Narrow Results

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form mΩ where Ω is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to ln 3. Therefore, it does not give support to Hod's statement that the area spectrum should be valid for a generic Kerr–Newman black hole.

In this paper we present the spectrum of entropy/area for Kehagias–Sfetsos (KS) black hole in Hořava–Lifshitz (HL) gravity via quasinormal modes (QNM) approach. We show that in the massive case, the mass parameter μ disappears in the entropy spectrum and the quasinormal modes are modified by a term proportional to the mass square term. Our calculations show that the charge-like parameter appears in the surface gravity and our calculations can be applied to any spherically symmetric spacetime which has only one physically acceptable horizon. Our main difference between our calculations and what was done in Ref. 1 is that we explicitly calculated the portion of charge and mass on the surface gravity and consequently in the QNM expression. Since the imaginary part of the QNM is related to the adiabatic invariance of the system and also to the entropy, surprisingly the mass parameter does not appear in the entropy spectrum. Our conclusion supported by some acclaims about the scalar field parameters (charges) cannot change the fundamental parameters in the four-dimensional black holes.

Motivated by the new interpretation on quasinormal modes by Maggiore, we investigate the quantization of the extreme Reissner–Nordström black hole in the four-dimensional spacetime. Following Kunstatter's method, we derive the equally spaced area spectrum and the entropy, however the spacing differs from Setare's result via Hod's proposal. Moreover, our result is in full agreement with Bekenstein's result as well as the claim that black hole's area is equidistant in Einstein's Gravity theory by Wei et al.

The area spectrum and entropy spectrum of the modified Schwarzschild black hole in gravity's rainbow are investigated via the quasinormal modes of the black hole. Using the modified Hod's method and Kunstatter's method that employ the proper frequency from the imaginary part other than the real part of the quasinormal modes, the area and entropy spacing of the black hole are calculated. The results obtained from these two methods agree with each other and the equally spaced area and entropy spectrum are derived. The obtained area and entropy spectrum are independent of the energies of test particles and are the same as from the usual Schwarzschild black hole.

The thermodynamic and spectroscopic behavior of Schwarzschild black hole surrounded by quintessence are studied. We have derived the thermodynamic quantities and studied their behavior for different values of quintessence parameter. We put the background spacetime into the Kruskal-like coordinate to find the period with respect to Euclidean time. Also assuming that the adiabatic invariant obeys Bohr–Sommerfeld quantization rule, detailed study of area spectrum and entropy spectrum have been done for special cases of the quintessence state parameter. We find that the spectra are equally spaced.

We study the thermodynamics and spectroscopy of a (2+1)-dimensional black hole proposed by Mandal et al.¹ [Mod. Phys. Lett. A6, 1685 (1991)]. We put the background spacetime in Kruskal like co-ordinate and find period with respect to Euclidean time. Different thermodynamic quantities like entropy, specific heat, temperature etc. are obtained. The adiabatic invariant for the black hole is found and quantized using Bohr–Sommerfeld quantization rule. The study shows that the area spectrum of MSW black hole is equally spaced and the value of spacing is found to be ℏ.

In this paper, we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the MTZ black hole. We have obtained exact values for the quasi-normal mode (QNM) frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schrödinger type equation with the well-known Pöschl–Teller potential. We have also used sixth-order WKB approximation to compute QNM frequencies to compare with exact values obtained via the Pöschl–Teller method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.

In this paper, we have studied the area and mass spectrum of a Lifshitz black hole in 2+1 dimensions. This black hole is obtained for conformal gravity in 2+1 dimensions and is asymptotic to z = 0 Lifshitz spacetime. Quasinormal modes (QNM) frequencies of the conformally coupled scalar field perturbations are employed for the purpose of analyzing the area spectrum of the black hole. We have used two methods: modified Hod's conjecture and Kunsttater's method. In both methods, the area and the mass spectrum is shown to be equally spaced. We compared our results with the area spectrum of the BTZ black hole and the z = 3 black hole and made suggestions to extend this work in the future.

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual general relativity (GR).

Earlier, we have proposed first-order representation of the minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like four-simplices or, say, cuboids into which ${ℝ}^4$ can be decomposed, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR.

In the Hamiltonian formalism, the tetrad bilinears are canonically conjugate to the orthogonal connection matrices. We evaluate the spectrum of the elementary areas, functions of the tetrad bilinears. The spectrum is discrete and proportional to the Faddeev analog ${\gamma }_{\mathrm{\text{F}}}$ of the Barbero–Immirzi parameter $\gamma$. The possibility of the tetrad and metric discontinuities in the Faddeev gravity allows to consider any surface as consisting of a set of virtually independent elementary areas and its spectrum being the sum of the elementary spectra. Requiring consistency of the black hole entropy calculations known in the literature we are able to estimate ${\gamma }_{\mathrm{\text{F}}}$.

In this paper, we analyze the area spectrum of BTZ three-dimensional black holes by considering an outgoing wave and relating its period of motion with the period of the gravitational system with respect to Euclidean time. The area spectra obtained for the rotating and non-rotating black holes are equally spaced and it is important to note that in this paper, we do not need to use the small angular momentum assumption which is necessary in the quasinormal mode approach for rotating black holes. The results suggest that the periodicity of the black hole gravitational system may be the origin of area quantization.