Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge

Abstract

The exact metric of a Schwarzschild black hole in the true radiation gauge was recently reported. In this work, we base on this gravity and calculate the gravitational deflection of relativistic massive particles up to the fourth post-Minkowskian order. It is found that the result is consistent with the previous formulations for both the case of dropping the fourth-order contribution and the case of light deflection. Our result might be helpful for future high-accuracy observations.