We construct infinite-dimensional families of non-singular static space-times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
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http://dx.doi.org/10.1007/s11005-017-0955-x | DOI Listing |
Ann Henri Poincare
December 2023
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany.
We consider the -dimensional Einstein equations with negative cosmological constant coupled to a spherically symmetric, massless scalar field and study perturbations around the anti-de Sitter spacetime. We derive the resonant systems, pick out vanishing secular terms and discuss issues related to small divisors. Most importantly, we rigorously establish (sharp, in most of the cases) asymptotic behaviour for all the interaction coefficients.
View Article and Find Full Text PDFEntropy (Basel)
October 2024
Department of Physics, Liaoning Normal University, Dalian 116029, China.
The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+αR2 and f(R)=R+2γR+8Λ under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter-RN spacetime) with Λ=-1.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
August 2024
Center for Cosmology and Computational Astrophysics, Institute for Advanced Study in Physics, Zhejiang University, Hangzhou 310027, China.
Philos Trans A Math Phys Eng Sci
March 2024
Mathematical Institute, Oxford University, Woodstock Road, Oxford OX2 6GG, UK.
When he first introduced the notion of a conformal boundary into the study of asymptotically empty space-times, Penrose noted that the boundary would be null, space-like or time-like according as the cosmological constant [Formula: see text] was zero, positive or negative. While most applications of the idea of a conformal boundary have been to the zero-[Formula: see text], asymptotically Minkowskian case, there also has been work on the non-zero cases. Here, we review work with a positive [Formula: see text], which is the appropriate case for cosmology of the universe in which we live.
View Article and Find Full Text PDFPhilos Trans A Math Phys Eng Sci
March 2024
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK.
This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on the properties of conformal geodesics. The use of this gauge, combined with the extended conformal Einstein field equations, yields evolution equations in the form of a symmetric hyperbolic system for which standard Cauchy stability results can be employed.
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