Particle creation rate for dynamical black holes
  We present the particle creation probability rate around a general black hole
as an outcome of quantum fluctuations. Using the uncertainty principle for
these fluctuation, we derive a new ultraviolet frequency cutoff for the
radiation spectrum of a dynamical black hole. Using this frequency cutoff, we
define the probability creation rate function for such black holes. We consider
a dynamical Vaidya model, and calculate the probability creation rate for this
case when its horizon is in a slowly evolving phase. Our results show that one
can expect the usual Hawking radiation emission process in the case of a
dynamical black hole when it has a slowly evolving horizon. Moreover,
calculating the probability rate for a dynamical black hole gives a measure of
when Hawking radiation can be killed off by an incoming flux of matter or
radiation. Our result strictly suggests that we have to revise the Hawking
radiation expectation for primordial black holes that have grown substantially
since they were created in the early universe. We also infer that this
frequency cut off can be a parameter that shows the primordial black hole
growth at the emission moment.
