The Fate of a Five-Dimensional Rotating Black Hole via Hawking Radiation

We study the evolution of a five-dimensional rotating black hole emitting scalar field radiation via the Hawking process for arbitrary initial values of the two rotation parameters a and b. It is found that any such black hole whose initial rotation parameters are both nonzero evolves toward an asymptotic state a/M 1/2 = b/M 1/2 =c onst( =0 ), where this constant is independent of the initial values of a and b. The conventional view of black hole evaporation is that, regardless of its initial state, Hawking radiation will cause a black hole to approach an uncharged, zero angular momentum state long before all its mass has been lost. For this reason, in some works, it is assumed that as a black hole evaporates close to the Planck scale, where quantum gravity is required to determine its evolution, the final asymptotic state is described by Schwarzschild solution. However, Chambers, Hiscock and Taylor 1) investigated, in some detail, the evolution of a Kerr black hole emitting scalar field radiation via the Hawking process, and showed that the ratio of the black hole’s specific angular momentum to its mass, ˜ = a/M , evolves toward a stable nonzero value (˜ a → 0.555). This means that a rotating black hole will evolve toward a final state with non-zero angular momentum if there is a scalar field. In this Letter, we extend the analysis of Chambers, Hiscock and Taylor to a higher-dimensional case for the reasons described below. Considering the five-dimensional case specifically, we investigate the evolution of a five-dimensional rotating Myers-Perry (MP) black hole 2) with two rotation parameters through scalar