621 research outputs found
Extremal black holes, gravitational entropy and nonstationary metric fields
We show that extremal black holes have zero entropy by pointing out a simple
fact: they are time-independent throughout the spacetime and correspond to a
single classical microstate. We show that non-extremal black holes, including
the Schwarzschild black hole, contain a region hidden behind the event horizon
where all their Killing vectors are spacelike. This region is nonstationary and
the time labels a continuous set of classical microstates, the phase space
, where is a three-metric induced on a
spacelike hypersurface and is its momentum conjugate. We
determine explicitly the phase space in the interior region of the
Schwarzschild black hole. We identify its entropy as a measure of an outside
observer's ignorance of the classical microstates in the interior since the
parameter which labels the states lies anywhere between 0 and 2M. We
provide numerical evidence from recent simulations of gravitational collapse in
isotropic coordinates that the entropy of the Schwarzschild black hole stems
from the region inside and near the event horizon where the metric fields are
nonstationary; the rest of the spacetime, which is static, makes no
contribution. Extremal black holes have an event horizon but in contrast to
non-extremal black holes, their extended spacetimes do not possess a bifurcate
Killing horizon. This is consistent with the fact that extremal black holes are
time-independent and therefore have no distinct time-reverse.Comment: 12 pages, 2 figures. To appear in Class. and Quant. Gravity. Based on
an essay selected for honorable mention in the 2010 gravity research
foundation essay competitio
Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity
We study the theory of Weyl conformal gravity with matter degrees of freedom
in a conformally invariant interaction. Specifically, we consider a triplet of
scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model
conformally coupled to Weyl gravity. We show that the equations of motion admit
solutions spontaneously breaking the conformal symmetry and the gauge symmetry,
providing a mechanism for supplying a scale in the theory. The vacuum solution
corresponds to anti-de-Sitter space-time, while localized soliton solutions
correspond to magnetic monopoles in asymptotically anti-de-Sitter space-time.
The resulting effective action gives rise to Einstein gravity and the residual
U(1) gauge theory. This mechanism strengthens the reasons for considering
conformally invariant matter-gravity theory, which has shown promising
indications concerning the problem of missing matter in galactic rotation
curves.Comment: 20 pages, 1 figure, revised and added reference
Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity
Using Penrose diagrams the causal structure of the static spherically
symmetric vacuum solution to conformal (Weyl) gravity is investigated. A
striking aspect of the solution is an unexpected physical singularity at
caused by a linear term in the metric. We explain how to calculate the
deflection of light in coordinates where the metric is manifestly conformal to
flat i.e. in coordinates where light moves in straight lines.Comment: 18 pages, 2 figures, title and abstract changed, contents essentially
unaltered accepted for publication in General Relativity and Gravitatio
Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities
The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force)
was previously calculated for the perfect Bose gas in the slab geometry for
various boundary conditions. The Casimir pressure due to {\it quantum}
fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC)
confined to a parallel plate geometry was recently calculated for Dirichlet
boundary conditions. In this paper we calculate the Casimir energy and pressure
due to quantum fluctuations in a zero-temperature homogeneous
weakly-interacting dilute BEC confined to a parallel plate geometry with
periodic boundary conditions and include higher-order corrections which we
refer to as Bogoliubov corrections. The leading order term is identified as the
Casimir energy of a massless scalar field moving with wave velocity equal to
the speed of sound in the BEC. We then obtain the leading order Casimir
pressure in a general three-dimensional rectangular cavity of arbitrary lengths
and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT
v.3: references adde
The Bright Side of Dark Matter
We show that it is not possible in the absence of dark matter to construct a
four-dimensional metric that explains galactic observations. In particular, by
working with an effective potential it is shown that a metric which is
constructed to fit flat rotation curves in spiral galaxies leads to the wrong
sign for the bending of light i.e. repulsion instead of attraction. Hence,
without dark matter the motion of particles on galactic scales cannot be
explained in terms of geodesic motion on a four- dimensional metric. This
reveals a new bright side to dark matter: it is indispensable if we wish to
retain the cherished equivalence principle.Comment: 7 pages, latex, no figures. Received an honorable mention in the 1999
Gravity research Foundation Essay Competition. Submitted to Phys. Rev. Let
Emergence of thin shell structure during collapse in isotropic coordinates
Numerical studies of gravitational collapse in isotropic coordinates have
recently shown an interesting connection between the gravitational Lagrangian
and black hole thermodynamics. A study of the actual spacetime was not the main
focus of this work and in particular, the rich and interesting structure of the
interior has not been investigated in much detail and remains largely unknown.
We elucidate its features by performing a numerical study of the spacetime in
isotropic coordinates during gravitational collapse of a massless scalar field.
The most salient feature to emerge is the formation of a thin shell of matter
just inside the apparent horizon. The energy density and Ricci scalar peak at
the shell and there is a jump discontinuity in the extrinsic curvature across
the apparent horizon, the hallmark that a thin shell is present in its
vicinity. At late stages of the collapse, the spacetime consists of two vacuum
regions separated by the thin shell. The interior is described by an
interesting collapsing isotropic universe. It tends towards a vacuum (never
reaches a perfect vacuum) and there is a slight inhomogeneity in the interior
that plays a crucial role in the collapse process as the areal radius tends to
zero. The spacetime evolves towards a curvature (physical) singularity in the
interior, both a Weyl and Ricci singularity. In the exterior, our numerical
results match closely the analytical form of the Schwarzschild metric in
isotropic coordinates, providing a strong test of our numerical code.Comment: 24 pages, 10 figures. version to appear in Phys. Rev.
Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas
Considering the Casimir effect due to phononic excitations of a weakly
interacting dilute {BEC}, we derive a re-normalized expression for the zero
temperature Casimir energy of a {BEC} confined to a parallel
plate geometry with periodic boundary conditions. Our expression is formally
equivalent to the free energy of a bosonic field at finite temperature, with a
nontrivial density of modes that we compute analytically. As a function of the
interaction strength, smoothly describes the transition from
the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}.
For the weakly interacting case, reduces to leading order to
the Casimir energy due to zero-point fluctuations of massless phonon modes. In
the limit of an ideal Bose gas, our result correctly describes the Casimir
energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version
with corrected typos and an additional appendi
Casimir interaction: pistons and cavity
The energy of a perfectly conducting rectangular cavity is studied by making
use of pistons' interactions. The exact solution for a 3D perfectly conducting
piston with an arbitrary cross section is being discussed.Comment: 10 pages, 2 figures, latex2
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