Black brane

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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.