scholarly journals THE GRAVITATIONAL ENERGY PROBLEM FOR COSMOLOGICAL MODELS IN TELEPARALLEL GRAVITY

2010 ◽  
Vol 19 (12) ◽  
pp. 1925-1935 ◽  
Author(s):  
S. C. ULHOA ◽  
J. F. DA ROCHA NETO ◽  
J. W. MALUF
Keyword(s):  
Average Energy ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Gravitational Energy ◽  
Cosmological Models ◽  
De Sitter ◽  
Energy Problem ◽  
First Case ◽  
Einstein's Equation ◽  
Average Energy Density

We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space–time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild–de Sitter solution of Einstein's equation, and then to the Robertson–Walker universe. We show that in the first case our method leads to an average energy density of the vacuum space–time, and in the latter case the energy vanishes in the case of null curvature.

scholarly journals On Gravitational Entropy of de Sitter Universe

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
S. C. Ulhoa ◽  
E. P. Spaniol
Keyword(s):  
Phase Transition ◽  
Cosmological Constant ◽  
De Sitter Space ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Gravitational Energy ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Gravitational Entropy ◽  
De Sitter Universe

The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure; thus we use those expressions to construct the gravitational entropy. We use the temperature as a function of the cosmological constant and write the first law of thermodynamics from which we obtain the entropy. In the limit Λ≪1 we find that the entropy is proportional to volume, for a specific temperature’s choice; we find that ΔS≥0 as well. We also identify a phase transition in de Sitter space-time by analyzing the specific heat.

Einstein flow and cosmology

2015 ◽  
Vol 30 (18n19) ◽  
pp. 1530047 ◽  
Author(s):  
J. Kouneiher
Keyword(s):  
Space Time ◽  
Cosmological Models ◽  
Point Of View ◽  
Continuous Family ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Global Topology ◽  
Einstein's Equation ◽  
Physical Case

The recent evolution of the observational technics and the development of new tools in cosmology and gravitation have a significant impact on the study of the cosmological models. In particular, the qualitative and numerical methods used in dynamical system and elsewhere, enable the resolution of some difficult problems and allow the analysis of different cosmological models even with a limited number of symmetries. On the other hand, following Einstein point of view the manifold [Formula: see text] and the metric should be built simultaneously when solving Einstein’s equation [Formula: see text]. From this point of view, the only kinematic condition imposed is that at each point of space–time, the tangent space is endowed with a metric (which is a Minkowski metric in the physical case of pseudo-Riemannian manifolds and an Euclidean one in the Riemannian analogous problem). Then the field [Formula: see text] describes the way these metrics depend on the point in a smooth way and the Einstein equation is the “dynamical” constraint on [Formula: see text]. So, we have to imagine an infinite continuous family of copies of the same Minkowski or Euclidean space and to find a way to sew together these infinitesimal pieces into a manifold, by respecting Einstein’s equation. Thus, Einstein field equations do not fix once and for all the global topology. [Formula: see text] Given this freedom in the topology of the space–time manifold, a question arises as to how free the choice of these topologies may be and how one may hope to determine them, which in turn is intimately related to the observational consequences of the space–time possessing nontrivial topologies. Therefore, in this paper we will use a different qualitative dynamical methods to determine the actual topology of the space–time.

scholarly journals LAGRANGE FORMULATION OF THE SYMMETRIC TELEPARALLEL GRAVITY

2006 ◽  
Vol 15 (05) ◽  
pp. 619-634 ◽  
Author(s):  
M. ADAK ◽  
M. KALAY ◽  
Ö. SERT
Keyword(s):  
Gravity Model ◽  
Teleparallel Gravity ◽  
Space Time ◽  
De Sitter ◽  
Lagrange Formulation

We develop a symmetric teleparallel gravity model in a space–time with only the nonmetricity as nonzero, in terms of a Lagrangian quadratic in the nonmetricity tensor. We present a detailed discussion of the variations that may be used for any gravitational formulation. We seek Schwarzschild-type solutions because of its observational significance and obtain a class of solutions that includes Schwarzschild-type, Schwarzschild–de Sitter-type, and Reissner–Nordström-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions.

scholarly journals Higher Dimensional Bianchi Type-III String Cosmological Models in Lyra Geometry

2021 ◽  
Author(s):  
Kangujam Priyokumar Singh ◽  
Jiten Baro ◽  
Asem Jotin Meitei ◽  
S. Romaleima Devi
Keyword(s):  
Bianchi Type ◽  
Dimensional Space ◽  
Big Bang ◽  
Lyra Geometry ◽  
Space Time ◽  
Cosmological Models ◽  
Model Universe ◽  
Type Iii ◽  
First Case ◽  
Dimensional Space Time

