Self-Gravitational Corrections to the Cardy-Verlinde Formula and the FRW Brane Cosmology in SdS_5 Bulk

The semiclassical corrections to the Cardy-Verlinde entropy of a five-dimensional Schwarzschild de-Sitter black hole (SdS_5) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitation effect. In addition, a four-dimensional spacelike brane is considered as the boundary of the SdS_5 bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. By exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of SdS_5 bulk black hole as the source for stiff matter. Furthermore, we rewrite the Friedmann-like equation in a such way that it represents the conservation equation of energy of a point particle moving in a one-dimensional effective potential. The self-gravitational corrections to the effective potential and, consequently, to the point particle's motion are obtained. A short analysis on the asymptotic behavior of the 4-dimensional brane is presented.Comment: 16 pages, LaTeX; (v2) references added and correcte

Near-horizon limit of the charged BTZ black hole and AdS_2 quantum gravity

We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, near-horizon AdS_2 geometry with constant dilaton and U(1) field and an asymptotic AdS_2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS_2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge c_as of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, c_as=3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, c_nh \propto l Q/\sqrt G.Comment: 11 pages, no figure

Microscopic entropy of the charged BTZ black hole

The charged BTZ black hole is characterized by a power-law curvature singularity generated by the electric charge of the hole. The curvature singularity produces ln r terms in the asymptotic expansion of the gravitational field and divergent contributions to the boundary terms. We show that these boundary deformations can be generated by the action of the conformal group in two dimensions and that an appropriate renormalization procedure allows for the definition of finite boundary charges. In the semiclassical regime the central charge of the dual CFT turns out to be that calculated by Brown and Henneaux, whereas the charge associated with time translation is given by the renormalized black hole mass. We then show that the Cardy formula reproduces exactly the Bekenstein-Hawking entropy of the charged BTZ black hole.Comment: 9 pages, no figure

Casimir densities for two spherical branes in Rindler-like spacetimes

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are evaluated for a scalar field obeying the Robin boundary conditions on two spherical branes in (D+1)-dimensional Rindler-like spacetime $Ri\times S^{D-1}$, with a two-dimensional Rindler spacetime $Ri$. This spacetime approximates the near horizon geometry of (D+1)-dimensional black hole. By using the generalized Abel-Plana formula, the vacuum expectation values are presented as the sum of single brane and second brane induced parts. Various limiting cases are studied. The vacuum forces acting on the branes are decomposed into the self-action and interaction terms. The interaction forces are investigated as functions of the brane locations and coefficients in the boundary conditions.Comment: 15 page

Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes

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 $m\Omega$ where $\Omega$ 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 $A_{n}=(4l^{2}_{p}ln 3)n$ should be valid for a generic Kerr-Newman black hole.Comment: 10 pages, no figure, LaTeX; v2: 12 pages, clarifying comments and an Appendix are added, version to appear in Mod. Phys. Lett.

Mapping of shape invariant potentials by the point canonical transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\"{o}schl-Teller type I and Hulth\'{e}n is SU(2)

Cardy-Verlinde Formula and Achucarro-Ortiz Black Hole

In this paper it is shown that the entropy of the black hole horizon in the Achucarro-Ortiz spacetime, which is the most general two-dimensional black hole derived from the three-dimensional rotating BTZ black hole, can be described by the Cardy-Verlinde formula. The latter is supposed to be an entropy formula of conformal field theory in any dimension.Comment: 10 pages, LaTeX, v2: minor changes, references added, to appear in Phys. Rev.

Algebraic approach to the Hulthen potential

In this paper the energy eigenvalues and the corresponding eigenfunctions are calculated for Hulthen potential. Then we obtain the ladder operators and show that these operators satisfy SU(2) commutation relation.Comment: 8 Pages, 1 Tabl

Quintom Cosmology: Theoretical implications and observations

We review the paradigm of quintom cosmology. This scenario is motivated by the observational indications that the equation of state of dark energy across the cosmological constant boundary is mildly favored, although the data are still far from being conclusive. As a theoretical setup we introduce a no-go theorem existing in quintom cosmology, and based on it we discuss the conditions for the equation of state of dark energy realizing the quintom scenario. The simplest quintom model can be achieved by introducing two scalar fields with one being quintessence and the other phantom. Based on the double-field quintom model we perform a detailed analysis of dark energy perturbations and we discuss their effects on current observations. This type of scenarios usually suffer from a manifest problem due to the existence of a ghost degree of freedom, and thus we review various alternative realizations of the quintom paradigm. The developments in particle physics and string theory provide potential clues indicating that a quintom scenario may be obtained from scalar systems with higher derivative terms, as well as from non-scalar systems. Additionally, we construct a quintom realization in the framework of braneworld cosmology, where the cosmic acceleration and the phantom divide crossing result from the combined effects of the field evolution on the brane and the competition between four and five dimensional gravity. Finally, we study the outsets and fates of a universe in quintom cosmology. In a scenario with null energy condition violation one may obtain a bouncing solution at early times and therefore avoid the Big Bang singularity. Furthermore, if this occurs periodically, we obtain a realization of an oscillating universe. Lastly, we comment on several open issues in quintom cosmology and their connection to future investigations.Comment: 105 pages, 36 figures, version published at Physics Report