3 research outputs found
Linear stability in billiards with potential
A general formula for the linearized Poincar\'e map of a billiard with a
potential is derived. The stability of periodic orbits is given by the trace of
a product of matrices describing the piecewise free motion between reflections
and the contributions from the reflections alone. For the case without
potential this gives well known formulas. Four billiards with potentials for
which the free motion is integrable are treated as examples: The linear
gravitational potential, the constant magnetic field, the harmonic potential,
and a billiard in a rotating frame of reference, imitating the restricted three
body problem. The linear stability of periodic orbits with period one and two
is analyzed with the help of stability diagrams, showing the essential
parameter dependence of the residue of the periodic orbits for these examples.Comment: 22 pages, LaTex, 4 Figure
Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA
Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany