Exact harmonic metric for a uniformly moving Schwarzschild black hole. (English) Zbl 1284.83082
Summary: The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.
MSC:
83C57 | Black holes |
83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
83C15 | Exact solutions to problems in general relativity and gravitational theory |
83C10 | Equations of motion in general relativity and gravitational theory |