Laws Of Black Hole Mechanics Research Articles

Zeroth and second laws of black hole mechanics in Einstein-Maxwell-scalar effective field theory

There has been recent progress in extending the zeroth and second laws of black hole mechanics to gravitational effective field theories (EFTs). We generalize these results to a much larger class of EFTs describing gravity coupled to electromagnetism and a real scalar field. We also show that the zeroth law holds for the EFT of gravity coupled to electromagnetism and a charged scalar field. Published by the American Physical Society 2024

Challenging event horizons with spin (3/2) fields

We attempt to destroy the event horizons of Kerr black holes by perturbing them with massless spin (3/2) fields. We carry out a detailed analysis by incorporating the explicit form of the absorption probabilities and backreaction effects due to the self energy of the test fields. For extremal and nearly extremal black holes, backreaction effects dominate for perturbations with large magnitudes. However, small perturbations can destroy the event horizons of extremal black holes and drive nearly extremal black holes closer to extremality. Eventually, nearly extremal black holes reach a certain stage where they can be continuously driven to extremality and beyond. Both the cosmic censorship conjecture and the third law of black hole dynamics can be violated by spin (3/2) fields. This directly follows from the fact that fermionic fields do not satisfy the null energy condition. Therefore this result does not contradict with the fact that cosmic censorship and the laws of black hole mechanics remain valid for perturbations satisfying the null energy condition.

Hawking Radiation: Image of the Invisible

Is it possible to quantify in General Relativity, GR, the entropy generated by Super-Massive Black Holes, SMBH, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere? The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of SMBH of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory, LIGO, and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law, GSL, that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH. This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula. The entropy of the evaporation time of SMBH proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the BH.

Preface of “Particles and Fields in Black Hole Environment”

This Special Issue is dedicated to the memory of the physicist Professor James Maxwell Bardeen (9 May 1939–20 June 2022), who is well known for his work on general relativity, particularly his role in formulating the laws of black hole mechanics, the pioneering idea on black hole shadow observation and the Bardeen solution to gravitational field equations [...]

Black hole zeroth law in the Horndeski gravity

The four laws of black hole mechanics have been put forward for a long time. However, the zeroth law, which states that the surface gravity of a stationary black hole is a constant on the event horizon, still lacks universal proof in various modified gravitational theories. In this paper, we study the zeroth law {in a special Horndeski gravity}, which is an interesting gravitational theory with a nonminimally coupled scalar field. After assuming that {the nonminimally coupled scalar field has the same symmetries with the spacetime,} the minimally coupled matter fields satisfy the dominant energy condition and the Horndeski gravity has a smooth limit to Einstein gravity when the coupling constant approaches zero, we prove the zeroth law based on the gravitational equation in Horndeski gravity without any assumption to the spacetime symmetries.

Black hole thermodynamics in the presence of nonlinear electromagnetic fields

As the interaction between the black holes and highly energetic infalling charged matter receives quantum corrections, the basic laws of black hole mechanics have to be carefully rederived. Using the covariant phase space formalism, we generalize the first law of black hole mechanics, both "equilibrium state" and "physical process" versions, in the presence of nonlinear electrodynamics fields, defined by Lagrangians depending on both quadratic electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star F}^{ab}$. Derivation of this law demands a specific treatment of the Lagrangian parameters, similar to embedding of the cosmological constant into thermodynamic context. Furthermore, we discuss the validity of energy conditions, several complementing proofs of the zeroth law of black hole electrodynamics and some aspects of the recently generalized Smarr formula, its (non-)linearity and relation to the first law.

Editorial: Black Holes, Extended Phase Space Thermodynamics and Phase Transitions

Black hole, as an outstanding prediction of Einstein gravity, is one of the most fascinating and mysterious compact subjects. This prediction is confirmed by observational data (1; 2). In addition, one of the remarkable achievements of theoretical physics is related to the discovery of a profound connection between the laws of black hole mechanics with the corresponding laws of ordinary thermodynamic systems (3; 5; 4). On the other hand, the study of black hole thermodynamics in an anti-de Sitter (AdS) space provides remarkable holographic inputs in our efforts to understand the quantum nature of gravity (6; 7; 8).In the context of AdS spacetimes, Hawking-Page phase transition(9) has already shown the existence of novel physics connecting black holes and finite temperature confirmal field theories(8), together with their interesting phase transition structure (10; 11). More recently, exciting developments are taking place due to the emergence of concrete relation between AdS black holes and van der Waals liquid-gas system (

Black hole mechanics and thermodynamics in the light of Weyl transformations

The fate of black hole thermodynamics under Weyl transformations is investigated by going back to the laws of black hole mechanics. It is shown that the transformed surface gravity, that one would identify with the black hole temperature in the conformal frame, as well as the black hole entropy, that one would identify with the horizon area, cannot be invariant. It is also shown that the conformally invariant surface gravity, attributed to the so-called ``conformal Killing horizon,'' cannot represent the black hole temperature in the conformal frame. Finally, using familiar thought experiments, we find that the effect a Weyl transformation should have on black hole thermodynamics becomes even subtler than what is suggested by the laws of black hole mechanics.

Revisiting Laws of Black Hole Mechanics and Violation of Null Energy Condition

Most of the important and powerful theorems in General Relativity such as singularity theorems and the theorems applied for null horizons depend strongly on the energy conditions. However, the energy conditions on which these theorems are based on, are beginning to look at less secure if one takes into accounts quantum effects which can violate these energy conditions. Even there are classical systems that can violate these energy conditions which would be problematic in validation of those theorems. In this article, we revisit to a class of such important theorems, the laws of black hole mechanics which are meant to be developed on null like killing horizons using null energy condition. Then we show some classical and quantum mechanical systems which violate null energy condition based on which the above theorem stands.

