# 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.[1]

In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon.[2] With the notion of a horizion in mind as well as identifying points as zero-branes, a generalization of a black hole is a black p-brane.[3] However, many physicists tend to define a black brane separate from a black hole, making the distinction that the singularity of a black brane is not a point like a black hole, but instead a higher dimensional object.

A BPS black brane is similar to a BPS black hole. They both have electric charges. Some BPS black branes have magnetic charges.[4]

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.

## References

1. ^ "black brane in nLab". ncatlab.org. Retrieved 2017-07-18.
2. ^ Gubser, Steven Scott (2010). The Little Book of String Theory. Princeton: Princeton University Press. p. 93. ISBN 9780691142890. OCLC 647880066.
3. ^ "String theory answers". superstringtheory.com. Retrieved 2017-07-18.
4. ^ Koji., Hashimoto, (2012). D-brane : superstrings and new perspective of our world. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg. ISBN 9783642235740. OCLC 773812736.