.
which we
Our work is exciting and rewarding, if we can say it. On the one hand, it bridges with works
from respected colleagues and friends as the paper [3] by the late J Barrow, on the other
hand it opens the possibility to test with cause, about
black hole thermodymanmics, namely ther area theorem that
given the range of our parameter 'alpha' for the allowed deviations; we actually include the
standard case as a particular limit.
Our work maintains the structure of either GR or quantum mechanics, we merely introduce a new
and interesting feature that causes
modifications that may be tested in black hole physics, including gravitational radiation as we also point to:
fractional calculus, an old idea back to Leibniz, worked by
Riemmann, Abel, Liouville and many other mathematical grandees,
is now of current use in many applications in engineering and material science. And fractional
quantum mecanics, too: The idea is to use derivatives of...fractional order, which have been of sucess in difusion
processes and others, path integrals as well, but then extend it to quantum mechanics (Feynman).
present an analysis of the thermodynamics of a "fractal" induced (by fractional quantum mechanics = FQM)
Schwarzschild black hole,
using a fractional calculus modified version of the Wheeler-DeWitt Equation.
Let us emphasize that the surface area of the black hole ie a measure of its entropy, but we show that in FQM it
can increase beyond the standard calculation, and thus the Bekenstein-Hawking bound
may need to be broaden into an area power law.
Thus, from the geometrical black hole surface, we may
admit that there may be more to unveil. In particular, we
may speculate that a behavior, suggesting a broader
dimensional dynamics at the horizon, can be explored
in the wider ranges of gractional quantum mechanics (and
calculus), actually supporting the conjecture proposed by J Barrow in [3], see page 12
therefore, be allowed to speculate about the possibility that at some realistic observable scale,
a broader surface area of a black hole
can be considered, encompassing the standard value
from Bekenstein-Hawking, because of the ''fractional'' structure of the horizon.
In this context, we propose a broader equation, for how
the entropy varies and how the Bekenstein-Hawking expressions fits in, and fitting too
It brings an interesting perspective
such that the entropy of a black hole
could instead be proportional to a power of its surface,
depending on the choice of 'alpha' and, for 1<alpha<2 (alpha=2 the stadard case of
and vindicating J Barrow's elegant bold but elegant conjecture.
