Nonspherically-symmetric black hole in Einstein-massless scalar theory

TL;DR

This paper presents a new static, nonspherically-symmetric black hole solution in Einstein gravity with a massless scalar field, revealing unique singularity structures and identical equatorial circular orbits to Schwarzschild black holes.

Contribution

It introduces a novel two-parameter black hole solution with scalar field dependence on polar angle, expanding the landscape of known black hole geometries.

Findings

The solution exhibits singularities on the axis and surfaces, with some hidden behind the horizon.

Energy conditions are satisfied by the scalar field.

Equatorial circular orbits are identical to those in Schwarzschild black holes.

Abstract

We introduce a two-parameter static, nonspherically-symmetric black hole solution in the Einstein theory of gravity coupled with a massless scalar field. The scalar field depends only on the polar coordinate $\theta$ in the spherical coordinates representation. The scalar invariant of the spacetime, namely, the Kretschmann scalar reveals that the black hole is singular on its axis of symmetry for all nonzero values of the scalar charge. It also manifests two surfaces of singularity for a certain interval of the value of the scalar charge. These singularities are hidden behind the event horizon's surface except the singularity on the axis which is naked. The energy-momentum of the scalar field satisfies all energy conditions. A simple investigation reveals that the circular orbit of massive and massless particles in the equatorial plane is identical to the Schwarzschild black hole.