Spherical accretion onto higher-dimensional Reissner-Nordstr\"{o}m Black Hole

TL;DR

This paper analyzes spherically symmetric accretion onto higher-dimensional Reissner-Nordström black holes using Hamiltonian formalism, revealing how accretion dynamics and critical radii vary with spacetime dimensions, fluid types, and black hole charge.

Contribution

It provides a novel Hamiltonian-based analysis of accretion flows in higher-dimensional RN black holes, including critical point behavior and mass accretion rates for different fluids and charges.

Findings

Critical radius decreases with increasing dimensions up to a point, then increases.

Maximum mass accretion rate is lowest for higher-dimensional Schwarzschild black holes.

Charge increases the mass accretion rate in higher-dimensional RN black holes.

Abstract

We obtain relativistic solutions of spherically symmetric accretion by a dynamical analysis of a generalised Hamiltonian for higher-dimensional Reissner-Nordstr\"{o}m (RN) Black Hole (BH). We consider two different fluids namely, an isotropic fluid and a non-linear polytropic fluid to analyse the critical points in a higher-dimensional RN BH. The flow dynamics of the fluids are studied in different spacetime dimensions in the framework of Hamiltonian formalism. The isotropic fluid is found to have both transonic and non-transonic flow behaviour, but in the case of polytropic fluid, the flow behaviour is found to exhibit only non-transonic flow, determined by a critical point that is related to the local sound speed. The critical radius is found to change with the spacetime dimensions. Starting from the usual four dimensions it is noted that as the dimension increases the critical radius decreases, attains a minimum at a specific dimension ($D>4$) and thereafter increases again. The mass accretion rate for isotropic fluid is determined using Hamiltonian formalism. The maximum mass accretion rate for RN BH with different equations of state parameters is studied in addition to spacetime dimensions. The flow behaviour and mass accretion rate for a change in BH charge is also studied analytically. It is noted that the maximum mass accretion rate in a higher-dimensional Schwarzschild BH is the lowest, which however, increases with the increase in charge parameter in a higher-dimensional RN BH.