AdS black hole

In theoretical physics, an anti-de Sitter (AdS) black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a negative cosmological constant. Such a solution asymptotically approaches anti-de Sitter space at spatial infinity, and is a generalization of the Kerr vacuum solution, which asymptotically approaches Minkowski spacetime at spatial infinity. ^[1]

In 3+1 dimensions, the metric is given by $${\displaystyle ds^{2}=-\left(k^{2}r^{2}+1-{\frac {C}{r}}\right)dt^{2}+{\frac {1}{k^{2}r^{2}+1-{\frac {C}{r}}}}dr^{2}+r^{2}d\Omega ^{2}}$$ where t is the time coordinate, r is the radial coordinate, Ω are the polar coordinates, C is a constant and k is the AdS curvature.

In general, in d + 1 dimensions, the metric is given by $${\displaystyle ds^{2}=-\left(k^{2}r^{2}+1-{\frac {C}{r^{d-2}}}\right)dt^{2}+{\frac {1}{k^{2}r^{2}+1-{\frac {C}{r^{d-2}}}}}dr^{2}+r^{2}d\Omega ^{2}}$$

According to the AdS/CFT correspondence, if gravity were quantized, an AdS black hole would be dual to a thermal state on the conformal boundary. ^[2] In the context of say, AdS/QCD, this would correspond to the deconfinement phase of the quark–gluon plasma.

Late-infall observers into AdS black holes may experience chaotic oscillations of spacetime of BKL type near their central singularities. ^[3]

See also

• BTZ black hole
• Black brane

References

1. Fan, Zhong-Ying (2016-09-21), "Critical phenomena of regular black holes in anti-de Sitter space-time", The European Physical Journal C, 77 (4) 266, arXiv: 1609.04489 , doi:10.1140/epjc/s10052-017-4830-9
2. Pourhassan, Behnam; Faizal, Mir (2015). "Thermal fluctuations in a charged AdS black hole". Europhysics Letters. 111 (4) 40006. arXiv: 1503.07418 . Bibcode:2015EL....11140006P. doi:10.1209/0295-5075/111/40006.
3. De Clerck, Marine; Hartnoll, Sean A.; Santos, Jorge E. (2024). "Mixmaster chaos in an AdS black hole interior". Journal of High Energy Physics (7) 202. arXiv: 2312.11622 . Bibcode:2024JHEP...07..202D. doi:10.1007/JHEP07(2024)202.