

4 Gravitational Collapse and
Black Holes on the Brane
The physics of brane-world compact objects and gravitational
collapse is complicated by a number of factors, especially the
confinement of matter to the brane, while the gravitational field
can access the extra dimension, and the nonlocal (from the brane
viewpoint) gravitational interaction between the brane and the
bulk. Extra-dimensional effects mean that the 4D matching
conditions on the brane, i.e., continuity of the induced metric and
extrinsic curvature across the 2-surface boundary, are much more
complicated to implement [110
, 78
, 314
, 109
]. High-energy
corrections increase the effective density and pressure of stellar
and collapsing matter. In particular this means that the effective
pressure does not in general vanish at the boundary 2-surface,
changing the nature of the 4D matching conditions on the brane. The
nonlocal KK effects further complicate the matching problem on the
brane, since they in general contribute to the effective radial
pressure at the boundary 2-surface. Gravitational collapse
inevitably produces energies high enough, i.e.,
, to make these corrections significant.
We expect that extra-dimensional effects will be
negligible outside the high-energy, short-range regime. The
corrections to the weak-field potential, Equation (41), are at the second
post-Newtonian (2PN) level [114, 150
]. However,
modifications to Hawking radiation may bring significant
corrections even for solar-sized black holes, as discussed
below.
A vacuum on the brane, outside a star or black
hole, satisfies the brane field equations
The Weyl term
will carry an imprint of high-energy
effects that source KK modes (as discussed above). This means that
high-energy stars and the process of gravitational collapse will in
general lead to deviations from the 4D general relativity problem.
The weak-field limit for a static spherical source,
Equation (41), shows that
must be nonzero, since this is the term responsible
for the corrections to the Newtonian potential.

