Testing the black hole no-hair theorem at the galactic center: Perturbing effects of stars in the surrounding cluster

TL;DR

This paper assesses how stellar perturbations near the galactic center affect measurements of black hole properties, finding that relativistic effects can be distinguished from stellar influences for stars close enough to the black hole.

Contribution

It provides an analytic estimate showing relativistic spin and quadrupole effects dominate stellar perturbations for stars near the galactic center, supporting tests of the no-hair theorem.

Findings

Relativistic effects surpass stellar perturbations for close-in stars.

Analytic estimates align with recent N-body simulation results.

Stellar cluster perturbations are manageable in black hole tests.

Abstract

Observations of the precessing orbits of stars very near the massive black hole in the galactic center could provide measurements of the spin and quadrupole moment of the hole and thereby test the no-hair theorem of general relativity. Since the galactic center is likely to be populated by a distribution of stars and small black holes, their gravitational interactions will perturb the orbit of any given star. We estimate the effects of such perturbations using analytic orbital perturbation theory, and show that for a range of possible stellar distributions, and for an observed star sufficiently close to the black hole, the relativistic spin and quadrupole effects will be larger than the effects of stellar cluster perturbations. Our results are consistent those from recent numerical N-body simulations by Merritt et al.