Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*

TL;DR

This paper proposes using high-precision astrometric observations of stars orbiting close to the galactic center black hole to test the general relativistic no-hair theorems by measuring its quadrupole moment and angular momentum.

Contribution

It introduces a method to test the no-hair theorems by observing orbital precessions of stars near SgrA* with future infrared instruments.

Findings

Orbital precessions can reach up to 10 microarcseconds per year.

Observations of two stars can determine the black hole's angular momentum and quadrupole moment.

This approach enables a fundamental test of general relativity in the strong-field regime.

Abstract

If a class of stars orbits the central black hole in our galaxy in short period (~ 0.1 year), high eccentricity (~ 0.9) orbits, they will experience precessions of their orbital planes induced by both relativistic frame-dragging and the quadrupolar gravity of the hole, at levels that could be as large as 10 microarcseconds per year, if the black hole is rotating faster than 1/2 of its maximum rotation rate. Astrometric observations of the orbits of at least two such stars can in principle lead to a determination of the angular momentum vector J of the black hole and its quadrupole moment Q_2. This could lead to a test of the general relativistic no-hair theorems, which demand that Q_2 = - J^2/M. Future high-precision adaptive infrared optics instruments make make such a fundamental test of the black-hole paradigm possible.