Area Law For Black Holes Research Articles

Testing the black hole area law with Event Horizon Telescope

Hawking's black hole area theorem can be tested by monitoring the evolution of a single black hole over time. Using current imaging observations of two supermassive black holes M87* and Sgr A* from the Event Horizon Telescope (EHT), we find their horizon area variation fractions are consistent with the prediction of the black hole area law at the confidence level. We point out that whether the black hole area law is valid or not could be determined by future high-precision EHT observations of Sgr A*.

Spherically symmetric counter examples to the Penrose inequality and the positive mass theorem under the assumption of the weak energy condition

Of the various energy conditions which can be assumed when studying mathematical general relativity, intuitively the simplest is the weak energy condition which simply states that the observed mass-energy density must be non-negative. This energy condition has not received as much attention as the so-called dominant energy condition. When the natural question of the Penrose inequality in the context of the weak energy condition arose, we could not find any results in the literature, and it was not immediately clear whether the inequality would hold, even in spherical symmetry. This led us to constructing a spherically symmetric asymptotically flat initial data set satisfying the weak energy condition which violates the ‘usual’ formulations of the Penrose conjecture. This does not contradict (Malec and Murchadha 1994 Phys. Rev. D 49 6931–4), as there the data is assumed to be maximal. Our result is unexpected and interesting because the heuristic argument behind the Penrose inequality relies on the black hole area law which holds when the weak energy condition is satisfied. Our methods also lead to a counter example to the positive mass theorem assuming the weak energy condition.

Binary mergers in bootstrapped Newtonian gravity: Mass gap and black hole area law

We study binary mergers in bootstrapped Newtonian gravity, where higher-order couplings are added to the non-relativistic Lagrangian for the Newtonian potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from both the proper mass of Newtonian gravity and the proper mass of general relativity, which affects the interpretation of astrophysical and cosmological events. The aforementioned difference particularly provides important phenomenological constraints for the mass of the emitted matter and the compactness of the final object after the merger. The interpretation of the GW150914 signal in this theory also shows that LIGO's findings do not violate the mass gap, contrary to usual claims. We indeed find that typical stellar black hole masses can fit LIGO's data for a considerable range of compactness values. We calculate the black hole entropy in this context, which leads to a generalised black hole area law. Non-linear effects are found to effectively change only the gravitational strength via the renormalisation of Newton's constant in this case.

Celestial amplitudes from UV to IR

Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe mathcal{S} -matrix for the scattering of hard particles.

Black Hole Area Law Tested

By comparing the sizes of black holes before and after a merger, researchers have tested Hawking’s theorem on black hole areas.

Infinite black hole entropies at infinite distances and tower of states

The aim of this paper is to elucidate a close connection between the black hole area law and the infinite distance conjecture in the context of the swampland. We consider families of black hole geometries, parametrized by their event horizon areas or by the values of their entropies, and show that the infinite entropy limit is always at infinite distance in the space of black hole geometries. It then follows from the infinite distance conjecture that there must be a tower of states in the infinite entropy limit, and that ignoring these towers on the horizon of the black hole would invalidate the effective theory when the entropy becomes large. We call this the black hole entropy distance conjecture. We then study two candidates for the tower of states. The first are the Kaluza-Klein modes of the internal geometry of extremal N=2 black holes in string theory, whose masses on the horizon are fixed by the N=2 attractor formalism, and given in terms of the black hole charges similarly to the entropy. However, we observe that it is possible to decouple their masses from the entropy, so that they cannot generically play the role of the tower. We thus consider a second kind of states: inspired by N-portrait quantum models of non-extremal black holes, we argue that the Goldstone-like modes that interpolate among the black hole microstates behave like the expected light tower of states.

Maxwell’s equal area law for black holes in power Maxwell invariant

In this paper, we consider the phase transition of black hole in power Maxwell invariant by means of Maxwell's equal area law. First, we review and study the analogy of nonlinear charged black hole solutions with the Van der Waals gas-liquid system in the extended phase space, and obtain isothermal $P$-$v$ diagram. Then, using the Maxwell's equal area law we study the phase transition of AdS black hole with different temperatures. Finally, we extend the method to the black hole in the canonical (grand canonical) ensemble in which charge (potential) is fixed at infinity. Interestingly, we find the phase transition occurs in the both ensembles. We also study the effect of the parameters of the black hole on the two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.

