Robust Areal Thermodynamics of the Schwarzschild Black Hole with Robin Boundary Conditions and Weyl Asymptotics

• URL: http://arxiv.org/abs/1807.09128v4
• Date: Sun, 14 Sep 2025 08:19:55 GMT
• Title: Robust Areal Thermodynamics of the Schwarzschild Black Hole with Robin Boundary Conditions and Weyl Asymptotics
• Authors: Thomas Schürmann,
• Abstract summary: We formulate an areal thermodynamics for the Schwarzschild black hole that takes the horizon area as the sole macroscopic variable.<n> Quantizing ultrarelativistic interior modes on a regular spacelike slice with a Robin boundary at a stretched horizon leads to a self-adjoint Laplace-Beltrami problem with Heun-type quantization.<n>A maximum-entropy area ensemble introduces an intensive areal temperature $T_A$, and Weyl/heat- Kernels control the resulting statistical mechanics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We formulate an areal thermodynamics for the Schwarzschild black hole that takes the horizon area as the sole macroscopic variable. Quantizing ultrarelativistic interior modes on a regular spacelike slice with a Robin boundary at a stretched horizon leads to a self-adjoint Laplace-Beltrami problem with Heun-type quantization. A maximum-entropy area ensemble introduces an intensive areal temperature $T_A$, and Weyl/heat-kernel asymptotics control the resulting statistical mechanics. The leading equations of state follow universally from the spatial Weyl volume coefficient: in a canonical ensemble of $N$ ultrarelativistic bosons one finds $A = 3 N k_B T_A$ up to a boundary-dependent constant, while in the massless grand-canonical sector $A \propto T_A^{4}$ with a generalized Planck spectrum and a Wien displacement relation. These scaling exponents are insensitive to Dirichlet/Neumann/Robin data and to the foliation; only numerical prefactors vary. Embedding the construction into a static four-dimensional background via Matsubara factorization reproduces the 4D Weyl law and yields a finite matter entropy $S_{\mathrm{rad}} \propto A^{3/4}$, parametrically subleading to the Bekenstein-Hawking term after standard renormalization. The framework provides a concise, mathematically controlled bridge between interior spectral data and macroscopic area relations, clarifying the scope and limitations of areal thermodynamics.

Related papers

• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion [6.113393367813894]
  We introduce an acceleration-based adiabatic criterion that separates adiabatic and diabatic dynamics across the $(T,v)$ plane.<n>We identify a broad Planckian domain in which the dimensionless diffusivity $!=!Dm/hbar$ is of order unity and only weakly depends on the parameters.
  arXiv  Detail & Related papers  (2025-12-06T03:23:22Z)
• Intrinsic Heisenberg-type lower bounds on spacelike hypersurfaces in general relativity [0.0]
  We prove a coordinate- and foliation-independent Heisenbergtype lower bound for quantum states strictly localized in geodesic balls of radius spacelike hypersurfaces of arbitrary spacetimes with matter and a constant.
  arXiv  Detail & Related papers  (2025-10-02T03:19:11Z)
• Enforced Gaplessness from States with Exponentially Decaying Correlations [0.0]
  We show that even certain exponentially decaying correlations can imply gaplessness.<n>Our findings have implications for identifying the subset of Hilbert space to which gapped ground states belong.
  arXiv  Detail & Related papers  (2025-03-03T19:00:37Z)
• Measurement-induced Lévy flights of quantum information [35.31418199674737]
  We explore a model of free fermions in one dimension subject to frustrated local measurements across adjacent sites.<n>For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate.<n>Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians.
  arXiv  Detail & Related papers  (2025-01-22T14:29:13Z)
• The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State [44.99833362998488]
  We consider the fermionic entanglement entropy for the free Dirac field in a bounded spatial region of Minkowski spacetime. An area law is proven in the limiting cases where the volume tends to infinity and/or the regularization length tends to zero.
  arXiv  Detail & Related papers  (2023-10-05T12:08:03Z)
• Black Hole from Entropy Maximization [0.0]
  One quantum characterization of a black hole motivated by (local) holography and thermodynamics is that it maximizes thermodynamic entropy for a given surface area.<n>We explore this possibility by solving the 4D semi-classical Einstein equation with many matter fields.<n>For highly-excited spherically-symmetric static configurations, we apply local typicality and estimate the entropy including self-gravity to derive its upper bound.
  arXiv  Detail & Related papers  (2023-09-01T17:44:24Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• The frustration-free fully packed loop model [4.965221313169878]
  We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
  arXiv  Detail & Related papers  (2022-06-03T18:00:04Z)
• Sparse Continuous Distributions and Fenchel-Young Losses [28.52737451408056]
  We extend $Omega$-regularized prediction maps and Fenchel-Young losses to arbitrary domains. For quadratic energy functions in continuous domains, the resulting densities are $beta$-Gaussians. We demonstrate our sparse continuous distributions for attention-based audio classification and visual question answering.
  arXiv  Detail & Related papers  (2021-08-04T12:07:18Z)
• Spectral statistics in constrained many-body quantum chaotic systems [0.0]
  We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints. In particular, we analytically argue that in a system of length $L$ that conserves the $mth$ multipole moment, $t_mathrmTh$ scales subdiffusively as $L2(m+1)$.
  arXiv  Detail & Related papers  (2020-09-24T17:59:57Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.