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Journal articles on the topic 'Raychaudhuri equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Pesci, Alessandro. "Effective Null Raychaudhuri Equation." Particles 1, no. 1 (October 23, 2018): 230–37. http://dx.doi.org/10.3390/particles1010017.

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The effects on Raychaudhuri’s equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e., in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence.

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2

Ellis, George F. R. "On the Raychaudhuri equation." Pramana 69, no. 1 (July 2007): 15–22. http://dx.doi.org/10.1007/s12043-007-0107-4.

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3

Cervantes, Aldrin. "Evolution of universe from Raychaudhuri equation for membranes." Modern Physics Letters A 34, no. 22 (July 20, 2019): 1950172. http://dx.doi.org/10.1142/s0217732319501724.

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We know that in general relativity the Raychaudhuri equation gives the congruence and evolution of the geodesics. In this work, it is proposed that in brane cosmology the Raychaudhuri equation, apart from giving the collapse of the brane, it gives the evolution of the brane. Therefore, the Raychaudhuri equation gives the same information as the one of Friedmann’s, in the context of evolution.

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4

Dadhich, Naresh. "Singularity: Raychaudhuri equation once again." Pramana 69, no. 1 (July 2007): 23–29. http://dx.doi.org/10.1007/s12043-007-0108-3.

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5

WANAS, M. I., and M. A. BAKRY. "EFFECT OF SPIN–TORSION INTERACTION ON RAYCHAUDHURI EQUATION." International Journal of Modern Physics A 24, no. 27 (October 30, 2009): 5025–32. http://dx.doi.org/10.1142/s0217751x09046291.

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Raychaudhuri equation is generalized in the parametrized absolute parallelism geometry. This version of absolute parallelism is more general than the conventional one. The generalization takes into account the suggested interaction between the quantum spin of the moving particle and the torsion of the background gravitational field. The generalized Raychaudhuri equation obtained contains some extra terms, depending on the torsion of space–time, that would have some effects on the singularity theorems of general relativity. Under a certain condition, this equation could be reduced to the original Raychaudhuri equation without any need for a vanishing torsion.

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6

Stepanov, Sergey E., and Josef Mikeš. "The generalized Landau–Raychaudhuri equation and its applications." International Journal of Geometric Methods in Modern Physics 12, no. 08 (September 2015): 1560026. http://dx.doi.org/10.1142/s0219887815600269.

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More than twenty years ago, the first of the two authors of this paper has deduced the generalized Landau–Raychaudhuri equation and demonstrated its numerous applications. Now we present some new interesting applications of the generalized Landau–Raychaudhuri equation.

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7

Stavrinos, Panayiotis C., and Maria Alexiou. "Raychaudhuri equation in the Finsler–Randers space-time and generalized scalar-tensor theories." International Journal of Geometric Methods in Modern Physics 15, no. 03 (February 20, 2018): 1850039. http://dx.doi.org/10.1142/s0219887818500391.

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In this work, we obtain the Raychaudhuri equations for various types of Finsler spaces as the Finsler–Randers (FR) space-time and in a generalized geometrical structure of the space-time manifold which contains two fibers that represent two scalar fields [Formula: see text]. We also derive the Klein–Gordon equation for this model. In addition, the energy conditions are studied in a FR cosmology and are correlated with FRW model. Finally, we apply the Raychaudhuri equation for the model [Formula: see text], where M is a FRW-space-time.

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8

Vagenas, Elias C., Lina Alasfar, Salwa M. Alsaleh, and Ahmed Farag Ali. "The GUP and quantum Raychaudhuri equation." Nuclear Physics B 931 (June 2018): 72–78. http://dx.doi.org/10.1016/j.nuclphysb.2018.04.004.

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9

Chakraborty, Sumanta, Dawood Kothawala, and Alessandro Pesci. "Raychaudhuri equation with zero point length." Physics Letters B 797 (October 2019): 134877. http://dx.doi.org/10.1016/j.physletb.2019.134877.

