Black brane
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
Whenthe 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 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.