Black 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:

${d s}^{2} = \left( \eta_{ab} + \frac{r_s^{n-p-3}}{r^{n-p-3}} u_a u_b \right) d \sigma^a d \sigma^b + \left(1-\frac{r_s^{n-p-3}}{r^{n-p-3}}\right)^{-1} dr^2 + r^2 d \Omega^2_{n-p-2}$

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.