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10

Fennelly, A. J., Jean P. Krisch, John R. Ray, and Larry L. Smalley. "Including spin in the Raychaudhuri equation." Journal of Mathematical Physics 32, no. 2 (February 1991): 485–87. http://dx.doi.org/10.1063/1.529439.

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11

EHLERS, J. "A. K. RAYCHAUDHURI AND HIS EQUATION." International Journal of Modern Physics D 15, no. 10 (October 2006): 1573–80. http://dx.doi.org/10.1142/s0218271806008966.

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12

Albareti, F. D., J. A. R. Cembranos, A. de la Cruz-Dombriz, and A. Dobado. "The Raychaudhuri equation in homogeneous cosmologies." Journal of Cosmology and Astroparticle Physics 2014, no. 03 (March 10, 2014): 012. http://dx.doi.org/10.1088/1475-7516/2014/03/012.

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13

Ehlers, J. "A K Raychaudhuri and his equation." Pramana 69, no. 1 (July 2007): 7–14. http://dx.doi.org/10.1007/s12043-007-0106-5.

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14

Ahmadi, N., and M. Nouri-Zonoz. "Raychaudhuri equation in quantum gravitational optics." Pramana 69, no. 1 (July 2007): 147–57. http://dx.doi.org/10.1007/s12043-007-0116-3.

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15

Choudhury, Shibendu Gupta, Ananda Dasgupta, and Narayan Banerjee. "Raychaudhuri equation in scalar–tensor theory." International Journal of Geometric Methods in Modern Physics 18, no. 08 (May 4, 2021): 2150115. http://dx.doi.org/10.1142/s0219887821501152.

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Implications of the Raychaudhuri equation in focusing of geodesic congruences are studied in the framework of scalar–tensor theory of gravity. Specifically, we investigate the Brans–Dicke theory and Bekenstein’s scalar field theory. In both of these theories, we deal with a static spherically symmetric distribution and a spatially homogeneous and isotropic cosmological model as specific examples. We find that it is possible to violate the convergence condition under reasonable physical assumptions. This leads to the possibility of avoiding a singularity.

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16

BORGMAN, J., and L. H. FORD. "STOCHASTIC GRAVITY AND THE LANGEVIN-RAYCHAUDHURI EQUATION." International Journal of Modern Physics A 20, no. 11 (April 30, 2005): 2364–73. http://dx.doi.org/10.1142/s0217751x05024638.

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We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources.

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17

Horwitz, Lawrence Paul, Vishnu S. Namboothiri, Gautham Varma K, Asher Yahalom, Yosef Strauss, and Jacob Levitan. "Raychaudhuri Equation, Geometrical Flows and Geometrical Entropy." Symmetry 13, no. 6 (May 28, 2021): 957. http://dx.doi.org/10.3390/sym13060957.

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The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. The equation turns into a harmonic oscillator form under suitable transformations. Thereby, a relation between geometrical entropy and mean geodesic deviation is established. This has a connection to chaos theory where the trajectories diverge exponentially. We discuss its application to cosmology and black holes. Thus, we establish a connection between chaos theory and general relativity.

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18

GUHA, PARTHA. "GEOMETRY OF THE RAYCHAUDHURI EQUATION — PROJECTIVE STRUCTURES AND INTEGRABILITY." International Journal of Modern Physics A 15, no. 18 (July 20, 2000): 2933–51. http://dx.doi.org/10.1142/s0217751x00001324.

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19

Minguzzi, E. "Raychaudhuri equation and singularity theorems in Finsler spacetimes." Classical and Quantum Gravity 32, no. 18 (September 1, 2015): 185008. http://dx.doi.org/10.1088/0264-9381/32/18/185008.

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20

Mukku, Chandrasekher, Swadesh M. Mahajan, and Bindu A. Bambah. "On a Raychaudhuri equation for hot gravitating fluids." Pramana 69, no. 1 (July 2007): 137–45. http://dx.doi.org/10.1007/s12043-007-0115-4.

