Shapiro effect for for relativistic particles - testing General Relativity in a new window

TL;DR

This paper investigates the Shapiro effect for relativistic particles in Schwarzschild gravity, revealing a speed-dependent gravitational repulsion for particles exceeding a certain velocity, with implications for satellite experiments.

Contribution

It introduces a new speed-dependent potential for relativistic particles in gravitational fields, predicting gravitational repulsion for particles faster than c/√2, and discusses experimental tests.

Findings

Relativistic particles faster than c/√2 are gravitationally repelled.

A new potential V=GM gamma(gamma^2 -2)/r describes relativistic particle dynamics.

Satellite experiments could detect the predicted gravitational repulsion.

Abstract

Propagation of relativistic particles in the Schwarzschild gravitational field is studied. Particles emitted radially outward with speed at infinity exceeding c/2^0.5 are observed to be accelerated in the gravitational field by a distant observer. This is the Shapiro effect for relativistic particles. Slower particles are decelerated, as in Newtonian gravity. A speed-dependent potential for relativistic particles corresponding to the speed measured in terms of the coordinate time is derived to be $V=GM gamma(gamma^2 -2)/r which is repulsive for v>c/2^0.5. The gravitational repulsion could be revealed in satellite experiments with beams of relativistic particles subject to very precise time measurements. Principles of laboratory measurements able to test kinetic energy changes of relativistic particles in the Earth gravitational field are discussed.