Validity of Maxwell equal area law for black holes conformally coupled to scalar fields in text {AdS}_5 spacetime

We investigate the P{-}V criticality and the Maxwell equal area law for a five-dimensional spherically symmetric AdS black hole with a scalar hair in the absence of and in the presence of a Maxwell field, respectively. Especially in the charged case, we give the exact P{-}V critical values. More importantly, we analyze the validity and invalidity of the Maxwell equal area law for the AdS hairy black hole in the scenarios without and with charges, respectively. Within the scope of validity of the Maxwell equal area law, we point out that there exists a representative van der Waals-type oscillation in the P{-}V diagram. This oscillating part, which indicates the phase transition from a small black hole to a large one, can be replaced by an isobar. The small and large black holes have the same Gibbs free energy. We also give the distribution of the critical points in the parameter space both without and with charges, and we obtain for the uncharged case the fitting formula of the co-existence curve. Meanwhile, the latent heat is calculated, which gives the energy released or absorbed between the small and large black hole phases in the isothermal–isobaric procedure.

RELIC RADIATION FROM AN EVAPORATING BLACK HOLE

This paper presents a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation, at fixed total energy E, from an evanescent, neutral, non-rotating four-dimensional black hole. The only conserved macroscopic quantity is the total energy E which, for a black hole that evaporates completely, is the total energy of the relic radiation. Through a boundary-value approach, in which data for massless, integer-spin perturbations are set on initial and final space-like hypersurfaces, the statistical-mechanics problem becomes, in effect, a one-dimensional problem, with the "volume" of the system determined by the real part of the time separation at spatial infinity — the variable conjugate to the total energy. We count the number of field configurations on the final space-like hypersurface that have total energy E, assuming that initial perturbations are weak. We find that the density of states resembles the well-known Cardy formula. The Bekenstein–Hawking entropy is recovered if the real part of the asymptotic time separation is of the order of the semi-classical black-hole lifetime. We thereby obtain a statistical interpretation of black-hole entropy. Corrections to the microcanonical entropy are computed, and we find agreement with other approaches in terms of a logarithmic correction to the black-hole area law, which is universal (independent of black-hole parameters). This result depends crucially upon the discreteness of the energy levels. We discuss the similarities of our approach with the transition from the black-hole to the fundamental-string regime in the final stages of black-hole evaporation. In addition, we find that the squared coupling, g2, which regulates the transition from a black hole to a highly-excited string state, and vice versa, can be related to the angle, δ, in the complex-time plane, through which we continue analytically the time separation at spatial infinity. Thus, in this scenario, the strong-coupling regime corresponds to a Euclidean black hole, while the physical limit of a Lorentzian space–time (the limit as δ → 0+) corresponds to the weak-coupling regime. This resembles the transition of a black hole to a highly-excited string-like state, which subsequently decays into massless particles, thereby avoiding the naked singularity.

Where are the degrees of freedom responsible for black-hole entropy?

Considering the entanglement between quantum field degrees of freedom inside and outside the horizon as a plausible source of black-hole entropy, we address the question: where are the degrees of freedom that give rise to this entropy located? When the field is in ground state, the black-hole area law is obeyed and the degrees of freedom near the horizon contribute most to the entropy. However, for excited state, or a superposition of ground state and excited state, power-law corrections to the area law are obtained, and more significant contributions from the degrees of freedom far from the horizon are shown.PACS Nos.: 04.60.–m, 04.62., 04.70.–s, 03.65.Ud

Log correction to the black hole area law

Various approaches to black hole entropy yield the area law with logarithmic corrections, many involving a coefficient 1/2, and some involving 3/2. It is pointed out here that the standard quantum geometry formalism is not consistent with 3/2 and favours 1/2.

Area law corrections from state counting and supergravity

Modifications of the Bekenstein-Hawking area law for black holes are crucial in order to find agreement between the microscopic entropy based on state counting and the macroscopic entropy based on an effective field theory computation. We discuss this and related issues for the case of four-dimensional N = 2 supersymmetric black holes. We also briefly comment on the state counting for N = 4 and 8 black holes.

Deviations from the Area Law for Supersymmetric Black Holes

We review modifications of the Bekenstein-Hawking area law for black hole entropy in the presence of higher-derivative interactions. In four-dimensional N = 2 compactifications of string theory or M-theory these modifications are crucial for finding agreement between the macroscopic entropy obtained from supergravity and the microscopic entropy obtained by counting states in string or M-theory. Our discussion is based on the effective Wilsonian action, which in the context of N = 2 supersymmetric theories is defined in terms of holomorphic quantities. At the end we briefly indicate how to incorporate non-holomorphic corrections.

Is there a general area theorem for black holes?

The general validity of the area law for black holes is still an open problem. We first show in detail how to complete the usually incompletely stated textbook proofs under the assumption of piecewise C2-smoothness for the surface of the black hole. Then we prove that a black hole surface necessarily contains points where it is not C1 (called “cusps”) at any time before caustics of the horizon generators show up, like, e.g., in merging processes. This implies that caustics never disappear in the past and that black holes without initial cusps will never develop such. Hence black holes which will undergo any nontrivial processes anywhere in the future will always show cusps. Although this does not yet imply a strict incompatibility with piecewise C2 structures, it indicates that the latter are likely to be physically unnatural. We conclude by calling for a purely measure theoretic proof of the area theorem.