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 horizon 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 spacetime is:


  • 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.


When  .

The Ricci Tensor becomes  ,  .

The Ricci Scalar becomes  .

Where  ,   are the Ricci Tensor and Ricci scalar of the metric  .

Black stringEdit

A black string is a higher dimensional (D>4) generalization of a black hole in which the event horizon is topologically equivalent to S2 × S1 and spacetime is asymptotically Md−1 × S1.

Perturbations of black string solutions were found to be unstable for L (the length around S1) greater than some threshold L′. The full non-linear evolution of a black string beyond this threshold might result in a black string breaking up into separate black holes which would coalesce into a single black hole. This scenario seems unlikely because it was realized a black string could not pinch off in finite time, shrinking S2 to a point and then evolving to some Kaluza–Klein black hole. When perturbed, the black string would settle into a stable, static non-uniform black string state.

Kaluza–Klein black holeEdit

A Kaluza–Klein black hole is a black brane (generalisation of a black hole) in asymptotically flat Kaluza–Klein space, i.e. higher-dimensional spacetime with compact dimensions. They may also be called KK black holes.[5]


  1. ^ "black brane in nLab". Retrieved 2017-07-18.
  2. ^ Gubser, Steven Scott (2010). The Little Book of String Theory. Princeton: Princeton University Press. pp. 93. ISBN 9780691142890. OCLC 647880066.
  3. ^ "String theory answers". Archived from the original on 2018-01-11. 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.
  5. ^ Obers (2009), p. 212–213