Regular black holes and the first law of black hole mechanics

Abstract

Singularity-free regular black holes are a popular alternative to the singular mathematical black holes predicted by general relativity. Here, we derive a generic condition that spherically symmetric dynamical regular black holes must satisfy to be compatible with the first law of black hole mechanics based on an expression for the surface gravity at the outer horizon. We examine the dynamical generalizations of models typically considered in the literature and demonstrate that none of them satisfies the condition required for compatibility with the first law, suggesting that modifications are required to maintain its physical meaning. We show that the need for corrections is inherently linked to the introduction of a minimal length scale and can therefore be seen as a direct consequence of the spacetime regularization. We explicitly identify the additional work terms in the extended first law, comment on their thermodynamic interpretation, and show that the linear coefficient of the Misner-Sharp mass suffices to determine the relevant thermodynamic properties.

arXiv comment11 pages. Published version. Comments welcome!

References in corpus (33)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Formation and evaporation of non-singular black holes
• Testing the nature of dark compact objects: a status report
• Isolated and dynamical horizons and their applications
• General Laws of Black-Hole Dynamics
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Jerusalem Lectures on Black Holes and Quantum Information
• Notes on non-singular models of black holes
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Essential and inessential features of Hawking radiation
• Minimal conditions for the existence of a Hawking-like flux
• Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes
• Corrected form of the first law of thermodynamics for regular black holes
• Testing the Kerr black hole hypothesis
• Dynamical surface gravity
• Inner horizon instability and the unstable cores of regular black holes
• Physical observability of horizons
• The physics of the relativistic counter-streaming instability that drives mass inflation inside black holes
• Foliation dependence of black hole apparent horizons in spherical symmetry
• Surface gravities for non-Killing horizons
• Trapped surfaces
• Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?
• Energy-momentum tensor and metric near the Schwarzschild sphere
• Closed trapping horizons without singularity
• Temperature and entropy-area relation of quantum matter near spherically symmetric outer trapping horizons
• Universal properties of the near-horizon geometry
• On the first law of black holes with a universal horizon
• Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes
• Semiclassical black holes and horizon singularities
• Paradoxes before the paradox: surface gravity and the information loss problem
• Physical black holes in fourth-order gravity
• Gliner Vacuum, Self-consistent Theory of Ruppeiner Geometry for Regular Black Holes

Cited by in corpus (10)

• Black holes as spherically-symmetric horizon-bound objects
• Formation of regular black hole from baryonic matter
• Kinematic and energy properties of dynamical regular black holes
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• Padé metrics for black hole perturbations and light rings
• Horizon-bound objects: Kerr--Vaidya solutions
• Simpson-Visser-AdS Black Holes: Thermodynamics and Binary Merger
• Different Regular Black Holes: Geodesic Structures of Test Particles
• Absorption and scattering of massless scalar waves by Frolov black holes
• Gibbons-Hawking action for electrically charged black holes in the canonical ensemble and Davies' thermodynamic theory of black holes