Precession of timelike bound orbits in Kerr spacetime

Parth Bambhaniya,Pankaj S Joshi,Dipanjan Dey,Vishva Patel,Divyesh N Solanki,Ashok B Joshi

doi:10.1140/epjc/s10052-021-08997-x

Abstract

Astrometric observations of S-stars provide a unique opportunity to probe the nature of Sagittarius-A* (Sgr-A*). In view of this, it has become important to understand the nature and behavior of timelike bound trajectories of particles around a massive central object. It is known now that whereas the Schwarzschild black hole does not allow the negative precession for the S-stars, the naked singularity spacetimes can admit the positive as well as negative precession for the bound timelike orbits. In this context, we study the perihelion precession of a test particle in the Kerr spacetime geometry. Considering some approximations, we investigate whether the timelike bound orbits of a test particle in Kerr spacetime can have negative precession. In this paper, we only consider low eccentric timelike equatorial orbits. With these considerations, we find that in Kerr spacetimes, negative precession of timelike bound orbits is not allowed.

Highlights

It is generally believed that super massive black holes (SMBHs) with masses between 106−109 M exist at the centers of most galaxies [1]
In order to predict the causal nature of the galactic centers, it is very important to investigate different possible observational features, such as the shadows of black holes, the relativistic orbits of the S-stars, accretion disk properties of the compact objects, etc
The Event Horizon Telescope (EHT) collaboration has released the first-ever image of the shadow of a black hole located at the center of the Messier 87 (M87) galaxy [2]

Summary

Introduction

It is generally believed that super massive black holes (SMBHs) with masses between 106−109 M exist at the centers of most galaxies [1]. GRAVITY collaboration has shown the possibility of the existence of general relativistic precession of the orbit of S2 star, where they consider Schwarzschild black hole at the center [9]. The. JMN and JNW naked singularity spacetimes allow both the negative and positive precession of timelike bound orbits. If the negative precession of the orbit of a test particle in other black holes spacetimes is possible that would be another example along with the spacetime configuration of [7], where a negative precession and shadow both can exist simultaneously In this context, in this paper, we investigate the possibility of a likely negative precession of bound timelike orbits in the. 3, we use an approximate solution of orbit equation and investigate the nature of perihelion precession of the timelike bound orbits in Kerr spacetime.

Timelike geodesics in Kerr spacetime

An approximate solution of orbit equation where

12 M 2 L2

Discussion and conclusion