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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.
In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon. 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. 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.
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.
The Ricci Tensor becomes , .
The Ricci Scalar becomes .
Where , are the Ricci Tensor and Ricci scalar of the metric .
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 hole
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.
- "black brane in nLab". ncatlab.org. Retrieved 2017-07-18.
- Gubser, Steven Scott (2010). The Little Book of String Theory. Princeton: Princeton University Press. p. 93. ISBN 9780691142890. OCLC 647880066.
- "String theory answers". superstringtheory.com. Retrieved 2017-07-18.
- Koji., Hashimoto, (2012). D-brane : superstrings and new perspective of our world. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg. ISBN 9783642235740. OCLC 773812736.
- Obers (2009), p. 212–213
- Obers, N.A. (2009). "Black Holes in Higher-Dimensional Gravity". Physics of Black Holes. pp. 211–258. Retrieved 2010-04-08.
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