571,424 research outputs found
The gravitational self-force
The self-force describes the effect of a particle's own gravitational field
on its motion. While the motion is geodesic in the test-mass limit, it is
accelerated to first order in the particle's mass. In this contribution I
review the foundations of the self-force, and show how the motion of a small
black hole can be determined by matched asymptotic expansions of a perturbed
metric. I next consider the case of a point mass, and show that while the
retarded field is singular on the world line, it can be unambiguously
decomposed into a singular piece that exerts no force, and a smooth remainder
that is responsible for the acceleration. I also describe the recent efforts,
by a number of workers, to compute the self-force in the case of a small body
moving in the field of a much more massive black hole. The motivation for this
work is provided in part by the Laser Interferometer Space Antenna, which will
be sensitive to low-frequency gravitational waves. Among the sources for this
detector is the motion of small compact objects around massive (galactic) black
holes. To calculate the waves emitted by such systems requires a detailed
understanding of the motion, beyond the test-mass approximation.Comment: 10 pages,2 postscript figures, revtex4. This article is based on a
plenary lecture presented at GR1
Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method
We consider an inverse boundary value problem for the heat equation
in , where
is a bounded domain of , the heat conductivity
admits a surface of discontinuity which depends on time and without any spatial
smoothness.
The reconstruction and, implicitly, uniqueness of the moving inclusion, from
the knowledge of the Dirichlet-to-Neumann operator, is realised by a dynamical
probe method based on the construction of fundamental solutions of the elliptic
operator , where is a large real parameter, and a
couple of inequalities relating data and integrals on the inclusion, which are
similar to the elliptic case.
That these solutions depend not only on the pole of the fundamental solution,
but on the large parameter also, allows the method to work in the very
general situation
Tidal deformation of a slowly rotating black hole
In the first part of this article I determine the geometry of a slowly
rotating black hole deformed by generic tidal forces created by a remote
distribution of matter. The metric of the deformed black hole is obtained by
integrating the Einstein field equations in a vacuum region of spacetime
bounded by r < r_max, with r_max a maximum radius taken to be much smaller than
the distance to the remote matter. The tidal forces are assumed to be weak and
to vary slowly in time, and the metric is expressed in terms of generic tidal
quadrupole moments E_{ab} and B_{ab} that characterize the tidal environment.
The metric incorporates couplings between the black hole's spin vector and the
tidal moments, and captures all effects associated with the dragging of
inertial frames. In the second part of the article I determine the tidal
moments by immersing the black hole in a larger post-Newtonian system that
includes an external distribution of matter; while the black hole's internal
gravity is allowed to be strong, the mutual gravity between the black hole and
the external matter is assumed to be weak. The post-Newtonian metric that
describes the entire system is valid when r > r_min, where r_min is a minimum
distance that must be much larger than the black hole's radius. The black-hole
and post-Newtonian metrics provide alternative descriptions of the same
gravitational field in an overlap r_min < r < r_max, and matching the metrics
determine the tidal moments, which are expressed as post-Newtonian expansions
carried out through one-and-a-half post-Newtonian order. Explicit expressions
are obtained in the specific case in which the black hole is a member of a
post-Newtonian two-body system.Comment: 32 pages, 2 figures, revised after referee comments, matches the
published versio
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