7,012 research outputs found

### The relativistic equations of stellar structure and evolution

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r

### An improved, "phase-relaxed" F-statistic for gravitational-wave data analysis

Rapidly rotating, slightly non-axisymmetric neutron stars emit nearly
periodic gravitational waves (GWs), quite possibly at levels detectable by
ground-based GW interferometers. We refer to these sources as "GW pulsars". For
any given sky position and frequency evolution, the F-statistic is the optimal
(frequentist) statistic for the detection of GW pulsars. However, in "all-sky"
searches for previously unknown GW pulsars, it would be computationally
intractable to calculate the (fully coherent) F-statistic at every point of a
(suitably fine) grid covering the parameter space: the number of gridpoints is
many orders of magnitude too large for that. Here we introduce a
"phase-relaxed" F-statistic, which we denote F_pr, for incoherently combining
the results of fully coherent searches over short time intervals. We estimate
(very roughly) that for realistic searches, our F_pr is ~10-15% more sensitive
than the "semi-coherent" F-statistic that is currently used. Moreover, as a
byproduct of computing F_pr, one obtains a rough determination of the
time-evolving phase offset between one's template and the true signal imbedded
in the detector noise. Almost all the ingredients that go into calculating F_pr
are already implemented in LAL, so we expect that relatively little additional
effort would be required to develop a search code that uses F_pr.Comment: 8 pages, 4 figures, submitted to PR

### 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 $g_{00}$. 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 generation of gravitational waves. 2: The post-linear formalism revisited

Two different versions of the Green's function for the scalar wave equation in weakly curved spacetime (one due to DeWitt and DeWitt, the other to Thorne and Kovacs) are compared and contrasted; and their mathematical equivalence is demonstrated. The DeWitt-DeWitt Green's function is used to construct several alternative versions of the Thorne-Kovacs post-linear formalism for gravitational-wave generation. Finally it is shown that, in calculations of gravitational bremsstrahlung radiation, some of our versions of the post-linear formalism allow one to treat the interacting bodies as point masses, while others do not

### 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.

### Gravitational-wave bursts from the nuclei of distant galaxies and quasars: Proposal for detection using Doppler tracking of interplanetary spacecraft

Supermassive black holes which exist in the nuclei of many quasars and galaxies are examined along with the collapse which forms these holes and subsequent collisions between them which produce strong, broad-band bursts of gravitational waves. Such bursts might arrive at earth as often as 50 times per year--or as rarely as once each 300 years. The detection of such bursts with dual-frequency Doppler tracking of interplanetary spacecraft is considered

### 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.

### Non-Gaussianity analysis of GW background made by short-duration burst signals

We study an observational method to analyze non-Gaussianity of a
gravitational wave (GW) background made by superposition of weak burst signals.
The proposed method is based on fourth-order correlations of data from four
detectors, and might be useful to discriminate the origin of a GW background.
With a formulation newly developed to discuss geometrical aspects of the
correlations, it is found that the method provides us with linear combinations
of two interesting parameters, I_2 and V_2 defined by the Stokes parameters of
individual GW burst signals. We also evaluate sensitivities of specific
detector networks to these parameters.Comment: 18 pages, to appear in PR

### 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

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