Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/9602003

Hamiltonian thermodynamics of the Reissner-Nordström-anti-de Sitter black hole

Jorma Louko·Stephen N. Winters-Hilt
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric Einstein-Maxwell spacetimes with a negative cosmological constant. We impose boundary conditions that enforce every classical solution to be an exterior region of a Reissner-Nordström-anti-de Sitter black hole with a nondegenerate Killing horizon, with the spacelike hypersurfaces extending from the horizon bifurcation two-sphere to the asymptotically anti-de Sitter infinity. The constraints are simplified by a canonical transformation, which generalizes that given by Kuchař in the spherically symmetric vacuum Einstein theory, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the grand partition function of a thermodynamical grand canonical ensemble is obtained by analytically continuing the Lorentzian time evolution operator to imaginary time and taking the trace. A~similar analysis under slightly modified boundary conditions leads to the partition function of a thermodynamical canonical ensemble. The thermodynamics in each ensemble is analyzed, and the conditions that the (grand) partition function be dominated by a classical Euclidean black hole solution are found. When these conditions are satisfied, we recover in particular the Bekenstein-Hawking entropy. The limit of a vanishing cosmological constant is briefly discussed. (This paper is dedicated to Karel Kuchař on the occasion of his sixtieth birthday.)

Explore related subjects

gr-qchep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jorma Louko, Stephen N. Winters-Hilt. 1996-09-07. Hamiltonian thermodynamics of the Reissner-Nordström-anti-de Sitter black hole. https://doi.org/10.1103/physrevd.54.2647

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Novel thermodynamic inequality for rotating AdS black holes

We propose a new thermodynamic inequality for stationary, asymptotically Anti-de Sitter rotating black holes, expressed in terms of their angular momentum, mass and thermodynamic volume as $ 4πJ^2/(3MV)<1 $. For the solutions considered, this inequality follows from the requirement that the thermodynamic identities admit a physical horizon with positive area. We examine Kerr(-Newman)-AdS, Kerr-Sen-AdS, pairwise-equal four-charge AdS black holes, charged rotating AdS black strings, and charged rotating AdS C-metrics, finding strong supporting evidence for the inequality across different horizon topologies. We then reformulate the inequality in terms of the underlying metric parameters and compare the resulting constraints with the corresponding regularity and horizon-existence conditions. This analysis shows that the proposed inequality has different physical content for different geometries. We further examine charged super-entropic black holes, for which the ultraspinning limit leads instead to a lower bound on the thermodynamic ratio. This result is consistent with the violation of the reverse isoperimetric inequality characteristic of super-entropic solutions. Moreover, when combined with the refined reverse isoperimetric inequality, the proposed bound ensures the physicality of the Kerr-AdS reference solution entering the refined bound and thereby yields the conventional reverse isoperimetric inequality. We also extend the proposed relation to higher dimensions and test it for singly spinning thin AdS black ring with nonspherical horizon topology, finding that the corresponding inequalities are satisfied throughout the thin-ring regime.

gr-qc↗
arXiv2026

Varying Newton constant, entropy and the black hole evaporation law

We assume that the Newton potential of a spherically symmetric body of mass $M$ is $V=-G(M)Mr^{-1}$, where the Newton constant $G$ may depend on $M$. We insert this assumption in the Schwarzschild solution. We discuss varying $G$ in the black hole thermodynamics and black hole evaporation law. We extend the Bekenstein-Hawking formula $\hbar GS=\frac{1}{4}A$, where $S$ is the entropy and $ A$ the area, to a varying $G$. It is shown that if $G(M)$ is of the form of a power-law $G\simeq M^{-Γ}$ then $G(M)S\simeq A$ is still preserved but the evaporation law substantially depends on the function $G(M)$.

gr-qc↗
arXiv2026

Relativistic mode sums for neutron-star tidal response

Time-dependent tidal interactions during the late inspiral of binary neutron stars encode valuable information about neutron-star structure, but systematically extending the familiar Newtonian mode-sum picture into full general relativity is nontrivial. In this paper, we develop a practical relativistic implementation of mode-sum tidal response for non-rotating neutron stars in Regge-Wheeler gauge. Using near-zone boundary conditions, we systematically define the interior tidal field, the relativistic overlap integrals, and the corresponding mode amplitudes. The good is that the dominant f-mode contribution is remarkably robust, reproducing the direct matching calculation to within $\sim 3$\% across the equations of state we consider. The bad is that the operator governing mode inner product is not positive definite on the full Regge-Wheeler-gauge function space, so the relativistic mode sum truncated at ${\cal{O}}(ω^2)$ is not expected to strictly converge to the direct matching solution. The subtle is that the tidal field inside the star is not unique, although this ambiguity has only a limited impact on the dominant f-mode response for the classes of extensions studied here. Our results establish the practical utility of relativistic mode-sum approximations, while making clear that their predictive power comes from a controlled low-mode description, rather than from a formally convergent strong-field expansion.

gr-qc↗