263 research outputs found
Quantum gravitational corrections to the stress-energy tensor around the rotating BTZ black hole
Modes emerging out of a collapsing black hole are red-shifted to such an
extent that Hawking radiation at future null infinity consists of modes that
have energies beyond the Planck scale at past null infinity. This indicates
that physics at the Planck scale may modify the spectrum of Hawking radiation
and the associated stress-energy tensor of the quantum field. Recently, it has
been shown that, the T-duality symmetry of string fluctuations along compact
extra dimensions leads to a modification of the standard propagator of point
particles in quantum field theory. At low energies (when compared to the string
scale), the modified propagator is found to behave as though the spacetime
possesses a minimal length, say, \lp, which we shall assume to be of the
order of the Planck length. We utilize the duality approach to evaluate the
modified propagator around the rotating Banados-Teitelboim-Zanelli black hole
and show that the propagator is finite in the coincident limit. We compute the
stress-energy tensor associated with the modified Green's function and
illustrate graphically that the quantum gravitational corrections turn out to
be negligibly small. We conclude by briefly commenting on the results we have
obtained.Comment: v1. 7 pages, 2 figures; v2. 11 pages, 4 figures, discussion extended
to the case of the rotating BTZ black hole, figures improve
Is there an imprint of Planck scale physics on inflationary cosmology?
We study the effects of the trans-Planckian dispersion relation on the
spectrum of the primordial density perturbations during inflation. In contrast
to the earlier analyses, we do not assume any specific form of the dispersion
relation and allow the initial state of the field to be arbitrary. We obtain
the spectrum of vacuum fluctuations of the quantum field by considering a
scalar field satisfying the linear wave equation with higher spatial derivative
terms propagating in the de Sitter space-time. We show that the power spectrum
does not strongly depend on the dispersion relation and that the form of the
dispersion relation does not play a significant role in obtaining the
corrections to the scale invariant spectrum. We also show that the signatures
of the deviations from the flat scale-invariant spectrum from the CMBR
observations due to quantum gravitational effects cannot be differentiated from
the standard inflationary scenario with an arbitrary initial state.Comment: 6 pages, uses RevTex4; References added; Final versio
Where are the black hole entropy degrees of freedom ?
Understanding the area-proportionality of black hole entropy (the `Area Law')
from an underlying fundamental theory has been one of the goals of all models
of quantum gravity. A key question that one asks is: where are the degrees of
freedom giving rise to black hole entropy located? Taking the point of view
that entanglement between field degrees of freedom inside and outside the
horizon can be a source of this entropy, we show that when the field is in its
ground state, the degrees of freedom near the horizon contribute most to the
entropy, and the area law is obeyed. However, when it is in an excited state,
degrees of freedom far from the horizon contribute more significantly, and
deviations from the area law are observed. In other words, we demonstrate that
horizon degrees of freedom are responsible for the area law.Comment: 5 pages, 3 eps figures, uses Revtex4, References added, Minor changes
to match published versio
Is entanglement entropy proportional to area?
It is known that the entanglement entropy of a scalar field, found by tracing
over its degrees of freedom inside a sphere of radius , is
proportional to the area of the sphere (and not its volume). This suggests that
the origin of black hole entropy, also proportional to its horizon area, may
lie in the entanglement between the degrees of freedom inside and outside the
horizon. We examine this proposal carefully by including excited states, to
check probable deviations from the area law.Comment: 6 pages. Based on talk by S. Das at Theory Canada 1, Vancouver, 3
June, 2005. To be published in a special edition of the Canadian Journal of
Physics. Minor changes to match published versio
Non-singular black-holes on the brane
We investigate the possibility of obtaining non-singular black-hole solutions
in the brane world model by solving the effective field equations for the
induced metric on the brane. The Reissner-Nordstrom solution on the brane was
obtained by Dadhich etal by imposing the null energy condition on the 3-brane
for a bulk having non zero Weyl curvature. In this work, we relax the condition
of vanishing scalar curvature , however, retaining the null condition. We
have shown that it is possible to obtain class of static non-singular
spherically symmetric brane space-times admitting horizon. We obtain one such
class of solution which is a regular version of the Reissner-Nordstrom solution
in the standard general relativity.Comment: 8 pages, References added, Version to appear in Int. J. Mod. Phys.
Entanglement as a source of black hole entropy
We review aspects of black hole thermodynamics, and show how entanglement of
a quantum field between the inside and outside of a horizon can account for the
area-proportionality of black hole entropy, provided the field is in its ground
state. We show that the result continues to hold for Coherent States and
Squeezed States, while for Excited States, the entropy scales as a power of
area less than unity. We also identify location of the degrees of freedom which
give rise to the above entropy.Comment: 12 pages, latex, 5 figures. Invited talk by SD at `Recent
Developments in Gravity' (NEB XII), Nafplion, Greece, 30 June 2006. To appear
in Journal of Physics: Conference Series; V2: References added, Minor changes
to match published versio
Where are the degrees of freedom responsible for black hole entropy?
