Kerr-de Sitter spacetime, Penrose process and the generalized area theorem

Abstract

We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $\Lambda$, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres -- associated with the black hole and the cosmological event horizons. We prove by analysing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both black hole and cosmological event horizons' areas increase, the later becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that arises due to the frame dragging effect due to spacetime rotation. While the current observed value of $\Lambda$ is much tiny, its effect in this process could be considerable in the early universe scenario endowed with a rather high value of it, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.

v2, 21pp; added references and discussions, improved presentation, accepted in PRD

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• Quantum Kerr-de Sitter black holes in three dimensions
• Particle creation by de Sitter black holes revisited
• Dirac fermion, cosmological event horizons and quantum entanglement
• Energy extraction from the Reissner-Nordström de Sitter black hole
• The maximum turnaround radius for axisymmetric cosmic structures
• de Sitter Black Holes, Schottky Peaks, and Continuous Heat Engines
• Nonlinear Evolution of unstable Charged de Sitter Black Holes with Hyperboloidal Formalism
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