[en] Recently, it was shown that the entropy of the black hole horizon in the Achucarro-Ortiz spacetime can be described by the Cardy-Verlinde formula. In this Letter, we compute the self-gravitational corrections to the Cardy-Verlinde formula of the two-dimensional Achucarro-Ortiz black hole. These corrections stem from the effect of self-gravitation and they are derived in the context of Keski-Vakkuri, Kraus and Wilczek (KKW) analysis. The black hole under study is therefore treated as a dynamical background. The self-gravitational corrections to the entropy as given by the Cardy-Verlinde formula of the Achucarro-Ortiz black hole, are found to be positive. This result provides evidence in support of the claim that the holographic bound is not universal in the framework of two-dimensional gravity models

[en] In this paper, the energy eigenvalues and the corresponding eigenfunctions are calculated for the Kratzer potential. Then we obtain the ladder operators for the one-dimensional (1D) and 3D Kratzer potential. Finally, we show that these operators satisfy the SU(2) commutation relation

[en] We extend the recent proposal of twofold hidden conformal symmetry to the four-dimensional Kerr-Bolt-AdS-dS black holes. The J-picture of holographic description of Kerr-Bolt-AdS-dS black holes previously has been studied in the paper. Here we present a new description, in view of the NUT charge of black hole. We consider the wave equation of a massless charged scalar field in our interesting background and show in the near horizon region, the wave equation can be reproduced by the SL(2,R)_L x SL(2,R)_R Casimir quadratic operators. Moreover, we compute the microscopic entropy of the dual CFT by Cardy formula and find a perfect match to Bekenstein-Hawking entropy of Kerr-Bolt-AdS-dS spacetimes. The absorption cross section of a near region scalar field also matches to microscopic absorption cross section of the dual CFT. (author)

[en] We show that extremal BMPV black holes have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal BMPV spacetime and find in the 'near region', the wave equation in extremal limit could be written in terms of the SL(2,R) quadratic Casimir. From the new conformal coordinates, the temperatures of the dual CFTs could be read directly. For the extremal black hole, the Hawking temperature is vanishing. Correspondingly, only the left (right) temperature of the dual CFT is non-vanishing and the excitations of the other sector are suppressed. Moreover, we obtain the microscopic entropy of the extremal BMPV black hole and find that the correlation function of a near-region scalar field matches to the microscopic greybody factor of the dual 2D CFT. (author)

[en] The properties of the charged particle in a certain varying magnetic field are outlined. A realization of the creation and annihilation operators for the wavefunctions is studied. It is shown that these operators satisfy the commutation relation of an SU(1,1) group. The closed analytical expressions for the matrix elements of different function ρ and ρ(d/dρ) are evaluated

[en] 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 x 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

[en] Exact analytical solutions for the s-wave Dirac equation with the reflectionless-type, Rosen-Morse and Manning-Rosen potentials are obtained, under the condition of spin symmetry. We obtained bound state energy eigenvalues and corresponding spinor wave function in the framework of the Nikiforov-Uvarov (NU) method.

[en] 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 AdS₂ geometry with constant dilaton and U(1) field and an asymptotic AdS₂ 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 AdS₂ 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∝lQ/√G.

[en] 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

[en] In this paper it is shown that the entropy of the black hole horizon in Achucarro-Ortiz spacetime, which is the most general two-dimensional black hole derived from the three-dimensional rotating Banados-Teitelboim-Zanelli 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