solved for m-quasi-Einstein metrics and complete metrics are described. L<sup>p</sup>-Poincaré inequalities for k-differentials on closed Riemann surfaces are shown. The estimates are uniform in the sense that the Poincaré constant only depends on p &GE;1, k &ge; 2 and the genus &gamma; &ge; 2 of the surface but not on its complex structure. Examples show that the analogous estimate for 1-differentials cannot be uniform. This part is based on joint work with Melanie Rupflin.
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Welly, Adam. "The Geometry of quasi-Sasaki Manifolds." Thesis, University of Oregon, 2016. http://hdl.handle.net/1794/20466.

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Let (M,g) be a quasi-Sasaki manifold with Reeb vector field xi. Our goal is to understand the structure of M when g is an Einstein metric. Assuming that the S^1 action induced by xi is locally free or assuming a certain non-negativity condition on the transverse curvature, we prove some rigidity results on the structure of (M,g). Naturally associated to a quasi-Sasaki metric g is a transverse Kahler metric g^T. The transverse Kahler-Ricci flow of g^T is the normalized Ricci flow of the transverse metric. Exploiting the transverse Kahler geometry of (M,g), we can extend results in Kahler-Ricci flow to our transverse version. In particular, we show that a deep and beautiful theorem due to Perleman has its counterpart in the quasi-Sasaki setting. We also consider evolving a Sasaki metric g by Ricci flow. Unfortunately, if g(0) is Sasaki then g(t) is not Sasaki for t>0. However, in some instances g(t) is quasi-Sasaki. We examine this and give some qualitative results and examples in the special case that the initial metric is eta-Einstein.
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Fanaai, Hamidreza. "Flot géodésique, mesures invariantes et métriques d'Einstein." Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10278.

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Nous etudions le probleme de conjugaison des flots geodesiques dans deux cas differents. Dans le premier chapitre, nous considerons les varietes riemanniennes compactes de courbure sectionnelle strictement negative et dans le deuxieme chapitre nous traitons le cas des nilvarietes de rang deux. Nous etudions aussi a la fin du premier chapitre, le probleme de l'invariance par symetrie des mesures de patterson-sullivan et harmoniques reliees au flot geodesique. Le dernier chapitre de cette these est consacre a l'etude de varietes homogenes d'einstein de courbure scalaire negative ou nous donnons quelques exemples de telles varietes en etudiant les algebres de lie nilpotentes de rang deux.
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Edmonds, Bartlett Douglas Jr. "Approaching the Singularity in Gowdy Universes." VCU Scholars Compass, 2006. http://scholarscompass.vcu.edu/etd/1083.

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It has been shown that the cosmic censorship conjecture holds for polarized Gowdy spacetimes. In the more general, unpolarized case, however, the question remains open. It is known that cylindrically symmetric dust can collapse to form a naked singularity. Since Gowdy universes comprise gravitational waves that are locally cylindrically symmetric, perhaps these waves can collapse onto a symmetry axis and create a naked singularity. It is known that in the case of cylindrical symmetry, event horizons will not form under gravitational collapse, so the formation of a singularity on the symmetry axis would be a violation of the cosmic censorship conjecture.To search for cosmic censorship violation in Gowdy spacetimes, we must have a better understanding of their singularities. It is known that far from the symmetry axes, the spacetimes are asymptotically velocity term dominated, but this property is not known to hold near the axes. In this thesis, we take the first steps toward understanding on and near axis behavior of Gowdy spacetimes with space-sections that have the topology of the three-sphere. Null geodesic behavior on the symmetry axes is studied, and it is found that in some cases, a photon will wrap around the universe infinitely many times on its way back toward the initial singularity.
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Gaset, Rifà Jordi. "A multisymplectic approach to gravitational theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/620740.

