Relativistic Tidal Accelerations in the Exterior Schwarzschild Spacetime

TL;DR

This paper explores how free particles near a Schwarzschild black hole can gain significant tidal energy through spacetime curvature, potentially reaching near-light speeds, with implications for astrophysical phenomena.

Contribution

It demonstrates that tidal acceleration to near-light speeds can occur in Schwarzschild spacetime for particles moving radially outward, extending previous Kerr-based results.

Findings

Particles can be tidally accelerated to near-light speeds in Schwarzschild spacetime.

Tidal energy gain depends on initial velocity and direction of motion.

Results have implications for understanding energy transfer in collapsed astrophysical systems.

Abstract

We study further a general relativistic mechanism for the acquisition of tidal energy by free test particles near a gravitationally collapsed configuration. Specifically, we investigate the solutions of timelike geodesic equation in a Fermi normal coordinate system established about the world line of an accelerated observer that remains spatially at rest in the exterior Schwarzschild spacetime. Such static observers in effect define the rest frame of the collapsed source. The gain in tidal energy is due to local spacetime curvature. Previous work in this direction in connection with astrophysical jets involved geodesic motion along the Kerr rotation axis where outward moving particles could be tidally accelerated to almost the speed of light if their initial speed, as measured by the reference observer, is above a certain threshold escape velocity. We focus here for simplicity on the exterior Schwarzschild spacetime and show that the effective tidal acceleration to near the speed of light can occur for geodesic motion in certain radially outward directions. The implications of these results for the physics of gravitationally collapsed systems are briefly discussed.