1107.2098 (Steven Detweiler)

Gravitational radiation reaction and second order perturbation theory    [PDF]

Steven Detweiler

A point particle of small mass m moves in free fall through a background
vacuum spacetime metric g_ab and creates a first-order metric perturbation
h^1ret_ab that diverges at the particle. Elementary expressions are known for
the singular m/r part of h^1ret_ab and for its tidal distortion determined by
the Riemann tensor in a neighborhood of m. Subtracting this singular part
h^1S_ab from h^1ret_ab leaves a regular remainder h^1R_ab. The self-force on
the particle from its own gravitational field adjusts the world line at O(m) to
be a geodesic of g_ab+h^1R_ab. The generalization of this description to
second-order perturbations is developed and results in a wave equation
governing the second-order h^2ret_ab with a source that has an O(m^2)
contribution from the stress-energy tensor of m added to a term quadratic in
h^1ret_ab. Second-order self-force analysis is similar to that at first order:
The second-order singular field h^2S_ab subtracted from h^2ret_ab yields the
regular remainder h^2R_ab, and the second-order self-force is then revealed as
geodesic motion of m in the metric g_ab+h^1R+h^2R.

View original: http://arxiv.org/abs/1107.2098