Einstein's General Theory Of Relativity

The European Physical Journal Plus, 2013

The Levi-Civita Bertotti Robinson (LBR) spacetime is investigated in various coordinate systems. By means of a general formalism for constructing coordinates in conformally flat spacetimes, coordinate transformations between the different coordinate systems are deduced. We discuss the motion of the reference frames in which the different coordinate systems are comoving. Furthermore we characterize the motion of the different reference frames by their normalized timelike Killing vector fields, i.e. by the four velocity fields of the reference particles. We also deduce the formulae in the different coordinate systems for the embedding of the LBR spacetime in a flat 6-dimensional manifold. In particular we discuss a scenario with a spherical domain wall having LBR spacetime outside the wall and flat spacetime inside. We also discuss the internal flat spacetime using the same coordinate systems as in the external LBR spacetime with continuous metric at the wall. Among the different cases one represents a Milne-LBR universe model with a part of the Milne universe inside the wall and an infinitely extended LBR universe outside it. In an appendix we define combinations of trigonometric and hyperbolic functions that we call k-functions and present a new k-function calculus.

The European Physical Journal Plus, 2013

Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes.

Astrophysics and Space Science, 2015

The aim of present work is to extend the application of Weitzeböck Induced Matter Theory (WIMT) to a dyonic Reissner-Nordström Black Hole (RNBH), in order to obtain a quantization relation between gravitational mass and both magnetic and electric charges from a geometric product defined as an invariant in 5D.

Classical and Quantum Gravity, 2015

We apply the causal Israel-Stewart theory of irreversible thermodynamics to model the matter content of the universe as a dissipative fluid possessing bulk and shear viscosity. Along with the full transport equations we consider their widely used truncated version. By implementing a dynamical systems approach to Bianchi type IV and V cosmological models with and without cosmological constant, we determine the future asymptotic states of such universes and show that the truncated Israel-Stewart theory leads to solutions essentially different from the full theory. The solutions of the truncated theory may also manifest unphysical properties. Finally, we find that in the full theory shear viscosity can give a substantial rise to dissipative fluxes, driving the fluid extremely far from equilibrium, where the linear Israel-Stewart theory ceases to be valid.

The European Physical Journal C, 2016

In this work, we investigate the thermodynamics of black p-branes (BB) in the context of Gravity's Rainbow. We investigate this using rainbow functions that have been motivated from loop quantum gravity and κ-Minkowski non-commutative spacetime. Then for the sake of comparison, we examine a couple of other rainbow functions that have also appeared in the literature. We show that, for consistency, Gravity's Rainbow imposes a constraint on the minimum mass of the BB, a constraint that we interpret here as implying the existence of a black p-brane remnant. This interpretation is supported by the computation of the black p-brane's heat capacity that shows that the latter vanishes when the Schwarzschild radius takes on a value that is bigger than its extremal limit. We found that the same conclusion is reached for the third version of rainbow functions treated here but not with the second one for which only standard black p-brane thermodynamics is recovered.

International Journal of Theoretical Physics, 2012

We compare the cosmological kinematics obtained via our law of linearly varying deceleration parameter (LVDP) with the kinematics obtained in the ΛCDM model. We show that the LVDP model is almost indistinguishable from the ΛCDM model up to the near future of our universe as far as the current observations are concerned, though their predictions differ tremendously into the far future.

The European Physical Journal C

We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl-type f(Q, T) gravity, in which the non-metricity Q is represented in the standard Weyl form, fully determined by the Weyl vector, while T represents the trace of the matter energy–momentum tensor. The effects of the Weyl geometry and of the extra force induced by the non-metricity–matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the non-metricity–matter coupling, are obtained in the weak-field approximation. The tidal motion o...

Gravitation and Cosmology

In this paper, spatially homogeneous and anisotropic Bianchi type-I cosmological models of Brans-Dicke theory of gravitation are investigated. The model represents accelerating universe at present and is considered to be dominated by dark energy. Cosmological constant Λ is considered as a candidate for the dark energy that has negative pressure and is responsible for the present acceleration. The derived model agrees at par with the recent SN Ia observations. We have set BD-coupling constant ω to be 40000, seeing the solar system tests and evidences. We have discussed the various physical and geometrical properties of the models and have compared them with the corresponding relativistic models.