Spacetime thermodynamics with contorsion

We prove that a conserved effective energy-momentum tensor for Einstein-Cartan theory can be identified from the Noether identities of the matter Lagrangian, using the torsion field equations relating them. More precisely, a one-parameter family labelled by the Immirzi parameter. We use this result and the contorsion description to show that Jacobson's thermodynamical derivation of the Einstein equations follows as in the metric theory, namely from the equilibrium Clausius relation and the fact that a Killing horizon is metric-geodetic. Our derivation works for an arbitrary torsion field. In the course of our discussion we review the laws of black hole mechanics and their dependence on torsion.

Entropy of black holes in $$\mathcal {N}=2$$N=2 supergravity

Using the formalism of isolated horizons, we construct space of solutions of asymptotically flat extremal black holes in $$\mathcal {N}=2$$ pure supergravity in 4 dimensions. We prove that the laws of black hole mechanics hold for these black holes. Further, restricting to constant area phase space, we show that the spherical horizons admit a Chern–Simons theory. Standard way of quantizing this topological theory and counting states confirms that entropy is indeed proportional to the area of horizon.

Massless charged particles: Cosmic censorship, and the third law of black hole mechanics

The formulation of the laws of black hole mechanics assumes the stability of black holes under perturbations in accordance with the "cosmic censorship hypothesis"(CCH). CCH prohibits the formation of a naked singularity by a physical process from a regular black hole solution with an event horizon. Earlier studies show that naked singularities can indeed be formed leading to the violation of CCH if a near-extremal black hole is injected with massive charged particles and the back reaction effects are neglected. We investigate the validity of CCH by considering the infall of charged massless particles as well as a charged null shell. We also discuss the issue of third law of black hole mechanics in the presence of null charged particles by considering various possibilities.

Towards a second law for Lovelock theories

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking’s area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

The Kerr metric

This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the ‘miraculous’ nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.

Black hole interior mass formula

AbstractWe argue by explicit computations that, although the area product, horizon radii product, entropy product, and irreducible mass product of the event horizon and Cauchy horizon are universal, the surface gravity product, the surface temperature product and the Komar energy product of the said horizons do not seem to be universal for Kerr–Newman black hole spacetimes. We show the black hole mass formula on the Cauchy horizon following the seminal work by Smarr [Phys Rev Lett 30:71 (1973), Phys Rev D 7:289 (1973)] for the outer horizon. We also prescribe the four laws of black hole mechanics for the inner horizon. A new definition of the extremal limit of a black hole is discussed.

First law of binary black hole mechanics in general relativity and post-Newtonian theory

First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly circular orbit. Our calculation is valid through 3PN order and includes, in addition, the contributions of logarithmic terms at 4PN and 5PN orders. This first law of binary point-particle mechanics is then derived from first principles in general relativity, and analogies are drawn with the single and binary black hole cases. Some consequences of the first law are explored for PN spacetimes. As one such consequence, a simple relation between the PN binding energy of the binary system and Detweiler's redshift observable is established. Through it, we are able to determine with high precision the numerical values of some previously unknown high-order PN coefficients in the circular-orbit binding energy. Finally, we propose new gauge-invariant notions for the energy and angular momentum of a particle in a binary system.

Horizon mechanics and asymptotic symmetries with an Immirzi-like parameter in 2 + 1 dimensions

Starting with a generalized theory of 2 + 1 gravity containing an Immirzi-like parameter, we derive the modified laws of black hole mechanics using the formalism of weak isolated horizons. Definitions of the horizon mass and angular momentum emerge naturally in this framework. We further go on to analyse the asymptotic symmetries, as first discussed by Brown and Henneaux, and analyse their implications in a completely covariant phase space framework.

Non-minimally coupled scalar fields, Holst action and black hole mechanics

The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation of black hole horizons to the non-minimally coupled scalar fields. In the early part of the paper, we introduce an appropriate Holst type action to incorporate scalar fields non-minimally coupled to gravity and construct the covariant phase space of the theory. Using this phase space, we proceed to prove the laws of black hole mechanics. Further, we show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern–Simons theory. The level of the Chern–Simons theory is shown to depend on the non-minimally coupled scalar field.

Laws of black hole mechanics from the Holst action

The formulation of weak isolated horizons (WIH) based on the standard isolated horizon formulation of black hole horizons has been reconsidered in the context of the Holst action. Both the zeroth and the first laws of WIH mechanics have been derived. While the zeroth law follows directly from the WIH boundary conditions, first law depends on the action chosen. We construct the covariant phase space of the Holst action for a space-time having WIH as the inner boundary. This requires the introduction of new potential functions so that the symplectic structure is foliation independent. We show that a precise cancellation among various terms leads to the usual first law. Subsequently, we show from the same covariant phase space that for spherically symmetric horizons, the effective theory on the inner boundary is a U(1) Chern-Simons theory.

Black holes and black hole thermodynamics without event horizons

We investigate whether black holes can be defined without using event horizons. In particular we focus on the thermodynamic properties of event horizons and the alternative, locally defined horizons. We discuss the assumptions and limitations of the proofs of the zeroth, first and second laws of black hole mechanics for both event horizons and trapping horizons. This leads to the possibility that black holes may be more usefully defined in terms of trapping horizons. We also review how Hawking radiation may be seen to arise from trapping horizons and discuss which horizon area should be associated with the gravitational entropy.