Black string

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:
$^ = \left( \eta_ + \frac u_a u_b \right) d \sigma^a d \sigma^b + \left(1-\frac\right)^ dr^2 + r^2 d \Omega^2_$
where:
* 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
$ds^2=g_dx^\mu dx^\nu + d\Omega_,$
the Ricci Tensor becomes
$\begin R_ &= R_^ + \frac\Gamma^r_, \\ R_ &= \delta_ g_ \left(\frac(1-g^) - \frac(\partial_ + \Gamma^\nu_)g^\right), \end$
and 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 () 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 (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