Tidal deformation of a slowly rotating material body: External metric
Abstract
We construct the external metric of a slowly rotating, tidally deformed material body in general relativity. The tidal forces acting on the body are assumed to be weak and to vary slowly with time, and the metric is obtained as a perturbation of a background metric that describes the external geometry of an isolated, slowly rotating body. The tidal environment is generic and characterized by two symmetric trace-free tidal moments Ea b and Ba b, and the body is characterized by its mass M , its radius R , and a dimensionless angular-momentum vector χa≪1 . The perturbation accounts for all couplings between χa and the tidal moments. The body's gravitational response to the applied tidal field is measured in part by the familiar gravitational Love numbers K2el and K2mag , but we find that the coupling between the body's rotation and the tidal environment requires the introduction of four new quantities, which we designate as rotational-tidal Love numbers. All these Love numbers are gauge invariant in the usual sense of perturbation theory, and all vanish when the body is a black hole.
- Publication:
-
Physical Review D
- Pub Date:
- May 2015
- DOI:
- 10.1103/PhysRevD.91.104018
- arXiv:
- arXiv:1503.07366
- Bibcode:
- 2015PhRvD..91j4018L
- Keywords:
-
- 04.20.-q;
- 04.25.-g;
- 04.25.Nx;
- 04.40.Dg;
- Classical general relativity;
- Approximation methods;
- equations of motion;
- Post-Newtonian approximation;
- perturbation theory;
- related approximations;
- Relativistic stars: structure stability and oscillations;
- General Relativity and Quantum Cosmology
- E-Print:
- 17 pages, 0 figures, matches the published version