Deformed black hole in Sagittarius A

TL;DR

This paper investigates how disformal deformations of Kerr black holes in scalar-tensor theories affect stellar orbits, revealing violations of the no-hair theorem and providing constraints based on observed star precession.

Contribution

It introduces a class of disformed Kerr solutions, analyzes their orbital signatures, and constrains the disformal parameter using stellar precession data.

Findings

Disformal parameter D causes deviations from Kerr quadrupole relations.

For small (1+D), leading corrections to Schwarzschild precession are derived.

Constraints on D are obtained from the S2 star precession measurements.

Abstract

We analyze the post-Newtonian orbit of stars around a deformed Kerr black hole. The deformation we consider is a class of disformal transformations of a nontrivial Kerr solution in scalar-tensor theory which are labeled via the disformal parameter $D$. We study different limits of the disformal parameter, and compare the trajectories of stars orbiting a black hole to the case of the Kerr spacetime in general relativity, up to 2PN order. Our findings show that for generic nonzero $D$, the no-hair theorem of general relativity is violated, in the sense that the black hole's quadrupole $Q$ is not determined by its mass $M$ and angular momentum $J$ through the relation $Q=-J^2/M$. Limiting values of $D$ provide examples of simple and exact noncircular metric solutions, whereas in a particular limit, where $1+D$ is small but finite, we obtain a leading correction to the Schwarzschild precession due to disformality. In this case, the disformal parameter is constrained using the recent measurement of the pericenter precession of the star S2 by the GRAVITY Collaboration.