Motion of particles on a Four-Dimensional Asymptotically AdS Black Hole with Scalar Hair

TL;DR

This paper investigates how scalar hair in a four-dimensional asymptotically AdS black hole affects particle motion, revealing modifications in orbital periods and classical tests, with potential implications for observational discrepancies.

Contribution

It introduces a detailed numerical analysis of particle geodesics in scalar-hairy AdS black holes and identifies specific scalar hair parameters that align theory with observations.

Findings

Bounded orbits similar to planetary orbits exist.

Scalar hair modifies periods of circular orbits.

Classical tests show standard GR values with additional corrections.

Abstract

Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields in the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with scalar hair. The geodesics are studied numerically and we discuss about the differences in the motion of particles between the four-dimensional asymptotically AdS black holes with scalar hair and their no-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found that there are bounded orbits like planetary orbits in this background. However, the periods associated to circular orbits are modified by the presence of the scalar hair. Besides, we found that some classical tests such as perihelion precession, deflection of light and gravitational time delay have the standard value of general relativity plus a correction term coming from the cosmological constant and the scalar hair. Finally, we found a specific value of the parameter associated to the scalar hair, in order to explain the discrepancy between the theory and the observations, for the perihelion precession of Mercury and light deflection.