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The theories of gravity are one of the most important topics in theoretical physics and mathematical physics nowadays. The classical formulation of gravity uses the Hilbert-Einstein Lagrangian, which is a singular second-order Lagrangian; hence it requires a geometric theory for second-order field theories which leads to several difficulties. Another standard formulation is the Einstein-Palatini or Metric-Affine, which uses a singular first order Lagrangian. Much work has been done with the aim of establishing the suitable geometrical structures for describing classical field theories. In particular, the multisymplectic formulation is the most general of all of them and, in recent years, some works have considered a multisymplectic approach to gravity. This formulation allows us to study and better understand several inherent characteristics of the models of gravity. The aim of this thesis is to use the multisymplectic formulation for first and second-order field theories in order to obtain a complete covariant description of the Lagrangian and Hamiltonian formalisms for the Einstein-Hilbert and the Metric-Affine models, and explain their characteristics; in particular: order reduction, constraints, symmetries and gauge freedom. Some properties of multisymplectic field theories have been developed in order to study the models. We have established the constraints generated by the projectability of the Poincaré-Cartan form. These constraints are related to the fact that the higher order velocities are strong gauge vector fields. The concept of gauge freedom for field theories also has been analyzed. We propose to use the term "gauge'' to refer to the non-regularity of the Poincaré-Cartan form. Therefore, the multiple solutions are characterized by two sources: the gauge related one, arising from gauge symmetries and related to the non-regularity; and the non-gauge related one, which arises exclusively from field theories. We studied in detail two models of gravity: the Einstein-Hilbert model and the Metric-Affine (or Einstein-Palatini) model. In both cases, a covariant Hamiltonian multisymplectic formalism has been presented. In every situation, we find the final submanifold where solutions exist, and we explicitly write all semi-holonomic multivector fields solution of the field equations. The natural Lagrangian symmetries are presented aswell. Furthermore, we emphasize different aspects in each model: The Einstein-Hilbert model is a singular second order field theory which, as a consequence of its non-regularity, it is equivalent to a regular first order theory. For this model we have presented the unified Lagrangian-Hamiltonian formalism. We have also considered the presence of energy-matter sources and we show how some relevant geometrical and physical characteristics of the theory depend on the source's type. The Metric-Affine model is a singular first order field theory which has a gauge symmetry. We recover and study this gauge symmetry, showing that there are no more. The constraints of the system are presented and analysed. Using the gauge freedom and the constraints, we establish the geometric relation between the Einstein-Palatini and the Einstein-Hilbert models, including the relation between the holonomic solutions in both formalisms. We also present a Hamiltonian model involving only the connection which is equivalent to the Hamiltonian Metric-Affine formalism.<br>Les teories de la gravetat són un dels temes més importants en física teòrica i física matemàtica avui en dia. La formulació clàssica de la gravetat utilitza el Lagrangià de Hilbert-Einstein, el qual és un Lagrangià singular de segon ordre; per tant requereix una teoria geomètrica per teories de camp de segon ordre, que comporten diverses dificultats. Una altra formulació estàndard és la d'Einstein-Palatini o Mètrica-Afí, la qual utilitza un Lagrangià singular de primer ordre. S'ha treballat molt per establir les estructures geomètriques adients per descriure teories de camps clàssiques. Particularment, la formulació multisimplèctica és la més general de totes i, recentment alguns treballs han considerat la gravetat des de un punt de vista multisimplèctic. Aquesta formulació ens permet estudiar i entendre millor diverses característiques inherents dels models gravitatoris. L'objectiu d'aquesta tesi és utilitzar la formulació multisimplèctica per a teories de camps de primer i segon ordre per obtenir una descripció covariant completa dels formalismes Lagrangià i Hamiltonià per als models d'Einstein-Hilbert i Mètrica-Afí, i explicar les seves característiques. Concretament: reducció de l'ordre, restriccions, simetries i llibertat gauge. Algunes propietats de les teories de camps multisimplèctiques han estat desenvolupades per estudiar els models. S'han establert les restriccions generades per la projectabilitat de la forma de Poincaré-Cartan. Aquestes restriccions tenen relació amb el fet que les velocitats d'ordre superior són camps vectorials gauge forts. El concepte de llibertat gauge per a teories de camps també ha estat analitzat. Es proposa la utilització del terme "gauge" per fer referència a la no regularitat de les formes de Poincaré-Cartan. Per tant, les múltiples solucions es caracteritzen a partir de dues fonts: la relativa al gauge, que està relacionada amb la no regularitat, i altres fonts no relacionades amb el gauge que són exclusives de teories de camps. S'ha estudiat en detall dos models de gravetat: el model d'Einstein-Hilbert i el de Mètrica-Afí (o Einstein-Palatinti). En ambdós casos s'ha presentat una formulació covariant multisimplèctica Hamiltoniana. En tots els casos trobem la subvarietat final on les solucions existeixen, i escrivim explícitament tots els camps multivectorials sem-holònoms solució de les equacions de camp. També presentem les simetries Lagrangianes naturals. A més emfatitzem aspectes diferents en cada model: El model d'Einstein-Hilbert és una teoria de camp singular de segon ordre, la qual, com a conseqüència de la seva no regularitat, és equivalent a una teoria regular de primer ordre. Per aquest model hem presentat el formalisme unificat Lagrangià-Hamiltonià. També hem considerat la presència de fonts d'energia-matèria i es mostra com algunes característiques físiques i geomètriques rellevants de la teoria depenen del tipus de font. El model Mètrica-Afí és una teoria de camps singular de primer ordre que té una simetria gauge. Es recupera i s'estudia aquesta simetria gauge mostrant que és única. Les lligadures del sistema són presentades i analitzades. Utilitzant la llibertat gauge i les lligadures, s'estableix la relació geomètrica entre els models d'Einstein-Palatini i d'Einstein-Hilbert, inclosa la relació entre les solucions holònomes en ambdós formalismes. També es presenta un model Hamiltonià, que conté únicament la connexió, equivalent al formalisme Mètrica-Afí Hamiltonià
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Roth, John Charles. "Perturbations of Kähler-Einstein metrics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5737.

