205 research outputs found
A simple theorem to generate exact black hole solutions
Under certain conditions imposed on the energy-momentum tensor, a theorem
that characterizes a two-parameter family of static and spherically symmetric
solutions to Einstein's field equations (black holes), is proved. A discussion
on the asymptotics, regularity, and the energy conditions is provided. Examples
that include the best known exact solutions within these symmetries are
considered. A trivial extension of the theorem includes the cosmological
constant {\it ab-initio}, providing then a three-parameter family of solutions.Comment: 14 pages; RevTex; no figures; typos corrected; references adde
Properties of global monopoles with an event horizon
We investigate the properties of global monopoles with an event horizon. We
find that there is an unstable circular orbit even if a particle does not have
an angular momentum when the core mass is negative. We also obtain the
asymptotic form of solutions when the event horizon is much larger than the
core radius of the monopole, and discuss if they could be a model of galactic
halos.Comment: 5 pages, 7 figure
The Collapse of Large Extra Dimensions
In models of spacetime that are the product of a four-dimensional spacetime
with an ``extra'' dimension, there is the possibility that the extra dimension
will collapse to zero size, forming a singularity. We ask whether this collapse
is likely to destroy the spacetime. We argue, by an appeal to the
four-dimensional cosmic censorship conjecture, that--at least in the case when
the extra dimension is homogeneous--such a collapse will lead to a singularity
hidden within a black string. We also construct explicit initial data for a
spacetime in which such a collapse is guaranteed to occur and show how the
formation of a naked singularity is likely avoided.Comment: Uses revtex
Gravity wave analogs of black holes
It is demonstrated that gravity waves of a flowing fluid in a shallow basin
can be used to simulate phenomena around black holes in the laboratory. Since
the speed of the gravity waves as well as their high-wavenumber dispersion
(subluminal vs. superluminal) can be adjusted easily by varying the height of
the fluid (and its surface tension) this scenario has certain advantages over
the sonic and dielectric black hole analogs, for example, although its use in
testing quantum effects is dubious. It can be used to investigate the various
classical instabilities associated with black (and white) holes experimentally,
including positive and negative norm mode mixing at horizons. PACS: 04.70.-s,
47.90.+a, 92.60.Dj, 04.80.-y.Comment: 14 pages RevTeX, 5 figures, section VI modifie
Building blocks of a black hole
What is the nature of the energy spectrum of a black hole ? The algebraic
approach to black hole quantization requires the horizon area eigenvalues to be
equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be
exponentially degenerate with respect to the area quantum number if one is to
understand black hole entropy as reflecting degeneracy of the observable
states. Here we construct the black hole states by means of a pair of "creation
operators" subject to a particular simple algebra, a slight generalization of
that for the harmonic oscillator. We then prove rigorously that the n-th area
eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole
entropy qua logarithm of the number of states for fixed horizon area comes out
proportional to that area.Comment: PhysRevTeX, 14 page
Quantum Mechanical Carrier of the Imprints of Gravitation
We exhibit a purely quantum mechanical carrier of the imprints of gravitation
by identifying for a relativistic system a property which (i) is independent of
its mass and (ii) expresses the Poincare invariance of spacetime in the absence
of gravitation. This carrier consists of the phase and amplitude correlations
of waves in oppositely accelerating frames. These correlations are expressed as
a Klein-Gordon-equation-determined vector field whose components are the
``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. The
imprints themselves are deviations away from this vector field.Comment: 8 pages, RevTex. Html version of this and related papers on
accelerated frames available at http://www.math.ohio-state.edu/~gerlac
The bound on viscosity and the generalized second law of thermodynamics
We describe a new paradox for ideal fluids. It arises in the accretion of an
\textit{ideal} fluid onto a black hole, where, under suitable boundary
conditions, the flow can violate the generalized second law of thermodynamics.
The paradox indicates that there is in fact a lower bound to the correlation
length of any \textit{real} fluid, the value of which is determined by the
thermodynamic properties of that fluid. We observe that the universal bound on
entropy, itself suggested by the generalized second law, puts a lower bound on
the correlation length of any fluid in terms of its specific entropy. With the
help of a new, efficient estimate for the viscosity of liquids, we argue that
this also means that viscosity is bounded from below in a way reminiscent of
the conjectured Kovtun-Son-Starinets lower bound on the ratio of viscosity to
entropy density. We conclude that much light may be shed on the
Kovtun-Son-Starinets bound by suitable arguments based on the generalized
second law.Comment: 11 pages, 1 figure, published versio
Coulomb field of an accelerated charge: physical and mathematical aspects
The Maxwell field equations relative to a uniformly accelerated frame, and
the variational principle from which they are obtained, are formulated in terms
of the technique of geometrical gauge invariant potentials. They refer to the
transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge
invariant "2+2" decomposition is used to see how the Coulomb field of a charge,
static in an accelerated frame, has properties that suggest features of
electromagnetism which are different from those in an inertial frame. In
particular, (1) an illustrative calculation shows that the Larmor radiation
reaction equals the electrostatic attraction between the accelerated charge and
the charge induced on the surface whose history is the event horizon, and (2) a
spectral decomposition of the Coulomb potential in the accelerated frame
suggests the possibility that the distortive effects of this charge on the
Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at
http://www.math.ohio-state.edu/~gerlac
Focusing and the Holographic Hypothesis
The ``screen mapping" introduced by Susskind to implement 't Hooft's
holographic hypothesis is studied. For a single screen time, there are an
infinite number of images of a black hole event horizon, almost all of which
have smaller area on the screen than the horizon area. This is consistent with
the focusing equation because of the existence of focal points. However, the
{\it boundary} of the past (or future) of the screen obeys the area theorem,
and so always gives an expanding map to the screen, as required by the
holographic hypothesis. These considerations are illustrated with several
axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi
Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle
In this letter, we compute the corrections to the Cardy-Verlinde formula of
dimensional Schwarzschild black hole. These corrections stem from the
generalized uncertainty principle. Then we show, one can taking into account
the generalized uncertainty principle corrections of the Cardy-Verlinde entropy
formula by just redefining the Virasoro operator and the central charge
.Comment: 8 pages, no figure
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