5,061 research outputs found
A general maximum entropy principle for self-gravitating perfect fluid
We consider a self-gravitating system consisting of perfect fluid with
spherical symmetry. Using the general expression of entropy density, we
extremize the total entropy under the constraint that the total number of
particles is fixed. We show that extrema of coincides precisely with the
relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic
equilibrium. Furthermore, we apply the maximum entropy principle to a charged
perfect fluid and derive the generalized TOV equation. Our work provides a
strong evidence for the fundamental relationship between general relativity and
ordinary thermodynamics.Comment: 13 pages, no figure. The arguments have been improved so that the
assumption p=p(\rho) is no longer neede
The Effects of Stress Tensor Fluctuations upon Focusing
We treat the gravitational effects of quantum stress tensor fluctuations. An
operational approach is adopted in which these fluctuations produce
fluctuations in the focusing of a bundle of geodesics. This can be calculated
explicitly using the Raychaudhuri equation as a Langevin equation. The physical
manifestation of these fluctuations are angular blurring and luminosity
fluctuations of the images of distant sources. We give explicit results for the
case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices
B and
How far does the analogy between causal horizon-induced thermalization with the standard heat bath situation go?
After a short presentation of KMS states and modular theory as the unifying
description of thermalizing systems we propose the absence of transverse vacuum
fluctuations in the holographic projections as the mechanism for an area
behavior (the transverse area) of localization entropy as opposed to the volume
dependence of ordinary heat bath entropy. Thermalization through causal
localization is not a property of QM, but results from the omnipresent vacuum
polarization in QFT and does not require a Gibbs type ensemble avaraging
(coupling to a heat bath).Comment: 10 pages, based on talk given at the 2002 Londrina Winter Schoo
Nonsingular charged black holes \`{a} la Palatini
We argue that the quantum nature of matter and gravity should lead to a
discretization of the allowed states of the matter confined in the interior of
black holes. To support and illustrate this idea, we consider a quadratic
extension of General Relativity formulated \`{a} la Palatini and show that
nonrotating, electrically charged black holes develop a compact core at the
Planck density which is nonsingular if the mass spectrum satisfies a certain
discreteness condition. We also find that the area of the core is proportional
to the number of charges times the Planck area.Comment: 10 single column page
A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder
We prove a novel unique continuation result for weak bisolutions to the
massive Klein-Gordon equation on a 2-dimensional cylinder M. Namely, if such a
bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a
2-dimensional surface lying parallel to the diagonal in the product manifold of
M with itself, then it is (globally) translationally invariant. The proof makes
use of methods drawn from Beurling's theory of interpolation. An application of
our result to quantum field theory on 2-dimensional cylinder spacetimes will
appear elsewhere.Comment: LaTeX2e, 9 page
Distortion of Gravitational-Wave Packets Due to their Self-Gravity
When a source emits a gravity-wave (GW) pulse over a short period of time,
the leading edge of the GW signal is redshifted more than the inner boundary of
the pulse. The GW pulse is distorted by the gravitational effect of the
self-energy residing in between these shells. We illustrate this distortion for
GW pulses from the final plunge of black hole (BH) binaries, leading to the
evolution of the GW profile as a function of the radial distance from the
source. The distortion depends on the total GW energy released and the duration
of the emission, scaled by the total binary mass, M. The effect should be
relevant in finite box simulations where the waveforms are extracted within a
radius of <~ 100M. For characteristic emission parameters at the final plunge
between binary BHs of arbitrary spins, this effect could distort the simulated
GW templates for LIGO and LISA by a fraction of 0.001. Accounting for the wave
distortion would significantly decrease the waveform extraction errors in
numerical simulations.Comment: accepted for publication in Physical Review
A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
The entropy of stationary black holes has recently been calculated by a
number of different approaches. Here we compare the Noether charge approach
(defined for any diffeomorphism invariant Lagrangian theory) with various
Euclidean methods, specifically, (i) the microcanonical ensemble approach of
Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and
Zanelli which ultimately expresses black hole entropy in terms of the Hilbert
