Cosmic background radiation in the vicinity of a Schwarzschild black hole: no classic firewall

Abstract

The Cosmic Blackbody Background Radiation pervades the entire Universe, and so falls into every astrophysical black hole. The blueshift of the infalling photons, measured by a static observer, is infinite at the event horizon. This raises a question as to whether a "firewall" of high energy density may form just outside the horizon, or whether the effect can be attributed exclusively to a singular behavior of the static observer's frame at the horizon. In principle, the presence of such firewall may alter the motion of the infalling matter, influence the black hole evolution, or even invalidate the {\it vacuum} Einstein field equation solution as a realistic approximation for black holes. In this paper we show by means of analytic calculations that all these effects indeed exist, but their magnitude is typically negligibly small, even though the matter stress tensor is divergent in the static frame at $r=2M$. That is not surprising because of the divergent relation of that frame to a freely falling frame as $r \rightarrow 2M$; however it represents a kind of classical analogue for the Black Hole Complementarity principle that has been proposed for quantum effects near a black hole. What is perhaps more surprising is the divergence of the radiation stress tensor for massive particles moving on circular geodesic orbits for values of $r$ approaching $r = 3M$. However such orbits will not occur for infalling matter in realistic accretion discs.