Periapsis shifts in dark matter distribution around a black hole

TL;DR

This paper models the periapsis shifts of stars orbiting a black hole surrounded by dark matter, revealing how local matter density influences orbital precession and challenging exotic object interpretations.

Contribution

It introduces a simple formula for orbital precession in a dark matter environment around a black hole, accounting for both relativistic and matter density effects.

Findings

Precession rate includes positive relativistic and negative matter density contributions.

The model shows retrograde precession can occur without exotic objects.

Simulations confirm the impact of dark matter on orbital shifts.

Abstract

We consider the periapsis shifts of bound orbits of stars on static clouds around a black hole. The background spacetime is constructed from a Schwarzschild black hole surrounded by a static and spherically symmetric self-gravitating system of massive particles, which satisfies all the standard energy conditions and physically models the gravitational effect of dark matter distribution around a nonrotating black hole. Using nearly circular bound orbits of stars, we obtain a simple formula for the precession rate. This formula explicitly shows that the precession rate is determined by a positive contribution (i.e., a prograde shift) from the conventional general-relativistic effect and a negative contribution (i.e., a retrograde shift) from the local matter density. The four quantities for such an orbit (i.e., the orbital shift angle, the radial oscillation period, the redshift, and the star position mapped onto the celestial sphere) determine the local values of the background model functions. Furthermore, we not only evaluate the precession rate of nearly circular bound orbits in several specific models but also simulate several bound orbits with large eccentricity and their periapsis shifts. The present exact model demonstrates that the retrograde precession does not mean any exotic central objects such as naked singularities or wormholes but simply the existence of significant energy density of matters on the star orbit around the black hole.