action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli
(also used by Susskind and Uglum) which views black hole entropy as conjugate
to a conical deficit angle, and (iv) the pair creation approach of Garfinkle,
Giddings, and Strominger. All of these approaches have a more restrictive
domain of applicability than the Noether charge approach. Specifically,
approaches (i) and (ii) appear to be restricted to a class of theories
satisfying certain properties listed in section 2; approach (iii) appears to
require the Lagrangian density to be linear in the curvature; and approach (iv)
requires the existence of suitable instanton solutions. However, we show that
within their domains of applicability, all of these approaches yield results in
agreement with the Noether charge approach. In the course of our analysis, we
generalize the definition of Brown and York's quasilocal energy to a much more
general class of diffeomorphism invariant, Lagrangian theories of gravity. In
an appendix, we show that in an arbitrary diffeomorphism invariant theory of
gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a
time evolution vector field always can be expressed as the spatial
integral of , where are the constraints
associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late
A general worldline quantum inequality
Worldline quantum inequalities provide lower bounds on weighted averages of
the renormalised energy density of a quantum field along the worldline of an
observer. In the context of real, linear scalar field theory on an arbitrary
globally hyperbolic spacetime, we establish a worldline quantum inequality on
the normal ordered energy density, valid for arbitrary smooth timelike
trajectories of the observer, arbitrary smooth compactly supported weight
functions and arbitrary Hadamard quantum states. Normal ordering is performed
relative to an arbitrary choice of Hadamard reference state. The inequality
obtained generalises a previous result derived for static trajectories in a
static spacetime. The underlying argument is straightforward and is made
rigorous using the techniques of microlocal analysis. In particular, an
important role is played by the characterisation of Hadamard states in terms of
the microlocal spectral condition. We also give a compact form of our result
for stationary trajectories in a stationary spacetime.Comment: 19pp, LaTeX2e. The statement of the main result is changed slightly.
Several typos fixed, references added. To appear in Class Quantum Gra
Stability of pulse-like earthquake ruptures
Pulse-like ruptures arise spontaneously in many elastodynamic rupture
simulations and seem to be the dominant rupture mode along crustal faults.
Pulse-like ruptures propagating under steady-state conditions can be
efficiently analysed theoretically, but it remains unclear how they can arise
and how they evolve if perturbed. Using thermal pressurisation as a
representative constitutive law, we conduct elastodynamic simulations of
pulse-like ruptures and determine the spatio-temporal evolution of slip, slip
rate and pulse width perturbations induced by infinitesimal perturbations in
background stress. These simulations indicate that steady-state pulses driven
by thermal pressurisation are unstable. If the initial stress perturbation is
negative, ruptures stop; conversely, if the perturbation is positive, ruptures
grow and transition to either self-similar pulses (at low background stress) or
expanding cracks (at elevated background stress). Based on a dynamic
dislocation model, we develop an elastodynamic equation of motion for slip
pulses, and demonstrate that steady-state slip pulses are unstable if their
accrued slip is a decreasing function of the uniform background stress
. This condition is satisfied by slip pulses driven by thermal
pressurisation. The equation of motion also predicts quantitatively the growth
rate of perturbations, and provides a generic tool to analyse the propagation
of slip pulses. The unstable character of steady-state slip pulses implies that
this rupture mode is a key one determining the minimum stress conditions for
sustainable ruptures along faults, i.e., their ``strength''. Furthermore, slip
pulse instabilities can produce a remarkable complexity of rupture dynamics,
even under uniform background stress conditions and material properties
Sea surface temperature of the coastal zones of France
Thermal gradients in French coastal zones for the period of one year were mapped in order to enable a coherent study of certain oceanic features detectable by the variations in the sea surface temperature field and their evolution in time. The phenomena examined were mesoscale thermal features in the English Channel, the Bay of Biscay, and the northwestern Mediterranean; thermal gradients generated by French estuary systems; and diurnal heating in the sea surface layer. The investigation was based on Heat Capacity Mapping Mission imagery
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