6,882 research outputs found
The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r.
On the structure of line-driven winds near black holes
A general physical mechanism of the formation of line-driven winds at the
vicinity of strong gravitational field sources is investigated in the frame of
General Relativity. We argue that gravitational redshifting should be taken
into account to model such outflows. The generalization of the Sobolev
approximation in the frame of General Relativity is presented. We consider all
processes in the metric of a nonrotating (Schwarzschild) black hole. The
radiation force that is due to absorbtion of the radiation flux in lines is
derived. It is demonstrated that if gravitational redshifting is taken into
account, the radiation force becomes a function of the local velocity gradient
(as in the standard line-driven wind theory) and the gradient of . We
derive a general relativistic equation of motion describing such flow. A
solution of the equation of motion is obtained and confronted with that
obtained from the Castor, Abbott & Klein (CAK) theory. It is shown that the
proposed mechanism could have an important contribution to the formation of
line-driven outflows from compact objects.Comment: 20 pages, submitted to Ap
The Hoop Conjecture in Spherically Symmetric Spacetimes
We give general sufficient conditions for the existence of trapped surfaces
due to concentration of matter in spherically symmetric initial data sets
satisfying the dominant energy condition. These results are novel in that they
apply and are meaningful for arbitrary spacelike slices, that is they do not
require any auxiliary assumptions such as maximality, time-symmetry, or special
extrinsic foliations, and most importantly they can easily be generalized to
the nonspherical case once an existence theory for a modified version of the
Jang equation is developed. Moreover, our methods also yield positivity and
monotonicity properties of the Misner-Sharp energy
Tidal coupling of a Schwarzschild black hole and circularly orbiting moon
We describe the possibility of using LISA's gravitational-wave observations
to study, with high precision, the response of a massive central body to the
tidal gravitational pull of an orbiting, compact, small-mass object. Motivated
by this application, we use first-order perturbation theory to study tidal
coupling for an idealized case: a massive Schwarzschild black hole, tidally
perturbed by a much less massive moon in a distant, circular orbit. We
investigate the details of how the tidal deformation of the hole gives rise to
an induced quadrupole moment in the hole's external gravitational field at
large radii. In the limit that the moon is static, we find, in Schwarzschild
coordinates and Regge-Wheeler gauge, the surprising result that there is no
induced quadrupole moment. We show that this conclusion is gauge dependent and
that the static, induced quadrupole moment for a black hole is inherently
ambiguous. For the orbiting moon and the central Schwarzschild hole, we find
(in agreement with a recent result of Poisson) a time-varying induced
quadrupole moment that is proportional to the time derivative of the moon's
tidal field. As a partial analog of a result derived long ago by Hartle for a
spinning hole and a stationary distant companion, we show that the orbiting
moon's tidal field induces a tidal bulge on the hole's horizon, and that the
rate of change of the horizon shape leads the perturbing tidal field at the
horizon by a small angle.Comment: 14 pages, 0 figures, submitted to Phys. Rev.
Waveless Approximation Theories of Gravity
The analysis of a general multibody physical system governed by Einstein's
equations in quite difficult, even if numerical methods (on a computer) are
used. Some of the difficulties -- many coupled degrees of freedom, dynamic
instability -- are associated with the presence of gravitational waves. We have
developed a number of ``waveless approximation theories'' (WAT) which repress
the gravitational radiation and thereby simplify the analysis. The matter,
according to these theories, evolves dynamically. The gravitational field,
however, is determined at each time step by a set of elliptic equations with
matter sources. There is reason to believe that for many physical systems, the
WAT-generated system evolution is a very accurate approximation to that
generated by the full Einstein theory
Gravitational Wave Background from Phantom Superinflation
Recently, the early superinflation driven by phantom field has been proposed
and studied. The detection of primordial gravitational wave is an important
means to know the state of very early universe. In this brief report we discuss
in detail the gravitational wave background excited during the phantom
superinflation.Comment: 3 pages, 2 eps figures, to be published in PRD, revised with
published version, refs. adde
Relativistic Stellar Pulsations With Near-Zone Boundary Conditions
A new method is presented here for evaluating approximately the pulsation
modes of relativistic stellar models. This approximation relies on the fact
that gravitational radiation influences these modes only on timescales that are
much longer than the basic hydrodynamic timescale of the system. This makes it
possible to impose the boundary conditions on the gravitational potentials at
the surface of the star rather than in the asymptotic wave zone of the
gravitational field. This approximation is tested here by predicting the
frequencies of the outgoing non-radial hydrodynamic modes of non-rotating
stars. The real parts of the frequencies are determined with an accuracy that
is better than our knowledge of the exact frequencies (about 0.01%) except in
the most relativistic models where it decreases to about 0.1%. The imaginary
parts of the frequencies are determined with an accuracy of approximately M/R,
where M is the mass and R is the radius of the star in question.Comment: 10 pages (REVTeX 3.1), 5 figs., 1 table, fixed minor typos, published
in Phys. Rev. D 56, 2118 (1997
Parametric resonant acceleration of particles by gravitational waves
We study the resonant interaction of charged particles with a gravitational
wave propagating in the non-empty interstellar space in the presence of a
uniform magnetic field. It is found that this interaction can be cast in the
form of a parametric resonance problem which, besides the main resonance,
allows for the existence of many secondary ones. Each of them is associated
with a non-zero resonant width, depending on the amplitude of the wave and the
energy density of the interstellar plasma. Numerical estimates of the
particles' energisation and the ensuing damping of the wave are given.Comment: LaTeX file, 16 page
Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits
Tidal coupling between members of a compact binary system can have an
interesting and important influence on that binary's dynamical inspiral. Tidal
coupling also distorts the binary's members, changing them (at lowest order)
from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian
gravity, there are simple connections between the geometry of the distorted
ellipsoid and the impact of tides on the orbit's evolution. In this paper, we
develop tools for investigating tidal distortions of rapidly rotating black
holes using techniques that are good for strong-field, fast-motion binary
orbits. We use black hole perturbation theory, so our results assume extreme
mass ratios. We develop tools to compute the distortion to a black hole's
curvature for any spin parameter, and for tidal fields arising from any bound
orbit, in the frequency domain. We also develop tools to visualize the
horizon's distortion for black hole spin (leaving the more
complicated case to a future analysis). We then study how a
Kerr black hole's event horizon is distorted by a small body in a circular,
equatorial orbit. We find that the connection between the geometry of tidal
distortion and the orbit's evolution is not as simple as in the Newtonian
limit.Comment: 37 pages, 8 figures. Accepted for publication to Physical Review D.
This version corrects a number of typographical errors found when reviewing
the page proof
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