Spherical particle orbits around a rotating black hole in massive gravity

TL;DR

This paper introduces a rotating black hole solution in massive gravity, analyzes stable spherical particle orbits, and investigates their stability and dynamics through analytical and numerical methods.

Contribution

It presents a new rotating black hole solution in massive gravity and provides a detailed analysis of particle orbits, including stability and numerical simulations.

Findings

Existence of stable orbits at constant radii

Analytical solutions for angular equations of motion

Numerical simulations of spherical particle orbits

Abstract

In this paper, we present a rotating de Rham-Gabadadze-Tolley black hole with a positive cosmological constant in massive gravity, achieved by applying a modified Newman-Janis algorithm. The black hole exhibits stable orbits of constant radii, prompting a numerical study on the behavior of the solutions to a nonic equation governing the radii of planar orbits around the black hole. Additionally, we investigate the stability of orbits near the event horizon and provide a comprehensive analytical examination of the solutions to the angular equations of motion. This is followed by simulating some spherical particle orbits around the black hole.