162 research outputs found
Classical and Quantum Equations of Motion for a BTZ Black String in AdS Space
We investigate gravitational collapse of a -dimensional BTZ black
string in AdS space in the context of both classical and quantum mechanics.
This is done by first deriving the conserved mass per unit length of the
cylindrically symmetric domain wall, which is taken as the classical
Hamiltonian of the black string. In the quantum mechanical context, we take
primary interest in the behavior of the collapse near the horizon and near the
origin (classical singularity) from the point of view of an infalling observer.
In the absence of radiation, quantum effects near the horizon do not change the
classical conclusions for an infalling observer, meaning that the horizon is
not an obstacle for him/her. The most interesting quantum mechanical effect
comes in when investigating near the origin. First, quantum effects are able to
remove the classical singularity at the origin, since the wave function is
non-singular at the origin. Second, the Schr\"odinger equation describing the
behavior near the origin displays non-local effects, which depend on the energy
density of the domain wall. This is manifest in that derivatives of the
wavefunction at one point are related to the value of the wavefunction at some
other distant point.Comment: 9 pages, 1 figure. Minor Clarification and corrections. Accepted for
Publication in JHE
Phase structure of black branes in grand canonical ensemble
This is a companion paper of our previous work [1] where we studied the
thermodynamics and phase structure of asymptotically flat black -branes in a
cavity in arbitrary dimensions in a canonical ensemble. In this work we
study the thermodynamics and phase structure of the same in a grand canonical
ensemble. Since the boundary data in two cases are different (for the grand
canonical ensemble boundary potential is fixed instead of the charge as in
canonical ensemble) the stability analysis and the phase structure in the two
cases are quite different. In particular, we find that there exists an analog
of one-variable analysis as in canonical ensemble, which gives the same
stability condition as the rather complicated known (but generalized from black
holes to the present case) two-variable analysis. When certain condition for
the fixed potential is satisfied, the phase structure of charged black
-branes is in some sense similar to that of the zero charge black -branes
in canonical ensemble up to a certain temperature. The new feature in the
present case is that above this temperature, unlike the zero-charge case, the
stable brane phase no longer exists and `hot flat space' is the stable phase
here. In the grand canonical ensemble there is an analog of Hawking-Page
transition, even for the charged black -brane, as opposed to the canonical
ensemble. Our study applies to non-dilatonic as well as dilatonic black
-branes in space-time dimensions.Comment: 32 pages, 2 figures, various points refined, discussion expanded,
references updated, typos corrected, published in JHEP 1105:091,201
Entanglement generation outside a Schwarzschild black hole and the Hawking effect
We examine the Hawking effect by studying the asymptotic entanglement of two
mutually independent two-level atoms placed at a fixed radial distance outside
a Schwarzschild black hole in the framework of open quantum systems. We treat
the two-atom system as an open quantum system in a bath of fluctuating
quantized massless scalar fields in vacuum and calculate the concurrence, a
measurement of entanglement, of the equilibrium state of the system at large
times, for the Unruh, Hartle-Hawking and Boulware vacua respectively. We find,
for all three vacuum cases, that the atoms turn out to be entangled even if
they are initially in a separable state as long as the system is not placed
right at the even horizon. Remarkably, only in the Unruh vacuum, will the
asymptotic entanglement be affected by the backscattering of the thermal
radiation off the space-time curvature. The effect of the back scatterings on
the asymptotic entanglement cancels in the Hartle-Hawking vacuum case.Comment: 15 pages, no figures, Revte
Quantum catastrophe of slow light
Catastrophes are at the heart of many fascinating optical phenomena. The
rainbow, for example, is a ray catastrophe where light rays become infinitely
intense. The wave nature of light resolves the infinities of ray catastrophes
while drawing delicate interference patterns such as the supernumerary arcs of
the rainbow. Black holes cause wave singularities. Waves oscillate with
infinitely small wave lengths at the event horizon where time stands still. The
quantum nature of light avoids this higher level of catastrophic behaviour
while producing a quantum phenomenon known as Hawking radiation. As this letter
describes, light brought to a standstill in laboratory experiments can suffer a
similar wave singularity caused by a parabolic profile of the group velocity.
