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The Kerr Metric

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arxiv 1410.2130 v2 pith:TNF2YK2K submitted 2014-10-08 gr-qc astro-ph.HEhep-th

Saul A. Teukolsky This is my paper · ORCID
classification gr-qcastro-ph.HEhep-th
keywords blackholekerrmetricreviewsolutiondiscoverygeneral
verification ladder T0 review T1 audit T2 compute T3 formal
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This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.

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Forward citations

Cited by 6 Pith papers

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

  1. Kerr black holes without primary hairs

    gr-qc 2026-07 conditional novelty 6.0 of 10

    Explicit infinite family of axisymmetric black holes with a Kerr exterior, a regular or mildly singular interior controlled by free exponents n_i, and no additional asymptotic charges.

  2. Optimizing Neural Network Surrogate Models: Application to Black Hole Merger Remnants

    gr-qc 2025-01 conditional novelty 6.0 of 10

    A systematically optimized neural network surrogate for black-hole merger remnant properties, NRSur7dq4Remnant_NN, matches the accuracy of the GPR-based NRSur7dq4Remnant while evaluating up to 8 times faster on a CPU ...

  3. Formation of the Kerr black hole: an exact model

    gr-qc 2026-08 conditional novelty 5.0 of 10

    A family of metrics interpolating between regular Schwarzschild and Kerr black holes is proposed as an exact model of the final stage of rotating collapse.

  4. Matter environments around black holes: geodesics, light rings, and ultracompact configurations

    gr-qc 2025-12 conditional novelty 5.0 of 10

    Dark-matter halos modeled as Einstein clusters generically move the ISCO inward and the light ring outward, and ultracompact halos can add extra light rings, trapped modes, and secondary horizons.

  5. On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes

    gr-qc 2025-07 conditional novelty 4.0 of 10

    For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.

  6. Superradiance -- the 2020 Edition

    gr-qc 2015-01 unverdicted novelty 4.0 of 10

    Black-hole superradiance extracts energy via the ergoregion and can trigger instabilities with applications to dark matter, beyond-Standard-Model physics, and laboratory analogs.

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