Curvature-corrected dilatonic black holes and black hole—string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling g _s , the situation can tentatively be interpreted as classical indication on the black hole—string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of the theory with the S-duality symmetric dilaton function as required by the heterotic string theory. The article is published in the original.     

Entropy of the Kerr–Sen black hole

We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.     

Entropy and supersymmetry of D-dimensional extremal electric black holes versus string states

Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a p-dimensional torus, for D = (10 − p) = 4,…,9. We study in particular a one-parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identified with the entropy of the elementary string state with the corresponding quantum numbers.     

EVH black hole solutions with higher derivative corrections

We analyze the effect of higher derivative corrections to the near horizon geometry of the extremal vanishing horizon (EVH) black hole solutions in four dimensions. We restrict ourselves to a Gauss–Bonnet correction with a dilation dependent coupling in an Einstein–Maxwell-dilaton theory. This action may represent the effective action as it arises in tree level heterotic string theory compactified to four dimensions or the K3 compactification of type II string theory. We show that EVH black holes, in this theory, develop an AdS₃ throat in their near horizon geometry.     

Corrections to Hawking-like radiation for a Friedmann–Robertson–Walker universe

Recently, a Hamilton–Jacobi method beyond the semiclassical approximation in black hole physics was developed by Banerjee and Majhi. We generalize their analysis of black holes to the case of a Friedmann–Robertson–Walker (FRW) universe. It is shown that all the higher order quantum corrections in the single particle action are proportional to the usual semiclassical contribution. The corrections to the Hawking-like temperature and entropy of the apparent horizon for the FRW universe are also obtained. In the corrected entropy, the area law involves a logarithmic area correction together with the standard term with the inverse power of the area.     

Entropy correction to stationary black hole via fermions tunneling beyond semiclassical approximation

Recently, fermions tunneling beyond semiclassical approximation from an uncharged static black hole was investigated by Majhi, which was based on the work of Banerjee and Majhi, it was found that the black hole entropy correction can be produced as the quantum effect of a particle is taken into account. In this paper, we further extend this idea to the stationary Kerr black hole to discuss its entropy correction. To get the corrections correctly, the proportionality parameters of quantum corrections of action I _i to the semiclassical action I ₀ in this case are regarded as the inverse of the product of Planck Length and Planck Mass. The result shows that entropy corrections to the stationary black hole also include the logarithmic term and inverse area term in Bekenstein–Hawking entropy beyond semiclassical approximation.     

Quantum aspects of black hole entropy

This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly.     

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

In this overview of selected aspects of the black hole attractor mechanism, after introducing the necessary foundations, we examine the relationship between two ways to describe the attractor phenomenon in four‐dimensional N = 2 supergravity: the entropy function and the black hole potential. We also exemplify their practical application to finding solutions to the attractor equations for a conifold prepotential. Next we describe an extension of the original definition of the entropy function to a class of rotating black holes in five‐dimensional N = 2 supergravity based on cubic polynomials, exploiting a connection between four‐ and five‐dimensional black holes. This link allows further the derivation of five‐dimensional first‐order differential flow equations governing the profile of the fields from infinity to the event horizon and construction of non‐supersymmetric interpolating solutions in four dimensions by dimensional reduction. Finally, since four‐dimensional extremal black holes in N = 2 supergravity can be viewed as certain two‐dimensional string compactifications with fluxes, we discuss implications of the conifold example in the context of the entropic principle, which postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes.     

Entropy Corrections for a Charged Black Hole of String Theory

We study the entropy of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole, originated from the effective action thatemerges in the low-energy of string theory, beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics we derive the quantum correctionsto the entropy of the black hole. The leading (logarithmic) and non leading corrections to the area law are obtained.     

Black holes under external influence

The work on black holes immersed in external fields is reviewed in both test-field approximation and within exact solutions. In particular we pay attention to the effect of the expulsion of the flux of external fields across charged and rotating black holes which are approaching extremal states. Recently this effect has been shown to occur for black hole solutions in string theory. We also discuss black holes surrounded by rings and disks and rotating black holes accelerated by strings. The content corresponds to the lecture given at ICGC 2000 in Kharagpur. Sections 2–6 are based on the text of the lecture on ‘Electromagnetic fields around black holes and Meissner effect’ given at the 3rd ICRA workshop in Pescara 1999 (to be published with T Ledvinka in Nuovo Cimento).     

Nonquasinormal modes and black hole physics

The near-horizon geometry of a large class of extremal and near-extremal black holes in string and M-theory contains three-dimensional asymptotically anti-de Sitter space. Motivated by this structure, we are led naturally to a discrete set of complex frequencies defined in terms of the monodromy at the inner and outer horizons of the black hole. We show that the correspondence principle, whereby the real part of these "nonquasinormal frequencies" is identified with certain fundamental quanta, leads directly to the correct quantum behavior of the near-horizon Virasoro algebra, and thus the black hole entropy. Remarkably, for the rotating black hole in five dimensions we also reproduce the fractionization of conformal weights predicted in string theory.     

