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.

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 ''p''-brane in a ''n''-dimensional spacetime is:

:$^ = \left( \eta_ + \frac u_a u_b \right) d \sigma^a d \sigma^b + \left(1-\frac\right)^ dr^2 + r^2 d \Omega^2_$
where:
*''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.

Curvatures

When $ds^2=g_dx^\mu dx^\nu + d\Omega_$.

The Ricci Tensor becomes $R_=R_^+\frac\Gamma^r_$, $R_=\delta_ g_ (\frac(1-g^)-\frac(\partial_+\Gamma^\nu_)g^)$.

The Ricci Scalar becomes $R=R^+\fracg^\Gamma^r_+\frac(1-g^) -\frac(\partial_\mu g^+\Gamma^\nu_g^)$.

Where $R_^$, $R^$ are the Ricci Tensor and Ricci scalar of the metric $ds^2=g_dx^\mu dx^\nu$.

Black string

A black string is a higher dimensional (''D''>4) generalization of a black hole in which the event horizon is topologically equivalent to ''S''² × ''S''¹ and spacetime is asymptotically ''M''^''d''−1 × ''S''¹.

Perturbations of black string solutions were found to be unstable for ''L'' (the length around ''S''¹) 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 ''S''² 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.Obers (2009), p. 212–213

See also

* AdS black hole

References

Bibliography

*{{Cite book
, pages = 211–258
, last = Obers
, first = N.A.
, title = Physics of Black Holes
, volume = 769
, chapter = Black Holes in Higher-Dimensional Gravity
, year = 2009
, doi = 10.1007/978-3-540-88460-6_6
, series = Lecture Notes in Physics
, isbn = 978-3-540-88459-0
, arxiv = 0802.0519
, s2cid = 14911870

Black holes