Abstract
In this Chapter we present a theory of conservation laws on null hypersurfaces in general Lorentzian manifolds. These conservation laws are a generalization of the conservation laws on extremal event horizons. We also review their relevance to the characteristic gluing problem and provide necessary and sufficient conditions for their existence.
Keywords
- Null Hypersurface
- Admit Conservation Laws
- General Lorentzian Manifold
- Extremal Black Holes
- Extremal Myers-Perry Black Hole
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References
S. Aretakis, The characteristic gluing problem and conservation laws for the wave equation on null hypersurfaces. Ann. PDE 3(1) (2017), arXiv:1310.1365
S. Aretakis, On a foliation-covariant elliptic operator on null hypersurfaces. Int. Math. Res. Not. 15(15), 6433–6469 (2015)
J. Lucietti, H. Reall, Gravitational instability of an extreme Kerr black hole. Phys. Rev. D 86, 104030 (2012)
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Aretakis, S. (2018). A Theory of Conservation Laws on Null Hypersurfaces. In: Dynamics of Extremal Black Holes. SpringerBriefs in Mathematical Physics, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-95183-6_6
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DOI: https://doi.org/10.1007/978-3-319-95183-6_6
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