In general relativity, a black brane is a solution of the Einstein field equations that generalizes a black hole solution but it is also extended—and translationally symmetric—in additional spatial dimensions. That type of solution would be called a black -brane.
In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon. 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. 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.
The metric for a black -brane in a -dimensional spacetime is:
where: is the -Minkowski metric with signature , are the coordinates for the worldsheet of the black -brane, is its four-velocity, is the radial coordinate, is the metric for a -sphere, surrounding the brane.
Curvatures When
the Ricci Tensor becomes
and the Ricci Scalar becomes
where , are the Ricci Tensor and Ricci scalar of the metric
Black string
A black string is a higher dimensional () generalization of a black hole in which the event horizon is topologically equivalent to and spacetime is asymptotically .
Perturbations of black string solutions were found to be unstable for (the length around ) greater than some threshold . 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 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 hole A Kaluza–Klein black hole is a black brane (generalization 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.Obers (2009), p. 212–213
See also AdS black hole
References
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