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Desa, Zul Kepli Bin Mohd. "Riemannian manifolds with Einstein-like metrics." Thesis, Durham University, 1985. http://etheses.dur.ac.uk/7571/.

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In this thesis, we investigate properties of manifolds with Riemannian metrics which satisfy conditions more general than those of Einstein metrics, including the latter as special cases. The Einstein condition is well known for being the Euler- Lagrange equation of a variational problem. There is not a great deal of difference between such metrics and metrics with Ricci tensor parallel for the latter are locally Riemannian products of the former. More general classes of metrics considered include Ricci- Codazzi and Ricci cyclic parallel. Both of these are of constant scalar curvature. Our study is divided into three parts. We begin with certain metrics in 4-dimensions and conclude our results with three theorems, the first of which is equivalent to a result of Kasner [Kal] while the second and part of the third is known to Derdzinski [Del.2].Next we construct the metrics mentioned above on spheres of odd dimension. The construction is similar to Jensen's [Jel] but more direct and is due essentially to Gray and Vanhecke [GV]. In this way we obtain .beside the standard metric, the second Einstein metric of Jensen. As for the Ricci- Codazzi metrics, they are essentially Einstein, but the Ricci cyclic parallel metrics seem to form a larger class. Finally, we consider subalgebras of the exceptional Lie algebra g2. Making use of computer programmes in 'reduce' we compute all the corresponding metrics on the quotient spaces associated with G2.
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Pedersen, H. "Geometry and magnetic monopoles : Constructions of Einstein metrics and Einstein-Weyl geometries." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.353118.

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Books on the topic "Einstein metric"

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Asymptotically symmetric Einstein metrics. American Mathematical Society, 2006.

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Siu, Yum-Tong. Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics. Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7486-1.

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Kähler-Einstein metrics and integral invariants. Springer-Verlag, 1988.

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Futaki, Akito. Kähler-Einstein Metrics and Integral Invariants. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078084.

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Biquard, Olivier, ed. AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries. European Mathematical Society Publishing House, 2005. http://dx.doi.org/10.4171/013.

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Siu, Yum-Tong. Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics: Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986. Birkhäuser Verlag, 1987.

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Wentworth, Richard A., Duong H. Phong, Paul M. N. Feehan, Jian Song, and Ben Weinkove. Analysis, complex geometry, and mathematical physics: In honor of Duong H. Phong : May 7-11, 2013, Columbia University, New York, New York. American Mathematical Society, 2015.

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Siu, Yum-Tong. Lectures on Hermitian-Einstein Metric for Stable Bundles and Kahler-Einstein Metrics (DMV Seminar). Birkhauser Verlag AG, 1989.

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Deruelle, Nathalie, and Jean-Philippe Uzan. The Kerr solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0048.

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This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.
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Wittman, David M. General Relativity and the Schwarzschild Metric. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199658633.003.0018.

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Previously, we saw that variations in the time part of the spacetime metric cause free particles to accelerate, thus unifying gravity and relativity; and that orbits trace those accelerations, which follow the inverse‐square law around spherical source masses. But a metric that empirically models orbits is not enough; we want to understand how any arrangement of mass determines the metric in the surrounding spacetime. This chapter describes thinking tools, especially the frame‐independent idea of spacetime curvature, that helped Einstein develop general relativity. We describe the Einstein equation, which determines the metric given a source or set of sources. Solving that equation for the case of a static spherical mass (such as the Sun) yields the Schwarzschild metric. We compare Schwarzschild and Newtonian predictions for precession, the deflection of light, and time delay of light; and we contrast the effects of variations in the time and space parts of the metric.
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Book chapters on the topic "Einstein metric"

1

Tian, Gang. "Existence of Einstein Metrics on Fano Manifolds." In Metric and Differential Geometry. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0257-4_5.

