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 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:
μ ν
the Ricci Tensor becomes
μ ν
μ ν
μ ν
ν μ
{\displaystyle {\begin{aligned}R_{\mu \nu }&=R_{\mu \nu }^{(0)}+{\frac {n+1}{r}}\Gamma _{\mu \nu }^{r},\\R_{ij}&=\delta _{ij}g_{ii}\left({\frac {n}{r^{2}}}(1-g^{rr})-{\frac {1}{r}}(\partial _{\mu }+\Gamma _{\nu \mu }^{\nu })g^{\mu r}\right),\end{aligned}}}
and the Ricci Scalar becomes
μ ν
μ ν
ν μ
μ ν
are the Ricci Tensor and Ricci scalar of the metric
μ ν
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.
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.