1,272 research outputs found
The thermodynamic structure of Einstein tensor
We analyze the generic structure of Einstein tensor projected onto a 2-D
spacelike surface S defined by unit timelike and spacelike vectors u_i and n_i
respectively, which describe an accelerated observer (see text). Assuming that
flow along u_i defines an approximate Killing vector X_i, we then show that
near the corresponding Rindler horizon, the flux j_a=G_ab X^b along the ingoing
null geodesics k_i normalised to have unit Killing energy, given by j . k, has
a natural thermodynamic interpretation. Moreover, change in cross-sectional
area of the k_i congruence yields the required change in area of S under
virtual displacements \emph{normal} to it. The main aim of this note is to
clearly demonstrate how, and why, the content of Einstein equations under such
horizon deformations, originally pointed out by Padmanabhan, is essentially
different from the result of Jacobson, who employed the so called Clausius
relation in an attempt to derive Einstein equations from such a Clausius
relation. More specifically, we show how a \emph{very specific geometric term}
[reminiscent of Hawking's quasi-local expression for energy of spheres]
corresponding to change in \emph{gravitational energy} arises inevitably in the
first law: dE_G/d{\lambda} \alpha \int_{H} dA R_(2) (see text) -- the
contribution of this purely geometric term would be missed in attempts to
obtain area (and hence entropy) change by integrating the Raychaudhuri
equation.Comment: added comments and references; matches final version accepted in
Phys. Rev.
Geodesic Congruences in the Palatini f(R) Theory
We shall investigate the properties of a congruence of geodesics in the
framework of Palatini f(R) theories. We shall evaluate the modified geodesic
deviation equation and the Raychaudhuri's equation and show that f(R) Palatini
theories do not necessarily lead to attractive forces. Also we shall study
energy condition for f(R) Palatini gravity via a perturbative analysis of the
Raychaudhuri's equation
The French Atlantic littoral and the Massif Armoricain, part 1
The author has identified the following significant results. For interpretation of Isle of Jersey imagery, two types of taxons were defined according to their variability in time. On the whole, taxons with a similar spectral signature were opposed to those with strongly varying spectral signature. The taxon types were low diachronic variations and strong diachronic variation. Imagery interpretation was restricted to the landward part of the Fromentine area, including the sand beaches which were often difficult to spectrally separate from the barren coastal dunes in the southern part of Noirmoutier Island as well as along the Breton marsh. From 1972 to 1976, sandbanks reduced in area. Two high river discharge images showed over a two year period an identical outline for the Bilho bank to seaward, whereas upstream, the bank has receeded in the same time to a line joining Paimboeuf to Montoir. The Brillantes bank has receeded at both ends, partly due to dredging operations in the access channel to Donges harbor
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.
Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation
The first objective of this work is to obtain practical prescriptions to
calculate the absorption of mass and angular momentum by a black hole when
external processes produce gravitational radiation. These prescriptions are
formulated in the time domain within the framework of black-hole perturbation
theory. Two such prescriptions are presented. The first is based on the
Teukolsky equation and it applies to general (rotating) black holes. The second
is based on the Regge-Wheeler and Zerilli equations and it applies to
nonrotating black holes. The second objective of this work is to apply the
time-domain absorption formalisms to situations in which the black hole is
either small or slowly moving. In the context of this small-hole/slow-motion
approximation, the equations of black-hole perturbation theory can be solved
analytically, and explicit expressions can be obtained for the absorption of
mass and angular momentum. The changes in the black-hole parameters can then be
understood in terms of an interaction between the tidal gravitational fields
supplied by the external universe and the hole's tidally-induced mass and
current quadrupole moments. For a nonrotating black hole the quadrupole moments
are proportional to the rate of change of the tidal fields on the hole's world
line. For a rotating black hole they are proportional to the tidal fields
themselves.Comment: 36 pages, revtex4, no figures, final published versio
Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole
The center-of-mass energy of two particles colliding near the horizon of a
maximally rotating black hole can be arbitrarily high if the angular momentum
of either of the incident particles is fine-tuned, which we call a critical
particle. We study particle emission from such high-energy collision and
reaction in the equatorial plane fully analytically. We show that the
unconditional upper limit of the energy of the emitted particle is given by
218.6% of that of the injected critical particle, irrespective of the details
of the reaction and this upper limit can be realized for massless particle
emission. The upper limit of the energy extraction efficiency for this emission
as a collisional Penrose process is given by 146.6%, which can be realized in
the collision of two massive particles with optimized mass ratio. Moreover, we
analyze perfectly elastic collision, Compton scattering, and pair annihilation
and show that net positive energy extraction is really possible for these three
reactions. The Compton scattering is most efficient among them and the