Astrophysics and Space Science

In the present work we have searched the existence of the late time acceleration of the universe with string fluid as source of matter in anisotropic Heckmann-Suchking space-time by using 287 high red shift (0.3 ≤ z ≤ 1.4) SN Ia data of observed absolute magnitude along with their possible error from Union 2.1 compilation. It is found that the best fit values for (Ωm)0, (ΩΛ)0, (Ωσ)0 and (q)0 are 0.2820, 0.7177, 0.0002 &-0.5793 respectively. Several physical aspects and geometrical properties of the model are discussed in detail.

Pramana

We have developed an accelerating cosmological model for the present universe which is phantom for the period (0 ≤ z ≤ 1.99) and quintessence phase for (1.99 ≤ z ≤ 2.0315). The universe is assumed to be filled with barotropic and dark energy(DE) perfect fluid in which DE interact with matter. For a deceleration parameter(DP) having decelerating-accelerating transition phase of universe, we assume hybrid expansion law for scale factor. The transition red shift for the model is obtained as zt = 0.956. The model satisfies current observational constraints.

The European Physical Journal C

We consider the cosmological evolution in an osculating point Barthel–Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe the physical properties of the gravitational field, as well as the cosmological dynamics. For the Barthel–Randers geometry the connection is given by the Levi-Civita connection of the associated Riemann metric. The generalized Friedmann equations in the Barthel–Randers geometry are obtained by considering that the background Riemannian metric in the Randers line element is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equation is derived, and it is interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. The cosmological properties of the model are investigated in detail, and it is shown that the model admits a de Sitter type solution, and that an effective co...

2021

In this work, we present the thermodynamic study of a model that considers the black hole as a condensate of gravitons. In this model, the spacetime is not asymptotically flat because of a topological defect that introduces an angle deficit in the spacetime like in Global Monopole solutions. We have obtained a correction to the Hawking temperature plus a negative pressure associated with the black hole of mass M. In this way, the graviton condensate, which is assumed to be at the critical point defined by the condition $$\mu _{ch}=0,$$ μ ch = 0 , has well-defined thermodynamic quantities P, V, $$T_{h}$$ T h , S, and U as any other Bose–Einstein condensate (BEC). In addition, we present a formal equivalence between the Letelier spacetime and the line element that describes the graviton condensate. We also discuss the Kiselev black hole, which can parametrize the most well-known spherically symmetric black holes. Finally, we present a new metric, which we will call the BEC–Kiselev sol...

The European Physical Journal C, 2015

The aim of this work is to apply WIMT to Gullstränd-Painlevé and Reissner-Nordström metrics in the framework of Weitzeböck Induced Matter Theory (WIMT). This is a newly developed method that extends Induced Matter Theory(IMT) from a curved 5D manifold using the Weitzeböck's geometry, using the fact that the Riemann-Weitzeböck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles.

2014

In this work, we investigate black hole (BH) physics in the context of gravity rainbow. We investigate this through rainbow functions that have been proposed by Amelino-Camelia, et el. in [1, 2]. This modification will give corrections to both the temperature and the entropy of BH and hence it changes the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. It prevents BH from total evaporation, predicting the existence of BH remnant which may resolve the catastrophic behavior of Hawking radiation as the BH mass approaches zero.

The European Physical Journal C, 2009

In this paper, the model of the holographic Chaplygin gas has been extended to two general cases: first the case of a modified variable Chaplygin gas and second the case of the viscous generalized Chaplygin gas. The dynamics of the model is expressed by the use of scalar fields and scalar potentials.

Astrophysics and Space Science, 2010

Some features of the Bianchi type-I universes in the presence of a fluid that wields an anisotropic equation of state (EoS) parameter are discussed in the context of general relativity. The models that exhibit de Sitter volumetric expansion due to the constant effective energy density (the sum of the energy density of the fluid and the anisotropy energy density) are of particular interest. We also introduce two locally rotationally symmetric models, which exhibit de Sitter volumetric expansion in the presence of a hypothetical fluid that has been obtained by minimally altering the conventional vacuum energy. In the first model, the directional EoS parameter on the x axis is assumed to be-1, while the ones on the other axes and the energy density of the fluid are allowed to be functions of time. In the second model, the energy density of the fluid is assumed to be constant, while the directional EoS parameters are allowed to be functions of time.

