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Topological classes of BTZ black holes

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arxiv 2302.11189 v2 pith:3H7KJ73S submitted 2023-02-22 gr-qc

Topological classes of BTZ black holes

classification gr-qc
keywords topologicalblackclassesholesnumberzerodifferentenergy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In the recent paper [Phys. Rev. Lett. 129, 191101 (2022)], the black holes were viewed as topological thermodynamic defects by using the generalized off-shell free energy. Their work indicates that all black hole solutions in the pure Einstein-Maxwell gravity theory could be classified into three different topological classes for four and higher spacetime dimensions. In this paper, we investigate the topological number of BTZ black holes with different charges $(Q)$ and rotational $(J)$ parameters. By using generalized free energy and Duan's $\phi$-mapping topological current theory, we interestingly found only two topological classes for BTZ spacetime. Particularly, for $Q=J=0$ BTZ black hole, there has only one zero point and therefore the total topological number is 1. While for rotating or charged cases, there are always two zero points and the global topological number is zero.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Noncommutative black holes: Topological bulk-boundary correspondence and Binary Merger Bounds

    gr-qc 2026-07 reject novelty 4.0

    For noncommutative RN-AdS black holes, the paper claims bulk and boundary thermodynamic topological charges equal to zero and derives perturbative second-law corrections to the remnant-mass bound.

  2. Topology of black hole thermodynamics: A brief review

    gr-qc 2026-04 unverdicted novelty 2.0

    Topological numbers categorize black hole systems into universality classes based on thermodynamic behavior, with calculations for critical points and phase transitions.