In turn, the quantum vacuum is forced to create photon pairs with a
characteristic spectrum. The idea may initiate a theory of quantum
catastrophes, in addition to classical catastrophe theory, and the proposed
experiment may lead to the first direct observation of a phenomenon related to
Hawking radiation.Comment: Published as "A laboratory analogue of the event horizon using slow
light in an atomic medium
Sub-Planckian black holes and the Generalized Uncertainty Principle
The Black Hole Uncertainty Principle correspondence suggests that there could
exist black holes with mass beneath the Planck scale but radius of order the
Compton scale rather than Schwarzschild scale. We present a modified, self-dual
Schwarzschild-like metric that reproduces desirable aspects of a variety of
disparate models in the sub-Planckian limit, while remaining Schwarzschild in
the large mass limit. The self-dual nature of this solution under naturally implies a Generalized Uncertainty Principle
with the linear form . We also
demonstrate a natural dimensional reduction feature, in that the gravitational
radius and thermodynamics of sub-Planckian objects resemble that of -D
gravity. The temperature of sub-Planckian black holes scales as rather than
but the evaporation of those smaller than g is suppressed by
the cosmic background radiation. This suggests that relics of this mass could
provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy
Conformally rescaled spacetimes and Hawking radiation
We study various derivations of Hawking radiation in conformally rescaled
metrics. We focus on two important properties, the location of the horizon
under a conformal transformation and its associated temperature. We find that
the production of Hawking radiation cannot be associated in all cases to the
trapping horizon because its location is not invariant under a conformal
transformation. We also find evidence that the temperature of the Hawking
radiation should transform simply under a conformal transformation, being
invariant for asymptotic observers in the limit that the conformal
transformation factor is unity at their location.Comment: 22 pages, version submitted to journa
Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
We present a class of exact analytic and static, spherically symmetric black
hole solutions in the semi-classical Einstein equations with Weyl anomaly. The
solutions have two branches, one is asymptotically flat and the other
asymptotically de Sitter. We study thermodynamic properties of the black hole
solutions and find that there exists a logarithmic correction to the well-known
Bekenstein-Hawking area entropy. The logarithmic term might come from non-local
terms in the effective action of gravity theories. The appearance of the
logarithmic term in the gravity side is quite important in the sense that with
this term one is able to compare black hole entropy up to the subleading order,
in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE
Geometric phase outside a Schwarzschild black hole and the Hawking effect
We study the Hawking effect in terms of the geometric phase acquired by a
two-level atom as a result of coupling to vacuum fluctuations outside a
Schwarzschild black hole in a gedanken experiment. We treat the atom in
interaction with a bath of fluctuating quantized massless scalar fields as an
open quantum system, whose dynamics is governed by a master equation obtained
by tracing over the field degrees of freedom. The nonunitary effects of this
system are examined by analyzing the geometric phase for the Boulware, Unruh
and Hartle-Hawking vacua respectively. We find, for all the three cases, that
the geometric phase of the atom turns out to be affected by the space-time
curvature which backscatters the vacuum field modes. In both the Unruh and
Hartle-Hawking vacua, the geometric phase exhibits similar behaviors as if
there were thermal radiation at the Hawking temperature from the black hole.
So, a measurement of the change of the geometric phase as opposed to that in a
flat space-time can in principle reveal the existence of the Hawking radiation.Comment: 14 pages, no figures, a typo in the References corrected, version to
appear in JHEP. arXiv admin note: text overlap with arXiv:1109.033
Particle creation rate for dynamical black holes
We present the particle creation probability rate around a general black hole
as an outcome of quantum fluctuations. Using the uncertainty principle for
these fluctuation, we derive a new ultraviolet frequency cutoff for the
radiation spectrum of a dynamical black hole. Using this frequency cutoff, we
define the probability creation rate function for such black holes. We consider
a dynamical Vaidya model, and calculate the probability creation rate for this
case when its horizon is in a slowly evolving phase. Our results show that one
can expect the usual Hawking radiation emission process in the case of a
dynamical black hole when it has a slowly evolving horizon. Moreover,
calculating the probability rate for a dynamical black hole gives a measure of
when Hawking radiation can be killed off by an incoming flux of matter or
radiation. Our result strictly suggests that we have to revise the Hawking
radiation expectation for primordial black holes that have grown substantially
since they were created in the early universe. We also infer that this
frequency cut off can be a parameter that shows the primordial black hole
growth at the emission moment.Comment: 10 pages, 1 figure. The paper was rewritten in more clear
presentation and one more appendix is adde
Charged Dilatonic AdS Black Branes in Arbitrary Dimensions
We study electromagnetically charged dilatonic black brane solutions in
arbitrary dimensions with flat transverse spaces, that are asymptotically AdS.
This class of solutions includes spacetimes which possess a bulk region where
the metric is approximately invariant under Lifshitz scalings. Given fixed
asymptotic boundary conditions, we analyze how the behavior of the bulk up to
the horizon varies with the charges and derive the extremality conditions for
these spacetimes.Comment: References update
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