107 research outputs found
Upper limits on gravitational-wave signals based on loudest events
Searches for gravitational-wave bursts have often focused on the loudest
event(s) in searching for detections and in determining upper limits on
astrophysical populations. Typical upper limits have been reported on event
rates and event amplitudes which can then be translated into constraints on
astrophysical populations. We describe the mathematical construction of such
upper limits.Comment: 8 pages, 1 figur
A matched expansion approach to practical self-force calculations
We discuss a practical method to compute the self-force on a particle moving
through a curved spacetime. This method involves two expansions to calculate
the self-force, one arising from the particle's immediate past and the other
from the more distant past. The expansion in the immediate past is a covariant
Taylor series and can be carried out for all geometries. The more distant
expansion is a mode sum, and may be carried out in those cases where the wave
equation for the field mediating the self-force admits a mode expansion of the
solution. In particular, this method can be used to calculate the gravitational
self-force for a particle of mass mu orbiting a black hole of mass M to order
mu^2, provided mu/M << 1. We discuss how to use these two expansions to
construct a full self-force, and in particular investigate criteria for
matching the two expansions. As with all methods of computing self-forces for
particles moving in black hole spacetimes, one encounters considerable
technical difficulty in applying this method; nevertheless, it appears that the
convergence of each series is good enough that a practical implementation may
be plausible.Comment: IOP style, 8 eps figures, accepted for publication in a special issue
of Classical and Quantum Gravit
The self-force on a static scalar test-charge outside a Schwarzschild black hole
The finite part of the self-force on a static scalar test-charge outside a
Schwarzschild black hole is zero. By direct construction of Hadamard's
elementary solution, we obtain a closed-form expression for the minimally
coupled scalar field produced by a test-charge held fixed in Schwarzschild
spacetime. Using the closed-form expression, we compute the necessary external
force required to hold the charge stationary. Although the energy associated
with the scalar field contributes to the renormalized mass of the particle (and
thereby its weight), we find there is no additional self-force acting on the
charge. This result is unlike the analogous electrostatic result, where, after
a similar mass renormalization, there remains a finite repulsive self-force
acting on a static electric test-charge outside a Schwarzschild black hole. We
confirm our force calculation using Carter's mass-variation theorem for black
holes. The primary motivation for this calculation is to develop techniques and
formalism for computing all forces - dissipative and non-dissipative - acting
on charges and masses moving in a black-hole spacetime. In the Appendix we
recap the derivation of the closed-form electrostatic potential. We also show
how the closed-form expressions for the fields are related to the infinite
series solutions.Comment: RevTeX, To Appear in Phys. Rev.
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