Stringy corrections to Kaluza-Klein black holes

We consider string theory corrections to 4D black holes which solve the 5D vacuum Einstein equations. We find that the corrections vanish only for the extremal electric solution. We also show that for the non-extremal electric black hole the mass corrections are related to the charge corrections. The implications to string states counting and the correspondence principle for black holes and strings are discussed.     

Absorption of scalars by extremal black holes in string theory

We show that the low frequency absorption cross section of minimally coupled test massless scalar fields by extremal spherically symmetric black holes in d dimensions is equal to the horizon area, even in the presence of string-theoretical \(\alpha '\) corrections. Classically one has the relation \(\sigma = 4 GS\) between that absorption cross section and the black hole entropy. By comparing in each case the values of the horizon area and Wald’s entropy, we discuss the validity of such relation in the presence of higher derivative corrections for extremal black holes in many different contexts: in the presence of electric and magnetic charges; for nonsupersymmetric and supersymmetric black holes; in \(d=4\) and \(d=5\) dimensions. The examples we consider seem to indicate that this relation is not verified in the presence of \(\alpha '\) corrections in general, although being valid in some specific cases (electrically charged maximally supersymmetric black holes in \(d=5\)). We argue that the relation \(\sigma = 4 GS\) should in general be valid for the absorption cross section of scalar fields which, although being independent from the black hole solution, have their origin from string theory, and therefore are not minimally coupled.     

Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole

We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes.     

Notes on Black Hole Phase Transitions

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios or mechanisms by which these transitions could take place. We begin with a review of the thermodynamics of a black hole system and emphasize that the phase transition is driven by the large entropy of the black hole horizon. Our first theme is illustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz–Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and antivortex topological defects. Finally, we compare the black hole phase transition to another transition driven by an (exponentially) increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory the Hagedorn transition is linked by the Maldacena conjecture to the Hawking–Page black hole phase transition in Anti-de Sitter (AdS) space, as observed by Witten. Thus, the dynamics of the Hagedorn transition may yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within the dynamics of classical string systems. Our third theme points to carrying out a full nonperturbative and nonequilibrium analysis of the large N behavior of classical SU(N) gauge theories to understand its Hagadorn transition. By invoking the Maldacena conjecture we can then gain valuable insight into black hole phase transitions in AdS space.     

Hamiltonian evolution and quantization for extremal black holes

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of the extremal hole surface gravity, and quantization yields a vanishing black hole entropy. Second, we give a Hamiltonian quantization that incorporates extremal black holes as a limiting case of nonextremal ones, and examine the classical limit in terms of wave packets. The spreading of the packets, even the ones centered about extremal black holes, is consistent with continuity of the entropy in the extremal limit, and thus with the Bekenstein-Hawking entropy even for the extremal holes. The discussion takes place throughout within Lorentz-signature spacetimes.     

Non-supersymmetric extremal RN-AdS black holes in $$ \mathcal{N} = 2 $$ gauged supergravity

We investigate extremal Reissner-Nordström-AdS black holes in fourdimensional \( \mathcal{N} = 2 \) abelian gauged supergravity. We find a new attractor equation which is not reduced to the one in the asymptotically flat spacetime. We also argue a formula which is available even in the presence of the scalar potential. We apply them to the T³-model and the STU-model in generic black hole charge distributions. In addition, focusing on the so-called T³-model with a single neutral vector multiplet, we obtain non-supersymmetric extremal Reissner-Nordström-AdS black hole solutions with regular event horizons in the D0-D4 and the D2-D6 black hole charge configurations. The negative cosmological constant emerges even without the Fayet-Iliopoulos parameters.     

The uncertainty principle and Bekenstein–Hawking entropy corrections

There is much attention on the corrections to Bekenstein–Hawking entropy in area with a model-dependent coefficient. The corrections are generally composed of two parts: quantum corrections and thermal corrections. The generalized uncertainty principle (GUP), which will reduce to the conventional Heisenberg relation in situations of weak gravity, is one of the candidates to be utilized to obtain the quantum corrections to the Bekenstein–Hawking entropy. Recently the extended uncertainty principle (EUP) and generalized extended uncertainty principle (GEUP) are introduced to calculate entropy corrections with large length scales limit. In this paper, we obtain the quantum corrections to Bekenstein–Hawking entropy in four-dimensional Schwarzschild black holes based on the EUP and GEUP. Some attractive results are derived.