The mechanism of blackbody radiation from an incipient black hole

Abstract

On the basis of the phenomenon of zero-point energy an account is given of the mechanism of the emission of blackbody radiation from an incipient (about-to-be-formed) black hole, which results from the gravitational collapse of a star. The account is given in terms of three related points of view: (1) the emitted blackbody radiation results from a Fourier spectrum analysis of the zero-point fluctuations on the surface of the collapsing star; (2) the radiation results from a parametric amplification by a time-dependent potential of waves emerging from the collapsing surface of the star; (3) the radiation results from the star passing continually through states of resonance mutual to the natural modes internal and those external to the star. These three points of view are related by virtue of the underlying principle that explains the blackbody radiation mechanism: the nonadiabatic red-shift process operating on the randomly correlated zero-point fluctuation modes. The picture that emerges from these analyses is that all zero-point oscillation modes emerging from the star give rise to statistically identical blackbody radiation packets. Their only difference lies in their time of emission. The packets are emitted in a time sequential order and each is created during a limited time interval at the surface of the star: those packets caused by low-frequency zero-point modes first, those caused by high-frequency modes later. The blackbody radiation continuously drains away the irreducible mass of the black hole at an ever increasing rate. The lifetime of the incipient black hole is therefore finite. Consequently, the total number of zero-point fluctuation modes taking part in the emission of blackbody radiation packets is finite. The logarithm of this number (multiplied by Boltzmann's constant) equals the entropy of a black hole. This suggests that the internal microscopic states (in the statistical-mechanical sense) of a macroscopic black hole, i.e., the "hairs" lost by the black hole, are to be identified with those degrees of freedom that are capable of and will be causing the emission of blackbody radiation. The statistical fluctuation spectrum of the emitted energy is exhibited and found to be identical to that associated with a blackbody, showing thereby that radiation emitted from a black hole is thermal radiation in the precise sense of the term. The relevance of these statistical fluctuations to the formation of a black hole is discussed briefly. Brief mention is made of the sense in which a radiating incipient black hole lends support to Sakharov's idea that gravitation is a manifestation of the alteration of the zero-point fluctuations of space. The formulation of the radiation mechanism in terms of successively amplified zero-point radiation modes allows us to conclude that a star can never pass through its instantaneous $r=2M$ surface. In view of the fact that the evaporation and the final demise of an incipient black hole are visible to a distant observer, it is necessary to reformulate the classical version of the issue of the final state of gravitational collapse. A qualitative account of the evolution of a classical incipient black hole is given. The issue of the final state of stellar gravitational collapse is restated in the form of a question: What is the ground state of an incipient black hole?