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21

Lashin, E. I. "On the correctness of cosmology from quantum potential." Modern Physics Letters A 31, no. 07 (March 2, 2016): 1650044. http://dx.doi.org/10.1142/s0217732316500449.

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We examine in detail the cosmology based on quantal (Bohmian) trajectories as suggested in a recent study [A. F. Ali and S. Das, Phys. Lett. B 741, 276 (2014)]. We disagree with the conclusions regarding predicting the value of the cosmological constant [Formula: see text] and evading the Big Bang singularity. Furthermore, we show that the approach of using a quantum corrected Raychaudhuri equation (QRE), as suggested in A. F. Ali and S. Das, Phys. Lett. B 741, 276 (2014), is unsatisfactory, because, essentially, it uses the Raychaudhuri equation (RE), which is a kinematical equation, in order to predict dynamics. In addition, even within this inconsistent framework, the authors have adopted unjustified assumptions and carried out incorrect steps leading to doubtful conclusions.

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22

Alsaleh, Salwa, Lina Alasfar, Mir Faizal, and Ahmed Farag Ali. "Quantum no-singularity theorem from geometric flows." International Journal of Modern Physics A 33, no. 10 (April 10, 2018): 1850052. http://dx.doi.org/10.1142/s0217751x18500525.

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In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space–time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

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23

Sharma, Manabendra. "Raychaudhuri equation in an anisotropic universe with anisotropic sources." Gravitation and Cosmology 21, no. 3 (July 2015): 252–56. http://dx.doi.org/10.1134/s0202289315030111.

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24

Das, Saurya. "Cosmic coincidence or graviton mass?" International Journal of Modern Physics D 23, no. 12 (October 2014): 1442017. http://dx.doi.org/10.1142/s0218271814420176.

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Using the quantum corrected Friedmann equation, obtained from the quantum Raychaudhuri equation, and assuming a small mass of the graviton (but consistent with observations and theory), we propose a resolution of the smallness problem (why is observed vacuum energy so small?) and the coincidence problem (why does it constitute most of the universe, about 70%, in the current epoch?).

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25

Stavrinos, P. C. "Weak gravitational field in Finsler–Randers space and Raychaudhuri equation." General Relativity and Gravitation 44, no. 12 (August 25, 2012): 3029–45. http://dx.doi.org/10.1007/s10714-012-1438-0.

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26

Bejancu, Aurel, and Hani Reda Farran. "On the (1 + 3) threading of an almost FLRW universe." International Journal of Geometric Methods in Modern Physics 13, no. 05 (April 21, 2016): 1650065. http://dx.doi.org/10.1142/s0219887816500651.

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Based on the Riemannian spatial connection and the kinematic quantities, we develop a new approach on the [Formula: see text] threading of an almost FLRW universe, with respect to a non-normalized vector field. By this method, we obtain simple expressions for geometric objects and equations involved in the theory of cosmological perturbations. We state three forms of Raychaudhuri equation, which lead us to more accurate intervals for the conformal time with respect to the existence of caustics in the congruence of geodesics.

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27

Rashki, M., M. Fathi, B. Mostaghel, and S. Jalalzadeh. "Interacting dark side of universe through generalized uncertainty principle." International Journal of Modern Physics D 28, no. 06 (April 2019): 1950081. http://dx.doi.org/10.1142/s0218271819500810.

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We investigate the impact of the generalized uncertainty principle proposed by some approaches to quantum gravity such as string theory and doubly special relativity on the cosmology. Using generalized Poisson brackets, we obtain the modified Friedmann and Raychaudhuri equations and suggest a dynamical dark energy to explain the late-time acceleration of the universe. After considering the interaction between dark matter and dark energy, originated from the minimal length, we obtain the effective cosmological parameters and equation of state parameter for dark matter and dark energy. Finally, we show that the resulting model is equivalent to the Phantom and Tachyon fields.

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28

Akhshabi, Siamak. "Light propagation and optical scalars in torsion theories of gravity." Modern Physics Letters A 34, no. 04 (February 10, 2019): 1950029. http://dx.doi.org/10.1142/s0217732319500299.

