The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

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Thomas Johnson, University of Cambridge
Fine Hall 314

The Schwarzschild family of spacetimes describe a 1-parameter family of stationary and spherically symmetric black hole solutions to the Einstein vacuum equations of general relativity. It is an open problem whether in the absence of symmetries this family, in particular the black hole property, are dynamically stable in the context of the theory's associated initial value formulation, a fundamental feature of which is a notion of gauge freedom. As a consequence of this freedom, to resolve the above stability problem for Schwarzschild it suffices to provide only a statement of non-linear stability for the Schwarzschild family as a family of solutions to the system of quasilinear wave equations that result from expressing the Einstein vacuum equations relative to a generalised wave gauge. In this talk we shall discuss our recent work which establishes the linear version of this statement. Our result thus in addition provides an alternative proof of the linear stability of the Schwarzschild family originally established by Dafermos--Holzegel--Rodnianski.