Nonlinear gravitational self-force: Field outside a small body

作者：Pound Adam^*

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2012, 86(8): 084019.

DOI：10.1103/PhysRevD.86.084019

A small extended body moving through an external spacetime g(alpha beta) creates a metric perturbation h(alpha beta), which forces the body away from geodesic motion in g(alpha beta). The foundations of this effect, called the gravitational self-force, are now well established, but concrete results have mostly been limited to linear order. Accurately modeling the dynamics of compact binaries requires proceeding to nonlinear orders. To that end, I show how to obtain the metric perturbation outside the body at all orders in a class of generalized wave gauges. In a small buffer region surrounding the body, the form of the perturbation can be found analytically as an expansion for small distances r from a representative worldline. Given only a specification of the body%26apos;s multipole moments, the field obtained in the buffer region suffices to find the metric everywhere outside the body via a numerical puncture scheme. Following this procedure at first and second order, I calculate the field in the buffer region around an arbitrarily structured compact body at sufficiently high order in r to numerically implement a second-order puncture scheme, including effects of the body%26apos;s spin. I also define nth-order (local) generalizations of the Detweiler-Whiting singular and regular fields and show that in a certain sense, the body can be viewed as a skeleton of multipole moments.

• 出版日期2012-10-3