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.

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:{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}


  • 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.


By Trinh Manh Do

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