Hawking radiation particle spectrum of a Kerr-Newman black hole

Abstract

Charged, rotating Kerr-Newman black holes represent the most general class of asymptotically flat black hole solutions to the Einstein-Maxwell equations of general relativity. Here, we consider a simplified model for the Hawking radiation produced by a Kerr-Newman black hole by utilizing a (1+1)-dimensional accelerated boundary correspondence (i.e. a flat spacetime mirror trajectory) in Minkowski spacetime. We derive the particle spectrum of the outgoing massless, scalar field and its late-time thermal distribution which reduces to the Kerr, Reissner-Nordström and Schwarzschild cases in the appropriate limits. We also compute the particle spectrum of the extremal Kerr-Newman system, showing that the total energy emitted is finite.

Analog Particle Production Model for General Classes of Taub-NUT Black Holes

“…where K n (x) is the modified Bessel function of the second kind, where n = 1 − iω/κ S , and we defined ω + = ω + ω . This spectrum is characteristically non-thermal, and accords with the results found in [17,37] in the appropriate limits. It is important to note that the corresponding trajectory dynamics of the analog extremal mirror completely differ from the non-extremal case.…”

“…As was found for the extremal Kerr-Newman analog mirror trajectory, the energy flux emitted by the extremal Kerr-Newman Taub-NUT mirror, Figure 7a, vanishes at late times, v → 0, and reduces to the result derived in [17] as l → 0. The total energy radiated by the mirror is given by:…”

“…This behaviour is comparable to the analog mirror trajectories for the Kerr and Kerr-Newman black holes [16,17], and is indicative of late-time thermal behaviour.…”

“…Here, a = J/M is the mass-normalised angular momentum and Q is the charge. Following [16,17], we further restricted our analysis to a plane of constant θ, φ which yields the simplified (1+1)-dimensional metric:…”

“…The relativistic trajectory of the mirror, which rapidly changes the boundary conditions of incoming field modes, induces particle production from the quantum vacuum [12,13]. Recently, this model has been applied to the well-known Schwarzschild [14], Reissner-Nordström (RN) [15], Kerr [16] and Kerr-Newman metrics [17], where analytic expressions for the spectra and the late-time thermal emission were derived.…”