Quantum hair, instantons, and black hole thermodynamics: some new results (original) (raw)

Discrete quantum hair on black holes and the non-abelian Aharonov-Bohm effect

Nuclear Physics B, 1990

In an abelian Higgs model where U(1) is broken to 7Z~,by a condensate of charge pe, the U(l) charge Q~in a finite volume V is an observable, but charge is screened, so (QV) falls exponentially to zero as V-.~. It is demonstrated that the ZL,., charge, Q~modulo pe, can be cast as a surface integral by evaluating exp(2~riQ~/pe) in states containing a shell of unbroken vacuum around the volume, and its value is unaffected by the presence of the condensate inside the shell. Thus in these states Q~modulo pe is not screened. This shows that black holes can indeed have hair. The extension to a non-abelian discrete gauge charge is discussed, and the detection of this charge by its non-ahelian Aharonov-Bohm interaction with cosmic strings is described.

Dirty Black Holes and Hairy Black Holes

Physical Review Letters, 1996

An approach based on considerations of the non-classical energy momentum tensor outside the event horizon of a black hole provides additional physical insight into the nature of discrete quantum hair on black holes and its effect on black hole temperature. Our analysis both extends previous work based on the Euclidean action techniques, and corrects an omission in that work. We also raise several issues related to the effects of instantons on black hole thermodynamics and the relation between these effects and results in two dimensional quantum field theory.

Thermal hair of a quantum black hole

Physical Review D, 1998

We investigate the possibility of statistical explanation of the black hole entropy by counting quasi-bounded modes of thermal fluctuation in two dimensional black hole spacetime. The black hole concerned is quantum in the sense that it is in thermal equilibrium with its Hawking radiation. It is shown that the fluctuation around such a black hole obeys a wave equation with a potential whose peaks are located near the black hole and which is caused by quantum effect. We can construct models in which the potential in the above sense has several positive peaks and there are quai-bounded modes confined between these peaks. This suggests that these modes contribute to the black hole entropy. However it is shown that the entropy associated with these modes dose not obey the ordinary area law. Therefore we can call these modes as an additional thermal hair of the quantum black hole.

On the thermodynamics of hairy black holes

Physics Letters B, 2015

We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild-AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawking-Page phase transition.

Aspects of Finite Temperature Quantum Field Theory in a Black Hole Background

arXiv: High Energy Physics - Theory, 2005

We quantize a scalar field at finite temperature T in the background of a classical black hole, adopting ’t Hooft’s “brick wall” model with generic mixed boundary conditions at the brick wall boundary. We first focus on the exactly solvable case of two dimensional space-time. As expected, the energy density is integrable in the limit of vanishing brick wall thickness only for T = TH - the Hawking temperature. Consistently with the most general stress energy tensor allowed in this background, the energy density shows a surface contribution localized on the horizon. We point out that the usual divergences occurring in the entropy of the thermal atmosphere are due to the assumption that the third law of thermodynamics holds for the quantum field in the black hole background. Such divergences can be avoided if we abandon this assumption. The entropy density also has a surface term localized on the horizon, which is open to various interpretations. The extension of these results to highe...

No-hair theorems for black holes in the Abelian Higgs model

Journal of High Energy Physics, 2009

Motivated by the study of holographic superconductors, we generalize no-hair theorems for minimally coupled scalar fields charged under an Abelian gauge field, in arbitrary dimensions and with arbitrary horizon topology. We first present a straightforward generalization of no-hair theorems for neutral scalar hair. We then consider the existence of extremal black holes with scalar hair, and in the case of

Instanton supported scalar hair on black holes

Arxiv preprint gr-qc/9702012, 1997

We present analytical perturbative, and numerical solutions of the Einstein equation which describe a black hole with a nontrivial dila-ton field and a purely topological gauge potential. The gauge potential has zero field strength and hence no stress-energy, but it does couple to virtual ...

Thermodynamical properties of hairy black holes in n spacetime dimensions

Physical Review D, 2008

The issue concerning the existence of exact black hole solutions in presence of non vanishing cosmological constant and scalar fields is reconsidered. With regard to this, in investigating no-hair theorem violations, exact solutions of gravity having as a source an interacting and conformally coupled scalar field are revisited in arbitrary dimensional non asymptotically flat space-times. New and known hairy black hole solutions are discussed. The thermodynamical properties associated with these solutions are investigated and the invariance of the black hole entropy with respect to different conformal frames is proven.

Hairy black holes in massive gravity: Thermodynamics and phase structure

Physical Review D, 2012

The thermodynamic properties of a static and spherically symmetric hairy black hole solution arising in massive gravity with spontaneous Lorentz breaking are investigated. The analysis is carried out by enclosing the black hole in a spherical cavity whose surface is maintained at a fixed temperature T. It turns out that the ensemble is well-defined only if the "hair" parameter Q characterizing the solution is conserved. Under this condition we compute some relevant thermodynamic quantities, such as the thermal energy and entropy, and we study the stability and phase structure of the ensemble. In particular, for negative values of the hair parameter, the phase structure is isomorphic to the one of Reissner-Nordstrom black holes in the canonical ensemble. Moreover, the phase-diagram in the plan (Q, T) has a line of first-order phase transition that at a critical value of Q terminates in a second-order phase transition. Below this line the dominant phase consists of small, cold black holes that are long-lived and may thus contribute much more to the energy density of the Universe than what is observationally allowed for radiating black holes. 1 In the context of the AdS/CFT correspondence [17], this transition turns out to be dual to the confinement-deconfinement phase transition in large-N gauge theories [18]. 2 In practice, we expect that the results obtained under this hypothesis can be extended to situations where Q varies very slowly.