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Brown, Harvey R. "The Behaviour of Rods and Clocks in General Relativity and the Meaning of the Metric Field." In Einstein Studies. Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4939-7708-6_2.

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Schumacher, Georg. "The Curvature of the Petersson-Weil Metric on the Moduli Space of Kähler-Einstein Manifolds." In Complex Analysis and Geometry. Springer US, 1993. http://dx.doi.org/10.1007/978-1-4757-9771-8_14.

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Aubin, Thierry. "Einstein-Kähler Metrics." In Some Nonlinear Problems in Riemannian Geometry. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-13006-3_7.

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Grøn, Øyvind, and Arne Næss. "The metric tensor." In Einstein's Theory. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0706-5_5.

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Besse, Arthur L. "Kähler-Einstein Metrics and the Calabi Conjecture." In Einstein Manifolds. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-540-74311-8_12.

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Siu, Yum-Tong. "Curvature of the Weil-Petersson Metric in the Moduli Space of Compact Kähler-Einstein Manifolds of Negative First Chem Class." In Contributions to Several Complex Variables. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-06816-7_13.

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Futaki, Akito. "Kähler-Einstein metrics and extremal Kähler metrics." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078087.

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Kotschick, D. "Entropies, Volumes, and Einstein Metrics." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_2.

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Siu, Yum-Tong. "The Heat Equation Approach to Hermitian-Einstein Metrics on Stable Bundles." In Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics. Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7486-1_1.

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Conference papers on the topic "Einstein metric"

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Poltorak, A. "General Relativity in Metric-Affine Space." In ALBERT EINSTEIN CENTURY INTERNATIONAL CONFERENCE. AIP, 2006. http://dx.doi.org/10.1063/1.2399608.

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Hasanuddin, A. Azwar, and B. E. Gunara. "Stationary axisymmetric four dimensional space-time endowed with Einstein metric." In THE 5TH ASIAN PHYSICS SYMPOSIUM (APS 2012). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4917121.

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Wijaya, R. N., M. F. Rozi, and B. E. Gunara. "Einstein and maximally symmetric space condition for 4D metric with torus symmetry." In THE 5TH ASIAN PHYSICS SYMPOSIUM (APS 2012). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4917124.

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Brozos-Vázquez, M., E. García-Río, and S. Gavino-Fernández. "Quasi-Einstein metrics and plane waves." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733376.

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Arvanitoyeorgos, A., V. V. Dzhepko, and Yu G. Nikonorov. "Invariant Einstein metrics on certain Stiefel manifolds." In Proceedings of the 10th International Conference on DGA2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790613_0004.

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Maschler, Gideon, Oscar J. Garay, Marisa Fernández, Luis Carlos de Andrés, and Luis Ugarte. "Uniqueness of Einstein metrics conformal to extremal Kähler metrics—a computer assisted approach." In SPECIAL METRICS AND SUPERSYMMETRY: Proceedings of the Workshop on Geometry and Physics: Special Metrics and Supersymmetry. AIP, 2009. http://dx.doi.org/10.1063/1.3089199.

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ARVANITOYEORGOS, Andreas, Yusuke SAKANE, and Marina STATHA. "EINSTEIN METRICS ON SPECIAL UNITARY GROUPS SU(2n)." In 6th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811206696_0002.

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Visinescu, Mihai. "Hidden symmetries of Sasaki-Einstein metrics on S2 × S3." In TIM 2012 PHYSICS CONFERENCE. AIP, 2013. http://dx.doi.org/10.1063/1.4832789.

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ARVANITOYEORGOS, Andreas, Yusuke SAKANE, and Marina STATHA. "EINSTEIN METRICS ON THE SYMPLECTIC GROUP WHICH ARE NOT NATURALLY REDUCTIVE." In 4th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814719780_0001.

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ARVANITOYEORGOS, Andreas, Yusuke SAKANE, and Marina STATHA. "HOMOGENEOUS EINSTEIN METRICS ON COMPLEX STIEFEL MANIFOLDS AND SPECIAL UNITARY GROUPS." In 5th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813220911_0001.

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Reports on the topic "Einstein metric"

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Marques, S. Einstein metrics and Brans-Dicke superfields. Office of Scientific and Technical Information (OSTI), 1988. http://dx.doi.org/10.2172/5460334.

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Vilasi, Gaetano. Einstein Metrics with Two-Dimensional Killing Leaves and Their Applications in Physics. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-329-341.

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