ar X iv : g r - qc / 0 30 20 36 v 1 1 0 Fe b 20 03 Trace anomaly and black holes evaporation

A model is proposed to describe a transition from a Schwarzschild black hole of mass M0 to a Schwarzschild black hole of mass M1 ≤ M0. The basic equations are derived from the non-vacuum Einstein field equations taking a source representing a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace anomaly of the scalar field prevents a complete evaporation. In the Hawking seminal paper in 1974 [3] it was shown that a Schwarzschild black-hole, the most attractive object of theoretical physics, does emit thermal radiation. This discovery provided deeper physical basis to the Bekenstein entropy [2] and to the black-hole thermodynamics. However, this new understanding of the black hole physics raised some highly nontrivial questions about the foundations of Quantum Field Theory (QFT). In particular, the black-hole evaporation led to an apparent breakdown of predictability [4] because of the thermal character of the emitted flux. Eventually, if the evaporation is complete, a loss of information and of unitarity occur since, in this case, a pure state evolves in a density matrix. Among all these proposals to overcome these difficulties, probably the three most popular are: (i) QFT has to be generalized to allow nonunitary processes [4] since it seems that a complete evaporation cannot be ruled out. However, up to now, this idea has been found to be incompatible with locality or conservation of energy [9], [8]; (ii) a Planckian remnant, which could store the lost information, is left [11]. Moreover, as showed by Bekenstein [12], the actual information loss due to the Hawking radiation is lower then that of a pure blackbody. Thus, a part of lost information could be detained by the remnant itself and the remaining part could be encoded in the Hawking radiation through the Bekenstein mechanism; (iii) a quantum theory of gravity, such as superstring theory [22] or loop quantum gravity [21], will disclose the information hidden in the detailed structure of the emitted quanta [5].