Geodesics in the linearized multipole solution: Distinguishing black holes from naked singularities

TL;DR

This paper investigates how geodesic motion in a specific axially symmetric vacuum solution can help distinguish black holes from naked singularities by analyzing stable orbits close to the horizon.

Contribution

It introduces the linearized multipole solution and demonstrates its ability to reveal differences in geodesic behavior compared to Schwarzschild black holes.

Findings

Existence of an ISCO close to the singular horizon.

Stable orbits exist closer than in Schwarzschild spacetime.

Splitting of the circular orbit region due to multipole structure.

Abstract

We analyze the behaviour of geodesic motion of test particles in the spacetime of a specific class of axially symmetric static vacuum solutions to the Einstein equations, hereafter referred to as linearized multipole solution (LM). We discuss about its suitability to describe a quasi-spherical spacetime. The existence of an ISCO (innermost stable circular orbit) very close to the (singular) horizon of the source, is established. The existence of such stable orbit, inner than the one of the Schwarzschild metric, as well as the appearance of a splitting in the admissible region of circular orbits, is shown to be due to the multipole structure of the solution, thereby providing additional potential observational evidence for distinguishing Schwarzschild black holes from naked singularities.