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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
The Effect of Remittance Inflows to India: An Empirical Analysis
This paper studies the relationship between remittance inflows and GDP in India. An empirical regression analysis is applied to India’s data to analyze the effect of remittance inflows to the level of GDP and GDP growth. Results show that remittance inflows have a positive and significant effect on the level of India’s GDP, and a positive but insignificant effect on GDP growth. Data used in this research come from the World Bank
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