Dark matter spike around Bumblebee black holes

Abstract

Abstract The effects of dark matter spike in the vicinity of the supermassive black hole, located at the center of M87 (the Virgo A galaxy), are investigated within the framework of the so-called Bumblebee Gravity. Our primary aim is to determine whether the background of spontaneous Lorentz symmetry breaking has a significant effect on the horizon, ergo-region, and shadow of the Kerr Bumblebee black hole in the spike region. For this purpose, we first incorporate the dark matter distribution in a Lorentz-violating spherically symmetric space-time as a component of the energy-momentum tensors in the Einstein field equations. This leads to a space-time metric for a Schwarzschild Bumblebee black hole with a dark matter distribution in the spike region and beyond. Subsequently, this solution is generalized to a Kerr Bumblebee black hole through the use of the Newman-Janis-Azreg-Aïnou algorithm. Then, according to the available observational data for the dark matter spike density and radius, and the Schwarzschild radius of the supermassive black hole in Virgo A galaxy, we examine the shapes of shadow and demonstrate the influence of the spin parameter a, the Lorentz-violating parameter ℓ and the corresponding dark matter halo parameters ρ 0 and r 0 on the deformation and size of the shadow.