Star Clusters and Dark Matter as Probes of the Spacetime Geometry of Massive Black Holes

TL;DR

This thesis explores using star orbits and dark matter profiles near supermassive black holes to test general relativity and understand dark matter distribution, highlighting the dominance of relativistic effects in the Galactic center.

Contribution

It introduces a relativistic phase-space formulation for dark matter near black holes and assesses the feasibility of no-hair theorem tests via star orbit precessions.

Findings

Relativistic precessions dominate for stars within 0.2 milliparsecs of Sgr A*.

Dark matter density spike is higher and more concentrated when considering relativistic effects.

Relativistic effects overshadow dark matter perturbations in star orbit dynamics.

Abstract

This thesis includes two main projects. In the first part, we assess the feasibility of a recently suggested strong-field general relativity test, in which future observations of a hypothetical class of stars orbiting very close to the supermassive black hole at the center of our galaxy, known as Sgr A*, could provide tests of the so-called no-hair theorem of general relativity through the measurement of precessions of their orbital planes. By considering how a distribution of stars and stellar mass black holes in the central cluster would perturb the orbits of those hypothetical stars, we show that for stars within about 0.2 milliparsecs (about 6 light-hours) of the black hole, the relativistic precessions dominate, leaving a potential window for tests of no-hair theorems. Our results are in agreement with N-body simulation results. In the second part, we develop a fully general relativistic phase-space formulation to consider the effects of the Galactic center supermassive black hole Sgr A* on the dark-matter density profile and its applications in the indirect detection of dark matter. We find significant differences from the non-relativistic result of Gondolo and Silk (1999), including a higher density for the spike and a larger degree of central concentration. Having the dark matter profile density in the presence of the massive black hole, we calculate its perturbing effect on the orbital motions of stars in the Galactic center, and find that for the stars of interest, relativistic effects related to the hair on the black hole will dominate the effects of dark matter.