Considering the entanglement between quantum field degrees of freedom inside
and outside the horizon as a plausible source of black hole entropy, we address
the question: {\it where are the degrees of freedom that give rise to this
entropy located?} When the field is in ground state, the black hole area law is
obeyed and the degrees of freedom near the horizon contribute most to the
entropy. However, for excited state, or a superposition of ground state and
excited state, power-law corrections to the area law are obtained, and more
significant contributions from the degrees of freedom far from the horizon are
shown.Comment: 6 pages, 4 figures, Invited talk at Theory Canada III, Edmonton,
Alberta, Canada, June 16, 200
On tunneling across horizons
The tunneling method for stationary black holes in the Hamilton-Jacobi
variant is reconsidered in the light of various critiques that have been moved
against. It is shown that once the tunneling trajectories have been correctly
identified the method isfree from internal inconsistencies, it is manifestly
covariant, it allows for the extension to spinning particles and it can even be
used without solving the Hamilton-Jacobi equation. These conclusions borrow
support on a simple analytic continuation of the classical action of a
pointlike particle, made possible by the unique assumption that it should be
analytic in complexified Schwarzschild or Kerr-Newman spacetimes. A more
general version of the Parikh-Wilczek method will also be proposed along these
lines.Comment: Latex Document, 5 pages, 2 figures, title changed, abstract changed,
added references, results unchange
Gauge-invariant perturbation theory for trans-Planckian inflation
The possibility that the scale-invariant inflationary spectrum may be
modified due to the hidden assumptions about the Planck scale physics -- dubbed
as trans-Planckian inflation -- has received considerable attention. To mimic
the possible trans-Planckian effects, among various models, modified dispersion
relations have been popular in the literature. In almost all the earlier
analyzes, unlike the canonical scalar field driven inflation, the
trans-Planckian effects are introduced to the scalar/tensor perturbation
equations in an ad hoc manner -- without calculating the stress-tensor of the
cosmological perturbations from the covariant Lagrangian. In this work, we
perform the gauge-invariant cosmological perturbations for the single-scalar
field inflation with the Jacobson-Corley dispersion relation by computing the
fluctuations of all the fields including the unit time-like vector field which
defines a preferred rest frame. We show that: (i) The non-linear effects
introduce corrections only to the perturbed energy density. The corrections to
the energy density vanish in the super-Hubble scales. (ii) The scalar
perturbations, in general, are not purely adiabatic. (iii) The equation of
motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is
different than those presumed in the earlier analyzes. (iv) The tensor
perturbation equation remains unchanged. We perform the classical analysis for
the resultant system of equations and also compute the power-spectrum of the
scalar perturbations in a particular limit. We discuss the implications of our
results and compare with the earlier results.Comment: 19 Pages, Revtex4; V2 Final version, To appear in Phys. Rev. D., 1
figure and references adde
Temperature and entropy of Schwarzschild-de Sitter space-time
In the light of recent interest in quantum gravity in de Sitter space, we
investigate semi-classical aspects of 4-dimensional Schwarzschild-de Sitter
space-time using the method of complex paths. The standard semi-classical
techniques (such as Bogoliubov coefficients and Euclidean field theory) have
been useful to study quantum effects in space-times with single horizons;
however, none of these approaches seem to work for Schwarzschild-de Sitter or,
in general, for space-times with multiple horizons. We extend the method of
complex paths to space-times with multiple horizons and obtain the spectrum of
particles produced in these space-times. We show that the temperature of
radiation in these space-times is proportional to the effective surface gravity
-- inverse harmonic sum of surface gravity of each horizon. For the
Schwarzschild-de Sitter, we apply the method of complex paths to three
different coordinate systems -- spherically symmetric, Painleve and Lemaitre.
We show that the equilibrium temperature in Schwarzschild-de Sitter is the
harmonic mean of cosmological and event horizon temperatures. We obtain
Bogoliubov coefficients for space-times with multiple horizons by analyzing the
mode functions of the quantum fields near the horizons. We propose a new
definition of entropy for space-times with multiple horizons analogous to the
entropic definition for space-times with a single horizon. We define entropy
for these space-times to be inversely proportional to the square of the
effective surface gravity. We show that this definition of entropy for
Schwarzschild-de Sitter satisfies the D-bound conjecture.Comment: Final version; To appear in Phys. Rev. D; 12 pages, 1 figure,
RevTex-4; Typos corrected; References adde
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