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

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.

11 pages, 5 figures, 3 tables. Several typos corrected. Published (september 19) in Physical Review D

References in corpus (13)

• Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Apparent shape of super-spinning black holes
• Can accretion disk properties observationally distinguish black holes from naked singularities?
• Gravitational Lensing by Rotating Naked Singularities
• Explicit multipole moments of stationary axisymmetric spacetimes
• Testing the existence of regions of stable orbits at small radii around black hole candidates
• Outflows from accreting super-spinars
• The Israel Theorem: What is Nature Trying to Tell Us?
• Calculation of, and bounds for, the multipole moments of stationary spacetimes
• Possible way out of the Hawking paradox: Erasing the information at the horizon
• From geodesics of the multipole solutions to the perturbed Kepler problem
• Linearized multipole solutions and their representation

Cited by in corpus (9)

• Spinning test particles in the $\gamma$ spacetime
• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• Negative Time Delay in Strongly Naked Singularity Lensing
• Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes
• On the Solutions of infinite systems of linear equations
• Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects
• Whom actually do multipole moments belong to?
• A quadrupolar generalization of the Erez-Rosen coordinates
• Gravitational fields of axially symmetric compact objects in 5D space-time-matter gravity