Wave and Dirac equations on manifolds

zbMATH Open1417.83003arXiv1710.04512MaRDI QIDQ4630729

Author name not available (Why is that?)

Publication date: 23 April 2019

Abstract: We review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial value problems, as well as results on the structure of these equations on black-hole spacetimes (in particular, on the Kerr solution), the index theorem for hyperbolic Dirac operators and properties of the class of Green-hyperbolic operators.

Full work available at URL: https://arxiv.org/abs/1710.04512

zbMATH Keywords

wave equationCauchy problemchiral anomalyDirac equationKilling spinorGoursat problemindex theoremKerr solutionblack hole spacetimeglobally hyperbolic Lorentzian manifoldGreen-hyperbolic operator

Mathematics Subject Classification ID

Black holes (83C57) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Wave equation (35L05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Spin and Spin({}^c) geometry (53C27) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60) Hyperbolic equations on manifolds (58J45)

Related Items (3)

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