387 research outputs found
Two-dimensional quantum-corrected black hole in a finite size cavity
We consider the gravitation-dilaton theory (not necessarily exactly
solvable), whose potentials represent a generic linear combination of an
exponential and linear functions of the dilaton. A black hole, arising in such
theories, is supposed to be enclosed in a cavity, where it attains thermal
equilibrium, whereas outside the cavity the field is in the Boulware state. We
calculate quantum corrections to the Hawking temperature , with the
contribution from the boundary taken into account. Vacuum polarization outside
the shell tend to cool the system. We find that, for the shell to be in the
thermal equilibrium, it cannot be placed too close to the horizon. The quantum
corrections to the mass due to vacuum polarization vanish in spite of non-zero
quantum stresses. We discuss also the canonical boundary conditions and show
that accounting for the finiteness of the system plays a crucial role in some
theories (e.g., CGHS), where it enables to define the stable canonical
ensemble, whereas consideration in an infinite space would predict instability.Comment: 21 pages. In v.2 misprints corrected. To appear in Phys. Rev.
General approach to potentials with two known levels
We present the general form of potentials with two given energy levels
, and find corresponding wave functions. These entities are
expressed in terms of one function and one parameter -. We show how the quantum numbers of both levels depend on
properties of the function . Our approach does not need resorting to
the technique of supersymmetric (SUSY) quantum mechanics but automatically
generates both the potential and superpotential.Comment: 14 pages, REVTeX 3.0. In v.2 misprints and inaccuracies in
presentation corrected, discussion of 3-dim. case added. In v.3 misprint in
eq. 41, several typos and inaccuracies in English corrected. To be published
in J. of Phys. A: Math. Ge
Quasi-exactly solvable quartic Bose Hamiltonians
We consider Hamiltonians, which are even polynomials of the forth order with
the respect to Bose operators. We find subspaces, preserved by the action of
Hamiltonian These subspaces, being finite-dimensional, include, nonetheless,
states with an \QTR{it}{infinite} number of quasi-particles, corresponding to
the original Bose operators. The basis functions look rather simple in the
coherent state representation and are expressed in terms of the degenerate
hypergeometric function with respect to the complex variable labeling the
representation. In some particular degenerate cases they turn (up to the power
factor) into the trigonometric or hyperbolic functions, Bessel functions or
combinations of the exponent and Hermit polynomials. We find explicitly the
relationship between coefficients at different powers of Bose operators that
ensure quasi-exact solvability of Hamiltonian.Comment: 21 pages, REVTeX 3.0, no figures. In v.2 couple of misprints in
English corrected. To be published in J. Phys. A: Math. Ge
Acceleration of particles by rotating black holes: near-horizon geometry and kinematics
Nowadays, the effect of infinite energy in the centre of mass frame due to
near-horizon collisions attracts much attention.We show generality of the
effect combining two seemingly completely different approaches based on
properties of a particle with respect to its local light cone and calculating
its velocity in the locally nonrotaing frame directly. In doing so, we do not
assume that particles move along geodesics. Usually, a particle reaches a
horizon having the velocity equals that of light. However, there is also case
of "critical" particles for which this is not so. It is just the pair of usual
and critical particles that leads to the effect under discussion. The similar
analysis is carried out for massless particles. Then, critical particles are
distinguishable due to the finiteness of local frequency. Thus, both approach
based on geometrical and kinematic properties of particles moving near the
horizon, reveal the universal character of the effect.Comment: 8 page
Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits
Using a thin shell, the first law of thermodynamics, and a unified approach,
we study the thermodymanics and find the entropy of a (2+1)-dimensional
extremal rotating Ba\~{n}ados-Teitelbom-Zanelli (BTZ) black hole. The shell in
(2+1) dimensions, i.e., a ring, is taken to be circularly symmetric and
rotating, with the inner region being a ground state of the anti-de Sitter
(AdS) spacetime and the outer region being the rotating BTZ spacetime. The
extremal BTZ rotating black hole can be obtained in three different ways
depending on the way the shell approaches its own gravitational or horizon
radius. These ways are explicitly worked out. The resulting three cases give
that the BTZ black hole entropy is either the Bekenstein-Hawking entropy,
, or it is an arbitrary function of , , where
is the area, i.e., the perimeter, of the event horizon in (2+1)
dimensions. We speculate that the entropy of an extremal black hole should obey
. We also show that the contributions from the
various thermodynamic quantities, namely, the mass, the circular velocity, and
the temperature, for the entropy in all three cases are distinct. This study
complements the previous studies in thin shell thermodynamics and entropy for
BTZ black holes. It also corroborates the results found for a (3+1)-dimensional
extremal electrically charged Reissner-Nordstr\"om black hole.Comment: 8 pages, 1 table, no figur
Quasiblack holes with pressure: General exact results
A quasiblack hole is an object in which its boundary is situated at a surface
called the quasihorizon, defined by its own gravitational radius. We elucidate
under which conditions a quasiblack hole can form under the presence of matter
with nonzero pressure. It is supposed that in the outer region an extremal
quasihorizon forms, whereas inside, the quasihorizon can be either nonextremal
or extremal. It is shown that in both cases, nonextremal or extremal inside, a
well-defined quasiblack hole always admits a continuous pressure at its own
quasihorizon. Both the nonextremal and extremal cases inside can be divided
into two situations, one in which there is no electromagnetic field, and the
other in which there is an electromagnetic field. The situation with no
electromagnetic field requires a negative matter pressure (tension) on the
boundary. On the other hand, the situation with an electromagnetic field
demands zero matter pressure on the boundary. So in this situation an
electrified quasiblack hole can be obtained by the gradual compactification of
a relativistic star with the usual zero pressure boundary condition. For the
nonextremal case inside the density necessarily acquires a jump on the
boundary, a fact with no harmful consequences whatsoever, whereas for the
extremal case the density is continuous at the boundary. For the extremal case
inside we also state and prove the proposition that such a quasiblack hole
cannot be made from phantom matter at the quasihorizon. The regularity
condition for the extremal case, but not for the nonextremal one, can be
obtained from the known regularity condition for usual black holes.Comment: 18 pages, no figures; improved introduction, added references,
calculations better explaine
Entropy of an extremal electrically charged thin shell and the extremal black hole
There is a debate as to what is the value of the the entropy of extremal
black holes. There are approaches that yield zero entropy , while there
are others that yield the Bekenstein-Hawking entropy , in Planck
units. There are still other approaches that give that is proportional to
or even that is a generic well-behaved function of . Here
is the black hole horizon radius and is its horizon area.
Using a spherically symmetric thin matter shell with extremal electric charge,
we find the entropy expression for the extremal thin shell spacetime. When the
shell's radius approaches its own gravitational radius, and thus turns into an
extremal black hole, we encounter that the entropy is , i.e., the
entropy of an extremal black hole is a function of alone. We speculate
that the range of values for an extremal black hole is .Comment: 11 pages, minor changes, added references, matches the published
versio
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