  We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian
brane embedded in a 5-dim bulk with an extra timelike dimension. By considering
the collapse of pure dust on the brane we derive a bouncing FLRW interior
solution and match it with a corrected Schwarzschild exterior geometry. In the
physical domain considered for the parameters of the solution, the analytical
extension is built, exhibiting an exterior event horizon and a Cauchy horizon,
analogous to the Reissner-Nordstr\"om solution. For such an exterior geometry
we examine the effects of the bulk-brane corrections in the Hawking radiation.
In this scenario the model extends Bekenstein's black hole geometrical
thermodynamics for quasi-extremal configurations, with an extra work term in
the laws associated with variations of the brane tension. We also propose a
simple statistical mechanics model for the entropy of the bouncing collapsed
matter by quantizing its fluctuations and constructing the associated partition
function. This entropy differs from the geometrical entropy by an additive
constant proportional to the area of the extremal black hole and satisfies an
analogous first law of thermodynamics. A possible connection between both
entropies is discussed.
