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 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:
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 .
The Ricci Tensor becomes , .
The Ricci Scalar becomes .
Where , are the Ricci Tensor and Ricci scalar of the metric .
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 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.
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.[5]
See also
- AdS black hole
- v
- t
- e
- Strings
- Cosmic strings
- History of string theory
- String theory landscape
- Anomalies
- Instantons
- Chern–Simons form
- Bogomol'nyi–Prasad–Sommerfield bound
- Exceptional Lie groups (G2, F4, E6, E7, E8)
- ADE classification
- Dirac string
- p-form electrodynamics
- Worldsheet
- Kaluza–Klein theory
- Compactification
- Why 10 dimensions?
- Kähler manifold
- Ricci-flat manifold
- Calabi–Yau manifold
- Hyperkähler manifold
- G2 manifold
- Spin(7)-manifold
- Generalized complex manifold
- Orbifold
- Conifold
- Orientifold
- Moduli space
- Hořava–Witten theory
- K-theory (physics)
- Twisted K-theory
- Matrix theory
- Introduction to M-theory
- Aganagić
- Arkani-Hamed
- Atiyah
- Banks
- Berenstein
- Bousso
- Curtright
- Dijkgraaf
- Distler
- Douglas
- Duff
- Dvali
- Ferrara
- Fischler
- Friedan
- Gates
- Gliozzi
- Gopakumar
- Green
- Greene
- Gross
- Gubser
- Gukov
- Guth
- Hanson
- Harvey
- 't Hooft
- Hořava
- Gibbons
- Kachru
- Kaku
- Kallosh
- Kaluza
- Kapustin
- Klebanov
- Knizhnik
- Kontsevich
- Klein
- Linde
- Maldacena
- Mandelstam
- Marolf
- Martinec
- Minwalla
- Moore
- Motl
- Mukhi
- Myers
- Nanopoulos
- Năstase
- Nekrasov
- Neveu
- Nielsen
- van Nieuwenhuizen
- Novikov
- Olive
- Ooguri
- Ovrut
- Polchinski
- Polyakov
- Rajaraman
- Ramond
- Randall
- Randjbar-Daemi
- Roček
- Rohm
- Sagnotti
- Scherk
- Schwarz
- Seiberg
- Sen
- Shenker
- Siegel
- Silverstein
- Sơn
- Staudacher
- Steinhardt
- Strominger
- Sundrum
- Susskind
- Townsend
- Trivedi
- Turok
- Vafa
- Veneziano
- Verlinde
- Verlinde
- Wess
- Witten
- Yau
- Yoneya
- Zamolodchikov
- Zamolodchikov
- Zaslow
- Zumino
- Zwiebach
References
- ^ "black brane in nLab". ncatlab.org. Retrieved 2017-07-18.
- ^ Gubser, Steven Scott (2010). The Little Book of String Theory. Princeton: Princeton University Press. pp. 93. ISBN 9780691142890. OCLC 647880066.
- ^ "String theory answers". superstringtheory.com. Archived from the original on 2018-01-11. 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
Bibliography
- Obers, N.A. (2009). "Black Holes in Higher-Dimensional Gravity". Physics of Black Holes. Lecture Notes in Physics. Vol. 769. pp. 211–258. arXiv:0802.0519. doi:10.1007/978-3-540-88460-6_6. ISBN 978-3-540-88459-0. S2CID 14911870.