Back reaction, the Hawking emission spectrum from the charged black hole

Abstract

The Hawking emission spectrum of the Schwarzschild-like black hole has been successfully described in the tunneling picture. In this paper, we develop the idea for the case of the charged black hole with back reaction. First, the most general, static spherically symmetric charged black hole, in the presence of back reaction, has been provided by solving the Einstein equations with a non-zero vacuum expectation value of the energy–momentum tensor ⟨Tμν(ϕ, gμν)⟩. At the one-loop corrections, we also produce the modified expressions for the Hawking temperature and Bekenstein–Hawking entropy. It is found that the leading correction to the semiclassical entropy is logarithmic and next to the leading order is inverse of the horizon area, just as the expected well-known results. In particular, as our main focus in this paper, we show that the modified black hole still radiates with a perfect blackbody spectrum, only the temperature undergoing quantum corrections. Also, the Hawking fluxes of the electric current and energy–momentum tensor to include the effect of back reaction are obtained. The results are interestingly found sharing the same form as that from the point of anomaly.