Quasinormal Modes of Charged Dilaton Black Holes in 2 + 1 Dimensions

We have studied the scalar perturbation of static charged dilaton black holes in 2 + 1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2 + 1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.     

Greybody factors of charged dilaton black holes in 2 + 1 dimensions

We have studied the scalar perturbation of charged dilaton black holes in 2+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2+1 dimensions. The exact decay rates and the grey body factors for the massless minimally coupled scalar is computed for both the charged and the uncharged dilaton black holes. The charged and the uncharged black hole show similar behavior for grey body factors, reflection coefficients and decay rates.This revised version was published online in April 2005. The publishing date was inserted.     

Scalar field radiation from dilatonic black holes

We study radiation of scalar particles from charged dilaton black holes. The Hamilton–Jacobi method has been used to work out the tunneling probability of outgoing particles from the event horizon of dilaton black holes. For this purpose we use WKB approximation to solve the charged Klein–Gordon equation. The procedure gives Hawking temperature for these black holes as well.     

On Born approximation in black hole scattering

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner–Nordström and Reissner–Nordström–de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.     

Effect of the Born–Infeld parameter in higher dimensional Hawking radiation

We show in detail that the Hawking temperature calculated from the surface gravity is in agreement with the result of exact semi-classical radiation spectrum for higher dimensional linear dilaton black holes in various theories. We extend the method derived first by Clément–Fabris–Marques for 4-dimensional linear dilaton black hole solutions to the higher dimensions in theories such as Einstein–Maxwell dilaton, Einstein–Yang–Mills dilaton and Einstein–Yang–Mills–Born–Infeld dilaton. Similar to the Clément–Fabris–Marques results, it is proved that whenever an analytic solution is available to the massless scalar wave equation in the background of higher dimensional massive linear dilaton black holes, an exact computation of the radiation spectrum leads to the Hawking temperature TH$T_H$ in the high frequency regime. The significance of the dimensionality on the value of TH$T_H$ is shown, explicitly. For a chosen dimension, we demonstrate how higher dimensional linear dilaton black holes interpolate between the black hole solutions with Yang–Mills and electromagnetic fields by altering the Born–Infeld parameter in aspect of measurable quantity TH$T_H$. Finally, we explain the reason of, why massless higher dimensional linear dilaton black holes cannot radiate.     

Thermodynamics and spectroscopy of charged dilaton black holes

The Bohr–Sommerfeld quantization rule is useful to study the area spectrum of black holes by employing adiabatic invariants. This method is extended to charged dilaton black holes in 2 $+$ + 1 dimensions. We put the background space-time into the Kruskal-like coordinate to find the period with respect to Euclidian time. Also assuming that the adiabatic invariant obeys Bohr–Sommerfeld quantization rule, detailed study of area and entropy spectrum has been done. It is dependent on the charge and is equally spaced as well. We also investigate the thermodynamics of the charged dilaton black hole.     

Integrable models of black holes and their generalizations in the theories of supergravity and superstrings

A new class of integrable models of (0+1)-and (1+1)-dimensional dilaton gravity coupled to any number of scalar fields is introduced and briefly discussed. These models can be reduced to a system of Liouville equations that are coupled through energy and momentum constraints. The constraints can be explicitly solved, thus giving an explicit analytic solution of the theory. In particular, these integrable models describe spherically symmetric black holes and branes of supergravity theories in higher dimensions.     

Dilatons and the dynamical collapse of charged scalar field

We studied the influence of dilaton field on the dynamical collapse of a charged scalar one. Different values of the initial amplitude of dilaton field as well as the altered values of the dilatonic coupling constant were considered. We described structures of spacetimes and properties of black holes emerging from the collapse of electrically charged scalar field in dilaton gravity. Moreover, we provided a meaningful comparison of the collapse in question with the one in Einstein gravity, when dilaton field is absent and its coupling with the scalar field is equal to zero. The course and results of the dynamical collapse process seem to be very sensitive to the amplitude of dilaton field and to the value of the coupling constant in the underlying theory.     

Scalar filed evolution and area spectrum for Lovelock-AdS black holes

We study the modes of evolution of massless scalar fields in the asymptotically AdS spacetime surrounding maximally symmetric black holes of large and intermediate size in the Lovelock model. It is observed that all modes are purely damped at higher orders. Also, the rate of damping is seen to be independent of order at higher dimensions. The asymptotic form of these frequencies for the case of large black holes is found analytically. Finally, the area spectrum for such black holes is found from these asymptotic modes.     

Black hole temperature: Minimal coupling vs conformal coupling

In this article, we discuss the propagation of scalar fields in conformally transformed spacetimes with either minimal or conformal coupling. The conformally coupled equation of motion is transformed into a one-dimensional Schrödinger-like equation with an invariant potential under conformal transformation. In a second stage, we argue that calculations based on conformal coupling yield the same Hawking temperature as those based on minimal coupling. Finally, it is conjectured that the quasi normal modes of black holes are invariant under conformal transformation.     