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We investigate the propagation of light rays and evolution of optical scalars in gauge theories of gravity where torsion is present. Recently, the modified Raychaudhuri equation in the presence of torsion has been derived. We use this result to derive the basic equations of geometric optics for several different interesting solutions of the Poincaré gauge theory of gravity. The results show that the focusing effects for neighboring light rays will be different than general relativity. This in turn has practical consequences in the study of gravitational lensing effects and also in determining the angular diameter distance for cosmological objects.

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29

RAYCHAUDHURI, A. K. "A NEW SINGULARITY THEOREM IN RELATIVISTIC COSMOLOGY." Modern Physics Letters A 15, no. 06 (February 28, 2000): 391–95. http://dx.doi.org/10.1142/s0217732300000372.

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It is shown that if the time-like eigenvector of the Ricci tensor is hypersurface orthogonal so that the space–time allows a foliation into space sections, then the space average of each of the scalars that appears in the Raychaudhuri equation vanishes provided that the strong energy condition holds good. This result is presented in the form of a singularity theorem.

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30

Sugiura, Norimasa, Naoshi Sugiyama, and Misao Sasaki. "Anisotropies in Luminosity Distance." Symposium - International Astronomical Union 183 (1999): 269. http://dx.doi.org/10.1017/s0074180900132863.

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Anisotropies in luminosity distance-redshift relation (dL − z relation) caused by the large-scale structure (LSS) of the universe are studied. We solve the Raychaudhuri equation on FRW models taking account of LSS by the linear perturbation method. Numerical calculations to evaluate the amplitude of the anisotropies are done on flat models with cosmological constant and open models, employing Cold Dark Matter models and COBE-normalization for the power spectrum of the density perturbations.

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31

Cervantes, Aldrin, and Miguel A. García-Aspeitia. "Predicting cusps or kinks in Nambu–Goto dynamics." Modern Physics Letters A 30, no. 39 (December 7, 2015): 1550210. http://dx.doi.org/10.1142/s0217732315502107.

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It is known that Nambu–Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri (Rh) equation for membranes to determine if there are cusps and kinks in the worldsheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu–Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.

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32

Zhong, Lan, Hao Chen, Zheng-Wen Long, Chao-Yun Long, and Hassan Hassanabadi. "The study of the generalized Klein–Gordon oscillator in the context of the Som–Raychaudhuri space–time." International Journal of Modern Physics A 36, no. 20 (July 14, 2021): 2150129. http://dx.doi.org/10.1142/s0217751x21501293.

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In this paper, we study the relativistic scalar particle described by the Klein–Gordon equation that interacts with the uniform magnetic field in the context of the Som–Raychaudhuri space–time. Based on the property of the biconfluent Heun function equation, the corresponding Klein–Gordon oscillator and generalized Klein–Gordon oscillator under considering the Coulomb potential are separately investigated, and the analogue of the Aharonov–Bohm effect is analyzed in this scenario. On this basis, we also give the influence of different parameters including parameter [Formula: see text] and oscillator frequency [Formula: see text], and the potential parameter [Formula: see text] on the energy eigenvalues of the considered systems.

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33

Gupta Choudhury, Shibendu, Ananda Dasgupta, and Narayan Banerjee. "Reconstruction of $f(R)$ gravity models for an accelerated universe using the Raychaudhuri equation." Monthly Notices of the Royal Astronomical Society 485, no. 4 (March 14, 2019): 5693–99. http://dx.doi.org/10.1093/mnras/stz731.

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34

Singh, Parampreet, and S. K. Soni. "On the relationship between modifications to the Raychaudhuri equation and the canonical Hamiltonian structures." Classical and Quantum Gravity 33, no. 12 (May 11, 2016): 125001. http://dx.doi.org/10.1088/0264-9381/33/12/125001.

