Periapsis shifts in dark matter distribution around a black hole

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.

30 pages, 7 figures; v2: added Tables, a few paragraphs in Introduction, and references, accepted for publication in the International Journal of Modern Physics D

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Cited by in corpus (9)

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• Charged black hole surrounded by a galactic halo in de Sitter universe
• Modelling Einstein cluster using Einasto profile
• Retrograde Precession of Relativistic Orbits and the Quest for Charged Black Holes
• Effect of generic dark matter halo on transonic accretion onto galactic black holes
• Distinguishing dark matter halos with Extreme mass ratio inspirals
• Extended mass and spheroidal deformation effects on epicyclic frequencies and periapsis shift in quasi-circular orbits
• Matter environments around black holes: geodesics, light rings, and ultracompact configurations