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Books on the topic 'Static and spherically symmetric'

Author: Grafiati

Published: 18 April 2022

Last updated: 30 July 2025

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1

Guo, Enli, and Xiaohuan Mo. The Geometry of Spherically Symmetric Finsler Manifolds. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1598-5.

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2

J, Wilson S., ed. Radiative transfer in moving media: Basic mathematical methods for radiative transfer in spherically symmetric moving media. Springer, 1998.

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3

Shen, Zhiyong. What Matter Can Sustain A Wormhole?: Quantized Massive Spin 1/2 Fields on Static Spherically Symmetric Wormhole Spacetimes. LAP Lambert Academic Publishing, 2012.

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4

Deruelle, Nathalie, and Jean-Philippe Uzan. The two-body problem: an effective-one-body approach. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0056.

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This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Ke

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5

Luneburg, Rudolf K. Maxwell's Equation in Spherically Symmetric Media. Andesite Press, 2017.

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6

Luneburg, Rudolf K. Maxwell's Equation in Spherically Symmetric Media. Franklin Classics Trade Press, 2018.

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7

Luneburg, Rudolf K. Maxwell's Equation in Spherically Symmetric Media. Creative Media Partners, LLC, 2018.

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8

Luneburg, Rudolf K. Maxwell's Equation in Spherically Symmetric Media. Franklin Classics Trade Press, 2018.

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9

Maxwell's Equation in Spherically Symmetric Media. Creative Media Partners, LLC, 2022.

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10

Maxwell's Equation in Spherically Symmetric Media. Creative Media Partners, LLC, 2022.

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11

Mo, Xiaohuan, and Enli Guo. The Geometry of Spherically Symmetric Finsler Manifolds. Springer, 2018.

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12

Mo, Xiaohuan, and Enli Guo. The Geometry of Spherically Symmetric Finsler Manifolds. Springer, 2018.

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13

Stability of Spherically Symmetric Wave Maps (Memoirs of the American Mathematical Society). American Mathematical Society, 2006.

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14

Groah, Jeffrey, Blake Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes. Springer London, Limited, 2007.

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15

Groah, Jeffrey, Blake Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes. Springer, 2010.

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16

Groah, Jeffrey, B. Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes (Springer Monographs in Mathematics). Springer, 2006.

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17

Deruelle, Nathalie, and Jean-Philippe Uzan. The Schwarzschild solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0046.

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This chapter deals with the Schwarzschild metric. To find the gravitational potential U produced by a spherically symmetric object in the Newtonian theory, it is necessary to solve the Poisson equation Δ‎U = 4π‎Gρ‎. Here, the matter density ρ‎ and U depend only on the radial coordinate r and possibly on the time t. Outside the source the solution is U = –GM/r, where M = 4π‎ ∫ ρ‎r2dr is the source mass. In general relativity the problem is to find the ‘spherically symmetric’ spacetime solutions of the Einstein equations, and the analog of the vacuum solution U = –GM/r is the Schwarzschild metri

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18

Deruelle, Nathalie, and Jean-Philippe Uzan. Self-gravitating fluids. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0015.

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This chapter briefly describes ‘perfect fluids’. These are characterized by their mass density ρ‎(t, xⁱ), pressure p(t, ⁱ), and velocity field v(t, ⁱ). The motion and equilibrium configurations of these fluids are determined by the equation of state, for example, p = p(ρ‎) for a barotropic fluid, and by the gravitational potential U(t, ⁱ) created at a point ⁱ by other fluid elements. The chapter shows that, given an equation of state, the equations of the problem to be solved are the continuity equation, the Euler equation, and the Poisson equation. It then considers static models with spheric

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19

Mannikko, Paul Douglas. Implementation of a full-wave/quasi-static hybrid method for analysis of axially symmetric thin-wire antennas with capacitive loads. 1988.

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20

Cates, M. Complex fluids: the physics of emulsions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198789352.003.0010.

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These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a mixture: coalescence, Ostwald ripening, its prevention by trapped species, coarsening of bicontinuous states, and the role of shear flow. The third topic addressed is the stabilization of emulsions by using surfactants to reduce or even eliminate the interfacial tension between phases; the physics of bending energy, which becomes relevant in the latter case, is the

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21

Deruelle, Nathalie, and Jean-Philippe Uzan. Newtonian cosmology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0016.

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This chapter discusses the construction of models of the universe, which is ambiguous in Newtonian theory. It presents some results recovered within the framework of general relativity, which in addition makes it possible to lay the foundation of the theory of the formation of large-scale structures in the universe such as galaxies and galactic clusters. The chapter first constructs models of an expanding sphere. If galaxies are treated as the particles of a uniform cloud which is spherically symmetric about the origin of an inertial frame, then these models describe a universe which expands a

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22

Mann, Peter. Energy and Work. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0002.

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This chapter discusses the work–energy theorem, which is developed from Newton’s second law, and defines the kinetic and potential energies of the system. While there is some vector calculus involved, it has been kept to the bare minimum and the reader should not require in-depth knowledge to understand the salient points. If there is a net force on the particle, it accelerates in the direction of the unbalanced force. The force is a central force if it depends only on the distance between the point on which the force acts and the coordinate origin. Using Stokes’s theorem, potential energies a

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23

Mercati, Flavio. Solutions of Shape Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0013.

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This chapter deals with the most important results in SD, namely, the classical solutions of the theory in which the equivalence with (GR) breaks down. Firstly, I study the case of homogeneous but not isotropic cosmologies, known as ‘Bianchi IX’ universes in detail. In this case, each solution that reaches the big bang singularity can be continued uniquely through it, just by requiring continuity of the conformally- and scale-invariant degrees of freedom. The result is a couple of cosmological solutions with opposite orientation glued at the big bang. This result is more general than the homog

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24

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.

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25

Mora, S., and Y. Pomeau. Capillarity with solids. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198789352.003.0007.

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Capillary phenomena occurring on soft solid interfaces are discussed over this lecture. The main goal is to show how a variational approach provides a deep understanding of the static effects coming from the self-capillarity of elastic solids. After an introduction, the general framework is introduced and then various situations are discussed. In each case, the physical phenomena are first briefly introduced, a theoretical analysis is presented, and then the predictions are compared with experiments when available. This lecture is intended as an introduction rather than as a comprehensive revi

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26

Mashhoon, Bahram. Extension of General Relativity. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803805.003.0005.

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Nonlocal general relativity (GR) requires an extension of the mathematical framework of GR. Nonlocal GR is a tetrad theory such that the orthonormal tetrad frame field of a preferred set of observers carries the sixteen gravitational degrees of freedom. The spacetime metric is then defined via the orthonormality condition. The preferred frame field is used to define a new linear Weitzenböck connection in spacetime. The non-symmetric Weitzenböck connection is metric compatible, curvature-free and renders the preferred (fundamental) frame field parallel. This circumstance leads to teleparallelis

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