zarei said:
if an anti-particle fall into the BH the volume of BH will reduce.
I am not sure what you are referring to, or if what you read confused you. An anti-particle has a positive mass. If an anti-particle falls into a BH, the mass of the BH increases.
Independently of this, in Hawking's first calculations, one can interpret an anti-particle
from the fluctuation of a pair as
the one carrying negative energy (by definition), the particle being the one carrying positive energy (and this can be a positron BTW). This split near the horizon makes it possible for the particle to escape at infinity, whereas the antiparticle must keep falling. From an outside observer, the BH has emitted a particle. The particle-antiparticle definition is almost irrelevant in this context, except for the amount of energy carried and the possibility to escape at infinity, since most of those pairs are photons. Strictly speaking once again, a black hole will emit as much positrons as electrons (provided it is not charged. In fact, once it has emitted one electron, it is more likely to emit a positron). You can not go further in the interpretation : the process occurs at the quantum level and only the outside observer interpretation is a valid one that can be measured. Strictly speaking, there is no such thing as a negative-energy
real (anti-)particle. What
is observed is the emission of thermal radiation, not negative-energy particles.
IMO, this discussion is not BtSM.