Relativistic redshift effects and the Galactic-center stars

TL;DR

This paper investigates relativistic redshift effects, including both post-Newtonian and post-Minkowskian contributions, on the observed spectra of stars near the Galactic center, highlighting their comparable magnitudes and potential detectability.

Contribution

It introduces a boundary-value formulation to compute light path perturbations and compares relativistic redshift effects, including spin, on stellar observations near the Galactic center.

Findings

Post-Newtonian and post-Minkowskian effects are both about a few km/s at S2's pericenter.

Post-Minkowskian spin effects are much smaller, around 0.1 km/s.

Both effects are of similar order, making them relevant for observations.

Abstract

The high pericenter velocities (up to a few percent of light) of the S stars around the Galactic-center black hole suggest that general relativistic effects may be detectable through the time variation of the redshift during pericenter passage. Previous work has computed post-Newtonian perturbations to the stellar orbits. We study the additional redshift effects due to perturbations of the light path (what one may call "post-Minkowskian'' effects), a calculation that can be elegantly formulated as a boundary-value problem. The post-Newtonian and post-Minkowskian redshift effects are comparable: both are O(beta^3) and amount to a few km/s at pericenter for the star S2. On the other hand, the post-Minkowskian redshift contribution of spin is O(beta^5) and much smaller than the O(beta^4) post-Newtonian effect, which would be approximately 0.1km/s for S2.