145 research outputs found
Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity
We study the membrane paradigm for horizons in Lanczos-Lovelock models of
gravity in arbitrary D dimensions and find compact expressions for the pressure
p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that
the membrane pressure is intimately connected with the Noether charge entropy
S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock
model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature
and A is the area of the horizon. Similarly, the viscosity coefficients are
expressible in terms of entropy and quasi-local energy associated with the
horizons. The bulk and shear viscosity coefficients are found to obey the
relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new
subsection added on the ratio \eta/s. (v3): some clarification added, typos
corrected, to appear in JHE
Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole
A spacetime horizon comprising with a black hole singularity acts like a
boundary of a thermal system associated with the notions of temperature and
entropy. In case of static metric of BTZ black hole, the field equations near
horizon boundary can be expressed as a thermal identity ,
where is the mass of BTZ black hole, is the change in the area of
the black hole horizon when the horizon is displaced infinitesimally small,
is the radial pressure provided by the source of Einstein equations,
is the entropy and is the Hawking temperature
associated with the horizon. This approach is studied further to generalize it
for non-static BTZ black hole and show that it is also possible to interpret
the field equation near horizon as a thermodynamic identity , where is the angular velocity and is the
angular momentum of BTZ black hole. These results indicate that the field
equations for BTZ black hole possess intrinsic thermodynamic properties near
horizon.Comment: 8 page
Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
It is well known that, for a wide class of spacetimes with horizons, Einstein
equations near the horizon can be written as a thermodynamic identity. It is
also known that the Einstein tensor acquires a highly symmetric form near
static, as well as stationary, horizons. We show that, for generic static
spacetimes, this highly symmetric form of the Einstein tensor leads quite
naturally and generically to the interpretation of the near-horizon field
equations as a thermodynamic identity. We further extend this result to generic
static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon
field equations again represent a thermodynamic identity in all these models.
These results confirm the conjecture that this thermodynamic perspective of
gravity extends far beyond Einstein's theory.Comment: RevTeX 4; 10 pages; no figure
Path integral duality modified propagators in spacetimes with constant curvature
The hypothesis of path integral duality provides a prescription to evaluate
the propagator of a free, quantum scalar field in a given classical background,
taking into account the existence of a fundamental length, say, the Planck
length, \lp, in a {\it locally Lorentz invariant manner}. We use this
prescription to evaluate the duality modified propagators in spacetimes with
{\it constant curvature} (exactly in the case of one spacetime, and in the
Gaussian approximation for another two), and show that: (i) the modified
propagators are ultra violet finite, (ii) the modifications are {\it
non-perturbative} in \lp, and (iii) \lp seems to behave like a `zero point
length' of spacetime intervals such that \l =
\l[\sigma^{2}(x,x')+ {\cal O}(1) \lp^2 \r], where is the
geodesic distance between the two spacetime points and , and the
angular brackets denote (a suitable) average over the quantum gravitational
fluctuations. We briefly discuss the implications of our results.Comment: v1. 10 pages, no figures; v2. 11 pages, acknowledgments adde
Effective temperature for black holes
The physical interpretation of black hole's quasinormal modes is fundamental
for realizing unitary quantum gravity theory as black holes are considered
theoretical laboratories for testing models of such an ultimate theory and
their quasinormal modes are natural candidates for an interpretation in terms
of quantum levels. The spectrum of black hole's quasinormal modes can be
re-analysed by introducing a black hole's effective temperature which takes
into account the fact that, as shown by Parikh and Wilczek, the radiation
spectrum cannot be strictly thermal. This issue changes in a fundamental way
the physical understanding of such a spectrum and enables a re-examination of
various results in the literature which realizes important modifies on quantum
physics of black holes. In particular, the formula of the horizon's area
quantization and the number of quanta of area result modified becoming
functions of the quantum "overtone" number n. Consequently, the famous formula
of Bekenstein-Hawking entropy, its sub-leading corrections and the number of
microstates are also modified. Black hole's entropy results a function of the
quantum overtone number too. We emphasize that this is the first time that
black hole's entropy is directly connected with a quantum number. Previous
results in the literature are re-obtained in the limit n \to \infty.Comment: 10 pages,accepted for publication in Journal of High Energy Physics.
Comments are welcom
Quantum corrections to the entropy of charged rotating black holes
Hawking radiation from a black hole can be viewed as quantum tunneling of
particles through the event horizon. Using this approach we provide a general
framework for studying corrections to the entropy of black holes beyond
semiclassical approximations. Applying the properties of exact differentials
for three variables to the first law thermodynamics, we study charged rotating
black holes and explicitly work out the corrections to entropy and horizon area
for the Kerr-Newman and charged rotating BTZ black holes. It is shown that the
results for other geometries like the Schwarzschild, Reissner-Nordstr\"{o}m and
anti-de Sitter Schwarzschild spacetimes follow easily
Entropy spectrum of a Kerr anti-de Sitter black hole
The entropy spectrum of a spherically symmetric black hole was derived
without the quasinormal modes in the work of Majhi and Vagenas. Extending this
work to rotating black holes, we quantize the entropy and the horizon area of a
Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area
are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic
invariance in the first way. By addressing the wave function of emitted
(absorbed) particles, the entropy and the area are quantized in the second one.
Both results show that the entropy and the area spectra are equally spaced.Comment: Accepted for publication in The European Physical Journal C, Volume
72, Issue
Optical 2-metrics of Schwarzschild-Tangherlini Spacetimes and the Bohlin-Arnold Duality
We consider the projection of null geodesics of the Schwarzschild-Tangherlini
metric in n+1 dimensions to the space of orbits of the static Killing vector
where the motion of a given light ray is seen to lie in a plane. The projected
curves coincide with the unparametrised geodesics of optical 2-metrics and can
be equally understood as describing the motion of a non-relativistic particle
in a central force. We consider a duality between the projected null curves for
pairs of values of n and interpret its mathematical meaning in terms of the
optical 2-metrics. The metrics are not projectively equivalent but the
correspondence can be exposed in terms of a third order differential equation.
We also explore the extension of this notion of duality to the
Reissner-Nordstrom case.Comment: 10 page
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