Possible connection between the reflection symmetry and existence of equatorial circular orbit

Abstract

We study a viable connection between the circular-equatorial orbits and reflection symmetry across the equatorial plane of a vacuum stationary axis-symmetric spacetime in general relativity. The behavior of the circular equatorial orbits in the direction perpendicular to the equatorial plane is studied, and different outcomes in the presence and in the absence of the reflection symmetry are discussed. We conclude that in the absence of the equatorial reflection symmetry neither stable nor unstable circular orbit can exist on the equatorial plane. Moreover, to address the observational aspects, we provide two possible examples relating gravitational wave astronomy and the thin accretion disk which can put constraints on the symmetry breaking parameters.

9 pages, 2 figures

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• Curved accretion disks around rotating black holes without reflection symmetry
• The ring-shaped shadow of rotating naked singularity with a complete photon sphere
• Resonant orbits of rotating black holes beyond circularity: Discontinuity along parameter shift
• Relativistic effects cannot explain galactic dynamics
• Observational features of reflection asymmetric black holes
• Frame-dragging: meaning, myths, and misconceptions
• Pure Gauss-Bonnet NUT Black Hole Solution: II