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35

Taṣer, Dog̃ukan, and Melis Ulu Dog̃ru. "Conformal symmetric Bianchi type-I cosmologies in f(R) gravity." Modern Physics Letters A 33, no. 23 (July 29, 2018): 1850134. http://dx.doi.org/10.1142/s0217732318501341.

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In this study, we investigate the Bianchi type-I cosmologies with string cloud attached to perfect fluid in f(R) gravity. The field equations and their exact solutions for Bianchi type-I cosmologies with string cloud attached to a perfect fluid are found by using the conformal symmetry properties. The obtained solutions under the varied selection of arbitrary constants indicate three cosmological models. Isotropy conditions for obtained cosmological models are investigated for large value of time. Whether or not the string cloud in conformal symmetric Bianchi type-I universe supports the isotropy condition for the large value of time has been investigated. Also, we examine the contracting and decelerating features of the obtained solutions by using Raychaudhuri equation. Finally, geometrical and physical results of the solutions are discussed.

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36

Addazi, Andrea. "Evaporation/Antievaporation and energy conditions in alternative gravity." International Journal of Modern Physics A 33, no. 04 (February 10, 2018): 1850030. http://dx.doi.org/10.1142/s0217751x18500306.

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We discuss the evaporation and antievaporation instabilities of Nariai solution in extended theories of gravity. These phenomena were explicitly shown in several different extensions of General Relativity, suggesting that a universal cause is behind them. We show that evaporation and antievaporation are originated from deformations of energy conditions on the Nariai horizon. Energy conditions get new contributions from the extra propagating degrees of freedom, which can provide extra focalizing or antifocalizing terms in the Raychaudhuri equation. We show the two explicit cases of [Formula: see text]-gravity and Gauss–Bonnet gravity.

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37

Bhattacharya, Swastik, and S. Shankaranarayanan. "How emergent is gravity?" International Journal of Modern Physics D 24, no. 12 (October 2015): 1544005. http://dx.doi.org/10.1142/s0218271815440058.

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General theory of relativity (or Lovelock extensions) is a dynamical theory; given an initial configuration on a spacelike hypersurface, it makes a definite prediction of the final configuration. Recent developments suggest that gravity may be described in terms of macroscopic parameters. It finds a concrete manifestation in the fluid-gravity correspondence. Most of the efforts till date has been to relate equilibrium configurations in gravity with fluid variables. In order for the emergent paradigm to be truly successful, it has to provide a statistical mechanical derivation of how a given initial static configuration evolves into another. In this paper, we show that the energy transport equation governed by the fluctuations of the horizon-fluid is similar to Raychaudhuri equation and hence gravity is truly emergent.

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38

Fathi, Mohsen. "Homothetic congruences in general relativity." Modern Physics Letters A 34, no. 01 (January 10, 2019): 1950001. http://dx.doi.org/10.1142/s0217732319500019.

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The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy–momentum deposit of the chosen gravitational system. This is pursued through the inclusion of the base manifold’s cotangent bundle in a generalized Raychaudhuri equation and its kinematical expressions. Exploiting an electromagnetic energy–momentum tensor as the source of non-gravitational effects, I investigate the evolution of the mentioned homothetic congruences, as they fall onto a Reissner–Nordström black hole. The results show remarkable differences to the common expectations from infalling congruences of massive particles.

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39

Choudhury, A. Ghose, Partha Guha, and Barun Khanra. "Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method." Journal of Mathematical Physics 50, no. 10 (October 2009): 102502. http://dx.doi.org/10.1063/1.3243455.

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40

Dempsey, David, and Sam R. Dolan. "Waves and null congruences in a draining bathtub." International Journal of Modern Physics D 25, no. 09 (August 2016): 1641004. http://dx.doi.org/10.1142/s0218271816410042.

