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Introduction to General Relativity and Black Hole Dynamics

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Dynamics of Extremal Black Holes

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 33))

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Abstract

In this Chapter we provide the general framework for curved spaces and introduce the notions of Lorentzian geometry which are necessary for understanding the mathematical aspects of general relativity and black hole dynamics. We also present rigorous results on the asymptotics of linear perturbations for sub-extremal black holes.

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Notes

  1. 1.

    For simplicity, we will drop the index and thus by g we will also mean \(g_{x}\).

  2. 2.

    Note that \(\mathcal {I}^{+}(x)\subset \mathcal {M}\) denotes the chronological future of x whereas \(\mathcal {I}^{+}_{x}\subset T_{x}\mathcal {M}\) denotes the set of all future-directed timelike vectors in \(T_{x}\mathcal {M}\).

  3. 3.

    The sharpness of the decay rate of the time derivative of \(\psi \) along the event horizon was first established by Luk and Oh [42].

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    Stefanos Aretakis

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Aretakis, S. (2018). Introduction to General Relativity and Black Hole Dynamics. In: Dynamics of Extremal Black Holes. SpringerBriefs in Mathematical Physics, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-95183-6_1

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