efficiency can reach 137.2%. On the other hand, our result is qualitatively
consistent with the earlier claim that the mass and energy of the emitted
particle are at most of order the total energy of the injected particles and
hence we can observe neither super-heavy nor super-energetic particles.Comment: 22 pages, 3 figures, typos corrected, reference updated, accepted for
publication in Physical Review D, typos correcte
Intermediate-mass-ratio-inspirals in the Einstein Telescope. II. Parameter estimation errors
We explore the precision with which the Einstein Telescope (ET) will be able
to measure the parameters of intermediate-mass-ratio inspirals (IMRIs). We
calculate the parameter estimation errors using the Fisher Matrix formalism and
present results of a Monte Carlo simulation of these errors over choices for
the extrinsic parameters of the source. These results are obtained using two
different models for the gravitational waveform which were introduced in paper
I of this series. These two waveform models include the inspiral, merger and
ringdown phases in a consistent way. One of the models, based on the transition
scheme of Ori & Thorne [1], is valid for IMBHs of arbitrary spin, whereas the
second model, based on the Effective One Body (EOB) approach, has been
developed to cross-check our results in the non-spinning limit. In paper I of
this series, we demonstrated the excellent agreement in both phase and
amplitude between these two models for non-spinning black holes, and that their
predictions for signal-to-noise ratios (SNRs) are consistent to within ten
percent. We now use these models to estimate parameter estimation errors for
binary systems with masses 1.4+100, 10+100, 1.4+500 and 10+500 solar masses
(SMs), and various choices for the spin of the central intermediate-mass black
hole (IMBH). Assuming a detector network of three ETs, the analysis shows that
for a 10 SM compact object (CO) inspiralling into a 100 SM IMBH with spin
q=0.3, detected with an SNR of 30, we should be able to determine the CO and
IMBH masses, and the IMBH spin magnitude to fractional accuracies of 0.001,
0.0003, and 0.001, respectively. We also expect to determine the location of
the source in the sky and the luminosity distance to within 0.003 steradians,
and 10%, respectively. We also assess how the precision of parameter
determination depends on the network configuration.Comment: 21 pages, 5 figures. One reference corrected in v3 for consistency
with published version in Phys Rev
Quadrupole moments of rotating neutron stars
Numerical models of rotating neutron stars are constructed for four equations
of state using the computer code RNS written by Stergioulas. For five selected
values of the star's gravitational mass (in the interval between 1.0 and 1.8
solar masses) and for each equation of state, the star's angular momentum is
varied from J=0 to the Keplerian limit J=J_{max}. For each neutron-star
configuration we compute Q, the quadrupole moment of the mass distribution. We
show that for given values of M and J, |Q| increases with the stiffness of the
equation of state. For fixed mass and equation of state, the dependence on J is
well reproduced with a simple quadratic fit, Q \simeq - aJ^2/M c^2, where c is
the speed of light, and a is a parameter of order unity depending on the mass
and the equation of state.Comment: ReVTeX, 7 pages, 5 figures, additional material, and references adde
Dynamical Surface Gravity in Spherically Symmetric Black Hole Formation
We study dynamical surface gravity in a general spherically symmetric setting
using Painlev\'{e}-Gullstrand (PG) coordinates. Our analysis includes several
definitions that have been proposed in the past as well as two new definitions
adapted to PG coordinates. Various properties are considered, including general
covariance, value at extremality, locality and static limit. We illustrate with
specific examples of "dirty" black holes that even for spacetimes possessing a
global timelike Killing vector, local definitions of surface gravity can differ
substantially from "non-local" ones that require an asymptotic normalization
condition. Finally, we present numerical calculations of dynamical surface
gravity for black hole formation via spherically symmetric scalar field
collapse. Our results highlight the differences between the various definitions
in a dynamical setting and provide further insight into the distinction between
local and non-local definitions of surface gravity.Comment: Final version to appear in Phys. Rev. D. Slight name change, further
improvements to numerics and presentation, 25 pages, 7 figure
Fermi Coordinates and Penrose Limits
We propose a formulation of the Penrose plane wave limit in terms of null
Fermi coordinates. This provides a physically intuitive (Fermi coordinates are
direct measures of geodesic distance in space-time) and manifestly covariant
description of the expansion around the plane wave metric in terms of
components of the curvature tensor of the original metric, and generalises the
covariant description of the lowest order Penrose limit metric itself, obtained
in hep-th/0312029. We describe in some detail the construction of null Fermi
coordinates and the corresponding expansion of the metric, and then study
various aspects of the higher order corrections to the Penrose limit. In
particular, we observe that in general the first-order corrected metric is such
that it admits a light-cone gauge description in string theory. We also
establish a formal analogue of the Weyl tensor peeling theorem for the Penrose
limit expansion in any dimension, and we give a simple derivation of the
leading (quadratic) corrections to the Penrose limit of AdS_5 x S^5.Comment: 25 page
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