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We study wave propagation in a draining bathtub: a black hole analogue in fluid mechanics whose perturbations are governed by a Klein–Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possesses an (effective) horizon, an ergosphere and null circular orbits. We propose here that a ‘pulse’ disturbance may be used to map out the light-cone of the effective geometry. First, we apply the eikonal approximation to elucidate the link between wavefronts, null geodesic congruences and the Raychaudhuri equation. Next, we solve the wave equation numerically in the time domain using the method of lines. Starting with Gaussian initial data, we demonstrate that a pulse will propagate along a null congruence and thus trace out the light-cone of the effective geometry. Our new results reveal features, such as wavefront intersections, frame-dragging, winding and interference effects, that are closely associated with the presence of null circular orbits and the ergosphere.

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41

PANIGRAHI, D., and S. CHATTERJEE. "FRW TYPE OF COSMOLOGY WITH A CHAPLYGIN GAS." International Journal of Modern Physics D 21, no. 10 (October 2012): 1250079. http://dx.doi.org/10.1142/s0218271812500794.

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The evolution of a universe modeled as a mixture of generalized Chaplygin gas (GCG) and ordinary matter field is studied for a Robertson–Walker type of spacetime. This model could interpolate periods of radiation-dominated, matter-dominated and cosmological constant-dominated universes. Depending on the arbitrary constants appearing in our theory, the instant of flip changes. Interestingly, we also get a bouncing model when the signature of one of the constants changes. The velocity of sound may become imaginary under certain situations pointing to a perturbative state and consequently the possibility of structure formation. We also discuss the whole situation in the backdrop of the well-known Raychaudhuri equation and a comparison is made with the previous results.

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42

WU, PUXUN, and HONGWEI YU. "BOUNDS ON f(G) GRAVITY FROM ENERGY CONDITIONS." Modern Physics Letters A 25, no. 27 (September 7, 2010): 2325–32. http://dx.doi.org/10.1142/s0217732310033384.

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The f(G) gravity is a theory to modify the general relativity and it can explain the present cosmic accelerating expansion without the need of dark energy. In this paper the f(G) gravity is tested with the energy conditions. Using the Raychaudhuri equation along with the requirement that the gravity is attractive in the FRW background, we obtain the bounds on f(G) from the SEC and NEC. These bounds can also be found directly from the SEC and NEC within the general relativity context by the transformations: ρ → ρm + ρE and p → pm + pE, where ρE and pE are the effective energy density and pressure in the modified gravity. With these transformations, the constraints on f(G) from the WEC and DEC are obtained. Finally, we examine two concrete examples with WEC and obtain the allowed region of model parameters.

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43

POLLOCK, M. D. "CHRONOMETRIC INVARIANCE AND STRING THEORY." Modern Physics Letters A 23, no. 11 (April 10, 2008): 797–813. http://dx.doi.org/10.1142/s0217732308026820.

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The Einstein–Hilbert Lagrangian R is expressed in terms of the chronometrically invariant quantities introduced by Zel'manov for an arbitrary four-dimensional metric gij. The chronometrically invariant three-space is the physical space γαβ = -gαβ+e2ϕ γαγβ, where e 2ϕ = g00 and γα = g0α/g00, and whose determinant is h. The momentum canonically conjugate to γαβ is [Formula: see text], where [Formula: see text] and ∂t≡ e -ϕ∂0 is the chronometrically invariant derivative with respect to time. The Wheeler–DeWitt equation for the wave function Ψ is derived. For a stationary space-time, such as the Kerr metric, παβ vanishes, implying that there is then no dynamics. The most symmetric, chronometrically-invariant space, obtained after setting ϕ = γα = 0, is [Formula: see text], where δαβ is constant and has curvature k. From the Friedmann and Raychaudhuri equations, we find that λ is constant only if k=1 and the source is a perfect fluid of energy-density ρ and pressure p=(γ-1)ρ, with adiabatic index γ=2/3, which is the value for a random ensemble of strings, thus yielding a three-dimensional de Sitter space embedded in four-dimensional space-time. Furthermore, Ψ is only invariant under the time-reversal operator [Formula: see text] if γ=2/(2n-1), where n is a positive integer, the first two values n=1,2 defining the high-temperature and low-temperature limits ρ ~ T±2, respectively, of the heterotic superstring theory, which are thus dual to one another in the sense T↔1/2π2α′T.