Absorption of fixed scalar in scattering off 4D N = 4 black holes

We perform the perturbation analysis of the black holes in the 4D, N = 4 supergravity. Analysis around the black holes reveals a complicated mixing between the dilation and other fields (metric and two U(1) Maxwell fields). It turns out that considering both s-wave (l = 0) and higher momentum modes (l ≠ 0), the dilaton as a fixed scalar is the only propagating mode when P = Q, h₁ = h₂ = 0 and F = −G = 2ϕ. We calculate the absorption cross-section for scattering of low frequency waves of fixed scalar and U(1) Maxwell fields off the extremal black hole.     

Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle–Horowitz–Strominger (GHS) dilaton spacetime and Gibbons–Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.     

Entropy of the Quantum Electromagnetic Field in Static, Spherically Symmetric Dilaton Black Holes

The quantum correction to the entropy of four-dimensional nonextreme static,spherically symmetric dilaton black holes arising from electromagnetic fields isinvestigated by 't Hooft's brick wall model. The Garfinkle-Horowitz-Strominger,Gibbons-Maeda, and Garfinkle-Horne dilaton black holes areconsidered. It is shown that the one-loop quantum correction arising from theelectromagnetic fields is exactly twice that due to a massless scalar field. Theresult agrees with that of the Schwarzschild and Reissner-Nordström blackholes.     

Spectroscopy of rotating linear dilaton black holes from boxed quasinormal modes

Numerical studies of the coupled Einstein‐Klein‐Gordon system have recently revealed that confined scalar fields generically collapse to form caged black holes. In the light of this finding, we analytically study the characteristic resonance spectra of the confined scalar fields in rotating linear dilaton black hole geometry. Confining mirrors (cage) are assumed to be placed in the near‐horizon region of a caged rotating linear dilaton black hole ( is the radius of the cage and r₂ represents the event horizon). The radial part of the Klein‐Gordon equation is written as a Schrödinger‐like wave equation, which reduces to a Bessel differential equation around the event horizon. Using analytical tools and proper boundary conditions, we obtain the boxed‐quasinormal mode frequencies of the caged rotating linear dilaton black hole. Finally, we employ Maggiore's method, which evaluates the transition frequency in the adiabatic invariant quantity from the highly damped quasinormal modes, in order to investigate the entropy/area spectra of the rotating linear dilaton black hole.     

Thermodynamics of higher dimensional black holes

We discuss the thermodynamics of higher dimensional black holes with particular emphasis on a new class of spinning black holes which, due to the increased number of Casimir invariants, have additional spin degrees of freedom. In suitable limits, analytic solutions in arbitrary dimensions are presented for their temperature, entropy, and specific heat. In 5 + 1 and 9 + 1 dimensions, more general forms for these quantities are given. It is shown that the specific heat for a higher dimensional black hole is negative definite if it has only one non-zero spin parameter, regardless of the value of this parameter. We also consider equilibrium configurations with both massless particles and massive string modes.     

Gravitational perturbation and quasi-normal modes of charged black holes in Einstein–Born–Infeld gravity

Born–Infeld electrodynamics has attracted considerable interest due to its relation to strings and D-branes. In this paper the gravitational perturbations of electrically charged black holes in Einstein–Born–Infeld gravity are studied. The effective potentials for axial perturbations are derived and discussed. The quasi normal modes for the gravitational perturbations are computed using a WKB method. The modes are compared with those of the Reissner–Nordström black hole. The relation of the quasi normal modes with the non-linear parameter and the spherical index are also investigated. Comments on stability of the black hole and on future directions are madeThis revised version was published online in April 2005. The publishing date was inserted.     

Dilaton driven Hawking radiation in AdS2 black hole

A recent study shows that Hawking radiation of a massless scalar field does not appear on the two-dimensional AdS₂ black hole background. We shall study this issue by calculating absorption and reflection coefficients under dilaton coupling with the matter field. If the scalar field does not couple to the dilaton, then it is fully absorbed into the black hole without any outgoing mode. On the other hand, once it couples to the dilaton field, the outgoing mode of the massless scalar field exists, and the nontrivial Hawking radiation appears. Finally, we comment on this dilaton dependence of Hawking radiation in connection with a three-dimensional black hole.     

Hawking radiation of linear dilaton black holes

We compute exactly the semi-classical radiation spectrum for a class of non-asymptotically flat charged dilaton black holes, the so-called linear dilaton black holes. In the high frequency regime, the temperature for these black holes generically agrees with the surface gravity result. In the special case where the black hole is massless, we show that, although the surface gravity remains finite, there is no radiation, in agreement with the fact that massless objects cannot radiate.     

Entropy Conservation of Linear Dilaton Black Holes in Quantum Corrected Hawking Radiation

It has been shown recently that information is lost in the Hawking radiation of the linear dilaton black holes in various theories when applying the tunneling formalism of Parikh and Wilczek without considering quantum gravity effects. In this paper, we recalculate the emission probability by taking into account the log-area correction to the Bekenstein-Hawking entropy and the statistical correlation between quanta emitted. The crucial role of the quantum gravity effects on the information leakage and black hole remnant is highlighted. The entropy conservation of the linear dilaton black holes is discussed in detail. We also model the remnant as an extreme linear dilaton black hole with a pointlike horizon in order to show that such a remnant cannot radiate and its temperature becomes zero. In summary, we show that the information can also leak out of the linear dilaton black holes together with preserving unitarity in quantum mechanics.