28 research outputs found
Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion
Analytic solutions of the Regge-Wheeler equation are presented in the form of
series of hypergeometric functions and Coulomb wave functions which have
different regions of convergence. Relations between these solutions are
established. The series solutions are given as the Post-Minkowskian expansion
with respect to a parameter , being the mass of
black hole. This expansion corresponds to the post-Newtonian expansion when
they are applied to the gravitational radiation from a particle in circular
orbit around a black hole. These solutions can also be useful for numerical
computations.Comment: 22 page
Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions
Analytic solutions of the Teukolsky equation in Kerr geometries are presented
in the form of series of hypergeometric functions and Coulomb wave functions.
Relations between these solutions are established. The solutions provide a very
powerful method not only for examining the general properties of solutions and
physical quantities when they are applied to, but also for numerical
computations. The solutions are given in the expansion of a small parameter
, being the mass of black hole, which corresponds
to Post-Minkowski expansion by and to post-Newtonian expansion when they
are applied to the gravitational radiation from a particle in circular orbit
around a black hole. It is expected that these solutions will become a powerful
weapon to construct the theoretical template towards LIGO and VIRGO projects.Comment: 24 pages, minor modification
Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole :Effects of Black Hole Absorption
When a particle moves around a Kerr black hole, it radiates gravitational
waves.Some of these waves are absorbed by the black hole. We calculate such
absorption of gravitational waves induced by a particle of mass mu in a
circular orbit on an equatorial plane around a Kerr black hole of mass M. We
assume that the velocity of the particle v is much smaller than the speed of
light c and calculate the energy absorption rate analytically. We adopt an
analytic technique for the Teukolsky equation developed by Mano, Suzuki and
Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to the
lowest order. We find that the black hole absorption occurs at O((v/c)^5)
beyond the Newtonian-quadrapole luminosity at infinity in the case when the
black hole is rotating, which is O((v/c)^3) lower than the non-rotating case.
Using the energy absorption rate, we investigate its effects on the orbital
evolution of coalescing compact binaries.Comment: 22 pages, ptptex, no figure
Analytic Solutions of Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries
The analytic solution of Teukolsky equation in Kerr-de Sitter and
Kerr-Newman-de Sitter geometries is presented and the properties of the
solution are examined. In particular, we show that our solution satisfies the
Teukolsky-Starobinsky identities explicitly and fix the relative normalization
between solutions with the spin weight and .Comment: 24 pages, LaTe