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.     

Microscopic and macroscopic entropy of extremal black holes in string theory

It has been observed on a number of occasions that complex transformations, of real solutions of the field equations to other real solutions, often preserve certain properties of the Weyl tensor. That is, the Petrov type and/or gravito-electromagnetic (GEM) properties of the Weyl tensor are preserved. In this context, we present an outstanding example of a complex windmill transformation of a static (non-physical) anisotropic fluid spacetime of Petrov type $I(M^+)$ that maps to a purely magnetic (PM) spacetime of Petrov type $I(M^{\infty })$ . The PM spacetime is analyzed and compared to the Arianrhod–Lun–McIntosh–Perjés spacetime. It is shown that these spacetimes, although similar in some aspects, are distinct solutions. The main distinction is that the generated PM spacetime satisfies all the standard energy-conditions. This intriguing but purely mathematical scenario may have implications in the area of GEM duality.     

Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.     

Electromagnetic quasinormal modes of D-dimensional black holes II

By using the sixth order WKB approximation we calculate for an electromagnetic field propagating in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes its quasinormal (QN) frequencies for the fundamental mode and first overtones. We study the dependence of these QN frequencies on the value of the cosmological constant and the spacetime dimension. We also compare with the results for the gravitational perturbations propagating in the same background. Moreover we compute exactly the QN frequencies of the electromagnetic field propagating in D-dimensional massless topological black hole and for the charged D-dimensional Nariai spacetime we calculate exactly the QN frequencies of the coupled electromagnetic and gravitational perturbations.     

Entropy spectrum of the D-dimensional massless topological black hole

There are exact solutions to Einstein’s equations with negative cosmological constant that represent black holes whose event horizons are manifolds of negative curvature, the so-called topological black holes. Among these solutions there is one, the massless topological black hole, whose mass is equal to zero. Hod proposes that in the semiclassical limit the asymptotic quasinormal frequencies determine the entropy spectrum of the black holes. Taking into account this proposal, we calculate the entropy spectrum of the massless topological black hole and we compare with the results on the entropy spectra of other topological black holes.     

Weak Gravity Conjecture and extremal black holes

Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4D. We use the entropy function formalism to extend previous analysis that dealt with neutral particles, and obtain the corrections to the horizon entropy for different regimes of black hole masses. These corrections are small in general. They are furthermore reduced when supersymmetry is present, and disappear in N = 4 supergravity. We provide some speculative arguments that in a theory with only sub-extremal particles, classical Reissner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer, as shown by the horizon entropy computation.     

Area spectra of near extremal black holes

Motivated by Maggiore’s new interpretation of quasinormal modes, we investigate area spectra of a near extremal Schwarzschild–de Sitter black hole and a higher-dimensional near extremal Reissner–Nordstrom–de Sitter black hole. The result shows that the area spectra are equally spaced and irrelevant to the parameters of the black holes.     

Critical behavior of extremal Kerr-Newman black holes

The previously suggested existence of second-order phase transitions in a series of Kerr-Newman holes is re-examined in the framework of equilibrium black-hole thermodynamics, to distinguish a true transition from another confusing phenomenon. By adopting a physical interpretation unique to the black-hole thermodynamics, various critical exponents are calculated for one side of the transition which is shown actually very likely to occur at the extremal limit.