Testing the Spacetime Geometry of Sgr A* with the Relativistic Orbit of S2 star

TL;DR

This study tests various theoretical models of Sgr A*'s spacetime using the orbit of star S2, combining observational data with relativistic simulations to constrain black hole properties.

Contribution

It introduces a comprehensive relativistic analysis of S2 star data across multiple spacetime models, including naked singularities and regular black holes.

Findings

Schwarzschild, Reissner-Nordstr"om, and Bardeen black holes are statistically indistinguishable with current data.

Constraints on the charge parameter q/M in non-Schwarzschild models are derived.

Future high-precision observations can further discriminate between models.

Abstract

In this work, we perform a relativistic test of the spacetime geometry of Sagittarius A* (Sgr A*) using the orbit of the S2 star. We consider a broad class of compact object models, including Schwarzschild, Reissner-Nordstr\"om, Bardeen, Hayward, and Simpson-Visser black holes, as well as the Janis-Newman-Winicour naked singularity spacetime. For each geometry, we integrate the timelike geodesic equations and consistently project the resulting trajectories onto astrometric and spectroscopic observables, incorporating R{\o}mer time delay and relativistic redshift effects. The theoretical predictions are tested with current Very Large Telescope (VLT) observations of the S2 star, while simultaneously imposing constraints from the Event Horizon Telescope shadow size. We find that several spacetimes that are degenerate at the level of shadow imaging, most notably Schwarzschild, Reissner-Nordstr\"om, and Bardeen regular black hole geometries, remain statistically indistinguishable when tested against present S2 data. We further carry out a statistical model comparison based on the Akaike and Bayesian information criteria (AIC and BIC) to evaluate the relative performance of the alternative spacetime models. Our analysis also constrains the generalized charge like parameter $q/M$ in non-Schwarzschild spacetimes based on current S2 star observations, and identifies specific black hole and horizonless geometries that can be further tested with forthcoming high precision astrometric observations from the VLT and Keck telescopes.