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44

Stavrinos, Panayiotis, Olivia Vacaru, and Sergiu I. Vacaru. "Modified Einstein and Finsler like theories on tangent Lorentz bundles." International Journal of Modern Physics D 23, no. 11 (October 2014): 1450094. http://dx.doi.org/10.1142/s0218271814500941.

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In this paper, we study modifications of general relativity, GR, with nonlinear dispersion relations which can be geometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravitational Lagrange density functionals f(R, T, F) with generalized/modified scalar curvature R, trace of matter field tensors T and modified Finsler like generating function F. In particular, there are defined extensions of GR with extra dimensional "velocity/momentum" coordinates. For four-dimensional models, we prove that it is possible to decouple and integrate in very general forms the gravitational fields for f(R, T, F)-modified gravity using nonholonomic 2 + 2 splitting and nonholonomic Finsler like variables F. We study the modified motion and Newtonian limits of massive test particles on nonlinear geodesics approximated with effective extra forces orthogonal to the four-velocity. We compute the constraints on the magnitude of extra-accelerations and analyze perihelion effects and possible cosmological implications of such theories. We also derive the extended Raychaudhuri equation in the framework of a tangent Lorentz bundle. Finally, we speculate on effective modeling of modified theories by generic off-diagonal configurations in Einstein and/or MGTs and Finsler gravity. We provide some examples for modified stationary (black) ellipsoid configurations and locally anisotropic solitonic backgrounds.

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45

Das, Saurya, Mohit Sharma, and Sourav Sur. "On the Quantum Origin of a Dark Universe." Physical Sciences Forum 2, no. 1 (February 22, 2021): 55. http://dx.doi.org/10.3390/ecu2021-09289.

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It has been shown beyond reasonable doubt that the majority (about 95%) of the total energy budget of the universe is given by dark components, namely Dark Matter and Dark Energy. What constitutes these components remains to be satisfactorily understood however, despite a number of promising candidates. An associated conundrum is that of the coincidence, i.e., the question as to why the Dark Matter and Dark Energy densities are of the same order of magnitude at the present epoch, after evolving over the entire expansion history of the universe. In an attempt to address these, we consider a quantum potential resulting from a quantum corrected Raychaudhuri–Friedmann equation in presence of a cosmic fluid, which is presumed to be a Bose–Einstein condensate (BEC) of ultralight bosons. For a suitable and physically motivated macroscopic ground state wave function of the BEC, we show that a unified picture of the cosmic dark sector can indeed emerge, thus resolving the issue of the coincidence. The effective Dark energy component turns out to be a cosmological constant, by virtue of a residual homogeneous term in the quantum potential. Furthermore, comparison with the observational data gives an estimate of the mass of the constituent bosons in the BEC, which is well within the bounds predicted from other considerations.

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46

Kar, Sayan. "Generalized Raychaudhuri equations: Examples." Physical Review D 53, no. 4 (February 15, 1996): 2071–77. http://dx.doi.org/10.1103/physrevd.53.2071.

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Jerie, M., and G. E. Prince. "A general Raychaudhuri’s equation for second-order differential equations." Journal of Geometry and Physics 34, no. 3-4 (July 2000): 226–41. http://dx.doi.org/10.1016/s0393-0440(99)00065-0.

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48

Valls, Claudia. "Darbouxian integrals for generalized Raychaudhuri equations." Journal of Mathematical Physics 52, no. 3 (March 2011): 032703. http://dx.doi.org/10.1063/1.3559065.

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Kar, Sayan, and Soumitra Sengupta. "The Raychaudhuri equations: A brief review." Pramana 69, no. 1 (July 2007): 49–76. http://dx.doi.org/10.1007/s12043-007-0110-9.

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Kar, Sayan. "An introduction to the Raychaudhuri equations." Resonance 13, no. 4 (April 2008): 319–33. http://dx.doi.org/10.1007/s12045-008-0013-1.

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