Journal of Cosmology and Astroparticle Physics, 2009

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.

Physical Review D, 2017

We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in [P. Bueno and P. A. Cano, arXiv:1607.06463] to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify LðRiemannÞ theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity. In addition, we show that the most general cubic gravity constructed in a dimension-independent way and which does not propagate the ghostlike spin-2 mode (but can propagate the scalar) is a linear combination of fðLovelockÞ invariants, plus the Einsteinian cubic gravity term, plus a new ghost-free gravity term. Next, we construct the generalized Newton potential and the post-Newtonian parameter γ for general LðRiemannÞ gravities in arbitrary dimensions, unveiling some interesting differences with respect to the four-dimensional case. We also study the emission and propagation of gravitational radiation from sources for these theories in four dimensions, providing a generalized formula for the power emitted. Finally, we review Wald's formalism for general LðRiemannÞ theories and construct new explicit expressions for the relevant quantities involved. Many examples illustrate our calculations.

Nonlinear Differential Equations and Applications NoDEA

We prove the existence of global in time solution with the small initial data for the semilinear equation of the spin-1 2 particles in the Friedmann-Lemaître-Robertson-Walker spacetime. Moreover, we also prove that if the initial function satisfies the Lochak-Majorana condition, then the global solution exists for arbitrary large initial value. The solution scatters to free solution for large time. The mass term is assumed to be complex-valued. The conditions on the imaginary part of mass are discussed by proving nonexistence of the global solutions if certain relation between scale function and the mass are fulfilled.

Classical and Quantum Gravity, 2020

We investigate a corner of the Bianchi models that has not received much attention: "extended FLRW models" (eFLRW) defined as a cosmological model with underlying anisotropic Bianchi geometry that nevertheless expands isotropically and can be mapped onto a reference FLRW model with the same expansion history. In order to investigate the stability and naturalness of such models in a dynamical systems context, we consider spatially homogeneous models that contain a massless scalar field ϕ and a non-tilted perfect fluid obeying an equation of state p = wρ. Remarkably, we find that matter anisotropies and geometrical anisotropies tend to cancel out dynamically. Hence, the expansion is asymptotically isotropic under rather general conditions. Although extended FLRW models require a special matter sector with anisotropies that are "fine-tuned" relative to geometrical anisotropies, our analysis shows that such solutions are dynamically preferred attractors in general relativity. Specifically, we prove that all locally rotationally symmetric Bianchi type III universes with space-like ∇ µ ϕ are asymptotically shear-free, for all w ∈ [−1, 1]. Moreover, all shear-free equilibrium sets with anisotropic spatial curvature are proved to be stable with respect to all homogeneous perturbations for w ≥ −1/3.

Indian Journal of Physics

We have probed a cosmological model in f (R)-gravity, which is a cubic equation in scalar curvature R. The terms arise due to nonlinear f (R) function are treated as energy due to curvature inspired geometry. As a result, we find accelerating expansion in the universe, which creates an anti-gravitating negative pressure in it. Some of the physical parameters are solved using numerical methods. The evolution of the model are examined by the latest observational Hubble data (46data points) and Pantheon data (the latest compilation of SNIa with 40 binned in the redshift range 0.014 z 1.62). Some important features of the model have been discussed by analyzing the plots of various dynamical parameters. The plots of deceleration parameter q and the Hubble parameter H describe the accelerating expansion in the evolution of the Universe at the present epoch. The transition from deceleration to acceleration for our model is obtained at redshift ztr 0.694069, which is in good agreement with ΛCDM. We have also carried out state finder analysis for our model. The analysis of specific features of the model confirms that our model is consistent with ΛCDM in late times.

Foundations of Physics

The Robertson-Walker (RW) metric allows us to apply general relativity to model the behavior of the Universe as a whole (i.e., cosmology). We can properly interpret various cosmological observations, like the cosmological redshift, the Hubble parameter, geometrical distances, and so on, if we identify fundamental observers with individual galaxies. That is to say that the interpretation of observations of modern cosmology relies on the RW metric. The RW model satisfies the cosmological principle in which the 3-space always remains isotropic and homogeneous. One can derive the cosmological redshift relation from this condition. We show that it is still possible for us to obtain consistent results in a specific timevarying speed of light model without spoiling the success of the standard model. The validity of this model needs to be determined by observations.

Physical Review D, 2022