  We explore some implications of our previous proposal, motivated in part by
the Generalised Uncertainty Principle (GUP) and the possibility that black
holes have quantum mechanical hair that the ADM mass of a system has the form
$M + \beta M_\mathrm{Pl}^2/(2M)$, where $M$ is the bare mass, $M_\mathrm{Pl}$
is the Planck mass and $\beta$ is a positive constant. This also suggests some
connection between black holes and elementary particles and supports the
suggestion that gravity is self-complete. We extend our model to charged and
rotating black holes, since this is clearly relevant to elementary particles.
The standard Reissner-Nordstr\"om and Kerr solutions include zero-temperature
states, representing the smallest possible black holes, and already exhibit
features of the GUP-modified Schwarzschild solution. However, interesting new
features arise if the charged and rotating solutions are themselves
GUP-modified. In particular, there is an interesting transition below some
value of $\beta$ from the GUP solutions (spanning both super-Planckian and
sub-Planckian regimes) to separated super-Planckian and sub-Planckian
solutions. Equivalently, for a given value of $\beta$, there is a critical
value of the charge and spin above which the solutions bifurcate into
sub-Planckian and super-Planckian phases, separated by a mass gap in which no
black holes can form.

General Relativity and Quantum Cosmology