Accretion onto a higher dimensional black hole

We examine the steady-state spherically symmetric accretion of relativistic fluids, with a polytropic equation of state, onto a higher dimensional Schwarzschild black hole. The mass accretion rate, critical radius, and flow parameters are determined and compared with results obtained in standard four dimensions. The accretion rate, \(\dot{M}\), is an explicit function of the black hole mass, \(M\), as well as the gas boundary conditions and the dimensionality, \(D\), of the spacetime. We also find the asymptotic compression ratios and temperature profiles below the accretion radius and at the event horizon. This analysis is a generalization of Michel's solution to higher dimensions and of the Newtonian expressions of Giddings and Mangano which considers the accretion of TeV black holes.