# Black brane

(Redirected from Black p-brane)

In general relativity, a black brane is a solution of the equations that generalizes a black hole solution but it is also extended—and translationally symmetric—in p additional spatial dimensions. That type of solution would be called a black p-brane. (http://ncatlab.org/nlab/show/black+brane)

In string theory, the solutions labeled as black branes provide us with an alternative description of the same objects called p-branes. Other descriptions of the same objects include D-branes. Some approximations of black branes might lead to entropy consistent with energy, from E=mc2.

The metric for a black p-brane in a n-dimensional space-time is:

${\displaystyle {ds}^{2}=\left(\eta _{ab}+{\frac {r_{s}^{n-p-3}}{r^{n-p-3}}}u_{a}u_{b}\right)d\sigma ^{a}d\sigma ^{b}+\left(1-{\frac {r_{s}^{n-p-3}}{r^{n-p-3}}}\right)^{-1}dr^{2}+r^{2}d\Omega _{n-p-2}^{2}}$

where:

• η is the (p+1)-Minkowski metric with signature (-,+,+,+,...),
• σ are the coordinates for the worldsheet of the black p-brane,
• u is its four-velocity,
• r is the radial coordinate and,
• Ω is the metric for a (n-p-2)-sphere, surrounding the brane.