What is the meaning of topological black holes?

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SUMMARY

Topological black holes are defined by their non-spherical event horizons, which can occur in asymptotically anti-de Sitter spacetimes with a negative cosmological constant. According to Hawking's theorem, black holes typically have a spherical topology when the metric is asymptotically flat or de Sitter. The existence of toroidal black holes exemplifies the concept of topological black holes, showcasing the diversity of black hole geometries under different cosmological conditions.

PREREQUISITES
  • Understanding of black hole topology
  • Familiarity with Hawking's theorem
  • Knowledge of asymptotic metrics (Minkowski and de Sitter)
  • Basic concepts of cosmological constants
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  • Research the implications of Hawking's theorem on black hole topology
  • Explore the characteristics of asymptotically anti-de Sitter spacetimes
  • Study the properties and formation of toroidal black holes
  • Investigate the role of cosmological constants in black hole physics
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Astronomers, theoretical physicists, and students of general relativity interested in advanced black hole geometries and their implications in cosmology.

supakorn
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what is the meaning of topological black holes?

thanks
 
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There is a theorem by Hawking that the topology of black hole (roughly, the shape of the event horizon) is spherical. This is assuming no cosmological constant, and the metric is asymptotically flat (Minkowski). If the metric is asymptotically de Sitter (here you have positive cosmological constant), the result also holds. However in asymptotically anti-de Sitter case (negative cosmological constant), then it is possible to have non-trivial (non-spherical) event horizon - e.g. a toroidal black hole. Such black holes are called topological black holes.
 
thank you so much
 

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