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

TL;DR

This paper investigates the link between reflection symmetry across the equatorial plane and the existence of circular equatorial orbits in stationary axis-symmetric spacetimes, with implications for gravitational wave and accretion disk observations.

Contribution

It establishes that without equatorial reflection symmetry, stable or unstable circular orbits cannot exist on the equatorial plane, and discusses observational constraints on symmetry breaking.

Findings

Absence of reflection symmetry prevents circular orbits on the equatorial plane.

Provides observational methods to constrain symmetry breaking.

Analyzes orbit behavior in symmetric and asymmetric spacetimes.

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.