Nonspherically-symmetric black hole in Einstein-massless scalar theory

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 θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} 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 orbits of massive and massless particles in the equatorial plane are identical to those near a Schwarzschild black hole.