20 research outputs found
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 , with a two-dimensional Rindler spacetime .
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 where 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 . Therefore, it does not give support to Hod's statement that the
area spectrum 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