205 research outputs found
Analytical solution methods for geodesic motion
The observation of the motion of particles and light near a gravitating
object is until now the only way to explore and to measure the gravitational
field. In the case of exact black hole solutions of the Einstein equations the
gravitational field is characterized by a small number of parameters which can
be read off from the observables related to the orbits of test particles and
light rays. Here we review the state of the art of analytical solutions of
geodesic equations in various space--times. In particular we consider the four
dimensional black hole space--times of Pleba\'nski--Demia\'nski type as far as
the geodesic equation separates, as well as solutions in higher dimensions, and
also solutions with cosmic strings. The mathematical tools used are elliptic
and hyperelliptic functions. We present a list of analytic solutions which can
be found in the literature.Comment: 11 pages, no figures; based on presentation at the conference "V.
Leopoldo Garc\'ia--Col\'in Mexican Meeting on Mathematical and Experimental
Physics", Mexico City, 201
Exact solution for two unequal counter-rotating black holes
The complete solution for two unequal counter-rotating black holes separated
by a massless strut, is developed in terms of four arbitrary parameters
involving two quantities \sigma 1 and \sigma 2 as the half length of the two
rods representing the black hole horizons, the total mass M and the relative
distance R between the centers of the horizons. A further attempt for
describing the explicit form of this solution in terms of the physical
parameters: The two Komar masses M1 and M2, Komar angular momenta per unit mass
a1 and a2 (a1 and a2 have opposite sign), and the coordinate distance R, guided
us to a 4-parameter subclass in which the five physical parameters satisfy a
simple algebraic relation and the interaction force in this scheme looks like
Schwarzschild type.Comment: This paper has been withdrawn for changes on i
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