Frame-dragging and the kinematics of Galactic-Center stars

TL;DR

This paper models the frame-dragging effects on stars near the Galactic Center using an approximation to the Kerr metric, predicting measurable kinematic effects that could reveal the black hole's spin.

Contribution

It introduces an approximation to the Kerr metric for slightly relativistic stars and computes the resulting kinematic effects, enabling potential black hole spin measurements.

Findings

Kinematic effect at pericenter is proportional to (a(1-e^2))^{-2}

Effect magnitude is about 10 m/s for known stars

Potential to measure black hole spin through stellar kinematics

Abstract

We calculate the effects of frame dragging on the Galactic-Center stars. Assuming the stars are only slightly relativistic, we derive an approximation to the Kerr metric, which turns out to be a weak field Schwarzschild metric plus a frame dragging term. By numerically integrating the resulting geodesic equations, we compute the effect on keplerian elements and the kinematics. We find that the kinematic effect at pericenter passage is proportional to (a(1-e^2))^{-2}. For known Galactic-center stars it is of order 10 m/s. If observed this would provide a measurement of the spin of the black hole.