Here we studied Bianchi type-III string cosmological models generated by means of a cloud of strings with particles connected to them in the framework of Lyra geometry considering five-dimensional space-time. To obtain the exact solutions of field equations we consider that the shear scalar and the scalar expansion are proportional, σ∞θ which leads to D=cn and secondly we adopt the assumption considering the Reddy String Condition, ρ+λ=0. From the two different cases obtained here, first case leads to the Bianchi type-III string cosmological model in Lyra geometry in five-dimensional space-time and the second case leads to the five-dimensional vacuum universe in general relativity. The Geometrical and physical properties of the model universe are studied comparing with the present day’s observational findings. The model universe obtained here starts with the big bang and as time progresses both particle density ρp and energy density ρ decreases with expansion of our Universe.

scholarly journals Evaporation phenomena in f(T) gravity

2015 ◽  
Vol 93 (4) ◽  
pp. 377-383 ◽  
Author(s):  
M.J.S. Houndjo ◽  
D. Momeni ◽  
R. Myrzakulov ◽  
M.E. Rodrigues
Keyword(s):  
Teleparallel Gravity ◽  
Space Time ◽  
Generic Model ◽  
Perturbation Equation ◽  
De Sitter ◽  
Field Equations ◽  
Initial State ◽  
Universal Feature ◽  
Limiting Case ◽  
Physical Phenomena

We formulate evaporation phenomena in a generic model of generalized teleparallel gravity in Weitzenbock space–time with a diagonal and nondiagonal tetrad basis. We also perform perturbation analysis around the constant torsion scalar solution called the Nariai space–time, which is an exact solution of the field equations as the limiting case of the Schwarzschild – de Sitter space–time and in the limit where two black holes and their cosmological horizons coincide. By a carefully analysis of the horizon perturbation equation, we show that (anti)evaporation cannot happen if we use a diagonal tetrad basis. This result implies that a typical black hole in any generic form of generalized teleparallel gravity is frozen in its initial state if we use diagonal tetrads, but in the case of nondiagonal tetrads the analysis is completely different. With a suitable nontrivial nondiagonal tetrad basis we investigate the linear stability of the model under simultaneous perturbations of the metric and torsion. We observe that in spite of the diagonal case, both evaporation and antievaporation can happen. These phenomena depend on the initial phase of the horizon perturbation. In the first mode, when we restrict ourselves to the first lower modes (anti)evaporation takes place. So, in the nondiagonal case, the physical phenomena are reasonable. This is an important advantage of using nondiagonal tetrads instead of diagonal ones. We also see that this is a universal feature, completely independent from the form of the model.

Conformal geodesics in general relativity

1987 ◽  
Vol 414 (1846) ◽  
pp. 171-195 ◽  
Keyword(s):  
Physical Space ◽  
Space Time ◽  
Parameter Family ◽  
Null Cone ◽  
De Sitter ◽  
Null Infinity ◽  
Physical Description ◽  
Past Time ◽  
First Case ◽  
Metric Structures

Conformal geodesics, space-time curves which are related to conformal structures in a similar way as geodesics are related to metric structures, are discussed. ‘Conformal normal coordinates’, ‘conformal Gauss systems’ and their associated ‘normal connections’, ‘normal frames’ and ‘normal metrics’ are introduced and used to study: (i) asymptotically simple solutions of Ric( ͠g ) Λ͠g near conformal infinity, (ii) asymptotically simple solutions of Ric( ͠g ) = 0 with a past null infinity, which can be represented as the future null cone of a point i - , past time-like infinity. In the first case we define an ∞-parameter family of (physical) Gauss systems near conformal infinity, in the second case a ten-parameter family of (physical) Gauss systems covering a neighbourhood of i - . The behaviour of physical geodesics can be analysed in a particularly simple way in these coordinate systems. Each of these systems allows an extremely simple transition from the conformal analysis to the physical description of space-time. For Λη 00 < 0 (De-Sitter type solutions) all solutions are characterized in terms of the physical space-time by their data on past time-like infinity. For Λ = 0 the conserved quantities of Newman and Penrose are characterized as the first non-trivial coefficient, given by the value of the rescaled Weyl tensor at i - , in an expansion of the physical field in a Gauss system of the type considered before.

scholarly journals Geometries with mismatched branes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Andreas Karch ◽  
Lisa Randall
Keyword(s):  
Boundary Conditions ◽  
Effective Action ◽  
Cosmological Models ◽  
Time Dependent ◽  
De Sitter ◽  
Stabilization Mechanism ◽  
New Class ◽  
Vacuum Solutions ◽  
Single Coordinate

Abstract We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

scholarly journals Bra-ket wormholes in gravitationally prepared states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yiming Chen ◽  
Victor Gorbenko ◽  
Juan Maldacena
Keyword(s):  
Hyperbolic Space ◽  
Path Integral ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
De Sitter ◽  
Euclidean Case ◽  
Fine Grained ◽  
Entropy Formula ◽  
First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

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