Kerr-scalaron Metric and Astronomical Consequences near the Galactic Center Black Hole

Abstract

Astronomical tests of spacetime metric and gravitation theory near the Galactic center (GC) black hole, Sgr A*, have gained momentum with the observations of compact stellar orbits near the black hole and measurement of the black hole shadow. Deviation from the Kerr metric is a potential signature of modified gravity theory. In this work, we use the Newman–Janis algorithm to construct an axially symmetric and asymptotically flat metric in f(R) scalaron gravity theory. We call it the Kerr-scalaron metric. To study the astronomical consequences of the new metric, we use the compact stellar orbits and the black hole shadow. We use the observed size of the emission ring of the GC black hole shadow for estimating the deviation of the new metric from general relativity. It has been found that scalarons with masses within 10−17–10−16 eV are compatible with the observed emission ring size for a black hole spin of χ = 0.9. The Schwarzschild limit of the pericenter shift is estimated for compact stellar orbits near the black hole. General relativistic pericenter shift in wider orbits, including S stars such as S4716 and S2, has been reproduced with these scalarons. The parameter f SP measuring the deviation from Schwarzschild pericenter shift has been found to be f SP = 1.00–1.04 within stellar orbits with semimajor axes of 45–100 au. Scalarons have the capability to dominate Schwarzschild precession for orbits with semimajor axes much smaller than 45 au. Lense–Thirring (LT) precession with the new metric is estimated for the compact orbits. The massive scalarons produce LT precession with magnitude (12.25–24.5) μas yr−1 in the orbit of S2. The LT precession timescale is within 0.1% of the age of the S stars.