scholarly journals DE SITTER TRANSITIVITY, CONFORMAL TRANSFORMATIONS AND CONSERVATION LAWS

2014 ◽  
Vol 23 (04) ◽  
pp. 1450035 ◽  
Author(s):  
J. G. PEREIRA ◽  
A. C. SAMPSON ◽  
L. L. SAVI
Keyword(s):  
Variational Principles ◽  
Matrix Representation ◽  
Minkowski Spacetime ◽  
The Other ◽  
Conformal Transformations ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Matrix Representations ◽  
Sitter Group ◽  
Sitter Spacetime

Minkowski spacetime is transitive under ordinary translations, a transformation that do not have matrix representations. The de Sitter spacetime, on the other hand, is transitive under a combination of translations and proper conformal transformations, which do have a matrix representation. Such matrix, however, is not by itself a de Sitter generator: it gives rise to a conformal re-scaling of the metric, a transformation not belonging to the de Sitter group, and in general not associated with diffeomorphisms in spacetime. When dealing with variational principles and Noether's theorem in de Sitter spacetime, it is necessary to regularize the transformations in order to eliminate the conformal re-scaling of the metric.

scholarly journals Relationship between Bondi–Sachs quantities and source of gravitational radiation in asymptotically de Sitter spacetime

2018 ◽  
Vol 27 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Xiaokai He ◽  
Jiliang Jing ◽  
Zhoujian Cao
Keyword(s):  
Cosmological Constant ◽  
Gravitational Wave ◽  
Gravitational Radiation ◽  
The Other ◽  
Perturbation Approach ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Sitter Spacetime ◽  
Explicit Expressions

Gravitational radiation plays an important role in astrophysics. Based on the fact that our universe is expanding, the gravitational radiation when a positive cosmological constant is presented has been studied along with two different ways recently, one is the Bondi–Sachs (BS) framework in which the result is shown by BS quantities in the asymptotic null structure, the other is the perturbation approach in which the result is presented by the quadrupoles of source. Therefore, it is worth to interpret the quantities in asymptotic null structure in terms of the information of the source. In this paper, we investigate this problem and find the explicit expressions of BS quantities in terms of the quadrupoles of source in asymptotically de Sitter spacetime. We also estimate how far away the source is, the cosmological constant may affect the detection of the gravitational wave.

scholarly journals Gravitational thermodynamics of causal diamonds in (A)dS

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Theodore Jacobson ◽  
Manus Visser
Keyword(s):  
Killing Vector ◽  
Minkowski Spacetime ◽  
Conformal Killing ◽  
De Sitter Spacetime ◽  
Conformal Killing Vector ◽  
De Sitter ◽  
Thermodynamic Relation ◽  
Killing Field ◽  
Sitter Spacetime ◽  
Gravitational Thermodynamics

The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a ``first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the ``entanglement equilibrium'' result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.

scholarly journals MINKOWSKI BRANE IN ASYMPTOTIC dS5 SPACETIME WITHOUT FINE-TUNING

2004 ◽  
Vol 19 (19) ◽  
pp. 1447-1451 ◽  
Author(s):  
ZHE CHANG ◽  
SHAO-XIA CHEN ◽  
XIN-BING HUANG
Keyword(s):  
Cosmological Constant ◽  
Minkowski Spacetime ◽  
Fine Tuning ◽  
Dimensional Manifold ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Coordinate Axis ◽  
Sitter Spacetime

We discuss properties of a three-brane in an asymptotic five-dimensional de Sitter spacetime. It is found that a Minkowski solution can be obtained without fine-tuning. In the model, the tiny observed positive cosmological constant is interpreted as a curvature of five-dimensional manifold, but the Minkowski spacetime, where we live, is a natural three-brane perpendicular to the fifth coordinate axis.

scholarly journals Born–Infeld-type modified gravity

2019 ◽  
Vol 16 (05) ◽  
pp. 1950070
Author(s):  
S. I. Kruglov
Keyword(s):  
Modified Gravity ◽  
Dimensionless Parameter ◽  
Cosmological Parameters ◽  
Minkowski Spacetime ◽  
Exponential Model ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Starobinsky Model ◽  
Sitter Spacetime ◽  
The Universe

We propose and investigate the modified Born–Infeld-type gravity model with the function [Formula: see text]. At different values of the dimensionless parameter [Formula: see text], the action is converted into some models including general relativity ([Formula: see text]), the Starobinsky model ([Formula: see text]), the exponential model of gravity ([Formula: see text]), and a model proposed in [S. I. Kruglov, Born–Infeld-like modified gravity, Int. J. Theor. Phys. 52 (2013) 2477–2484; S. I. Kruglov, Notes on Born–Infeld-like modified gravity, Astrophys. Space Sci. 361 (2016) 73] ([Formula: see text]). A bound on the parameters, [Formula: see text][Formula: see text]cm2, are due to local tests. The constant curvature solutions are obtained, and we found the potential, and the mass of the scalaron in the Einstein frame. The model describes the inflation of the universe. The de Sitter spacetime is unstable and a Minkowski spacetime is stable. We investigate the cosmological parameters and some critical points of autonomous equations.

scholarly journals Discrete O(1,4) Transformations And New Scalar Quantum Modes On The De Sitter Spacetime

2012 ◽  
Vol 56 (1) ◽  
pp. 38-42
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Time Reversal ◽  
Isometry Group ◽  
Three Dimensional ◽  
Minkowski Spacetime ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Scalar Quantum ◽  
Abelian Subgroups

AbstractIt is shown that the isometry group of the de Sitter spacetime includes two different three-dimensional Abelian subgroups which transform between themselves through a discrete isometry corresponding to the time reversal in the five-dimensional Minkowski spacetime embedding the de Sitter one. The eigenfunctions of the generators of these Abelian subgroups form two different sets of quantum modes correlated by the mentioned isometry.

scholarly journals An exact black hole spacetime with scalar field and its shadow together with quasinormal modes

2020 ◽  
Vol 35 (31) ◽  
pp. 2050256 ◽  
Author(s):  
Shuang Yu ◽  
Changjun Gao
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Black Hole Solution ◽  
Quasinormal Modes ◽  
The Other ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Sitter Spacetime ◽  
Black Hole Spacetime

We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution.

scholarly journals Entropy in locally-de Sitter spacetimes

2015 ◽  
Vol 24 (14) ◽  
pp. 1550099 ◽  
Author(s):  
A. Araujo ◽  
J. G. Pereira
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
A Priori ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Schwarzschild Solution ◽  
Sitter Group ◽  
Quotient Spaces ◽  
Sitter Spacetime ◽  
Definition Of

As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known a priori, independently of Einstein equation. They represent different nongravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincaré, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild solution, in which the black hole and the de Sitter horizons show up as a unique entangled system. Such entanglement, together with energy conservation, create a constraint between the black hole activity and the evolution of the de Sitter radius, providing a new scenario for the study of cosmology.

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

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