Linear stability of Schwarzschild under perturbations which are non-vanishing on the bifurcation 2-sphere

Details Linear stability of Schwarzschild under perturbations which are non-vanishing on the bifurcation 2-sphere Linear stability of Schwarzschild under perturbations which are non-vanishing on the bifurcation 2-sphere

Jul 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cqgra...4..893k&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 4, July 1, 1987, p. 893-898. Research supported by the Tomalla Foundation a

Astronomy and Astrophysics

Astronomy

54

Cauchy Problem, Klein-Gordon Equation, Numerical Stability, Perturbation Theory, Schwarzschild Metric, Space-Time Functions, Black Holes (Astronomy), Gravitational Collapse, Linear Equations, Stellar Physics

Scientific paper

Boundedness on an exterior Schwarzschild wedge is proven for C(infinity) solutions of the covariant Klein-Gordon equation which have compact support on Cauchy surfaces in Kruskal spacetime. Previously used methods enable such boundedness to be proven only for solutions whose initial data satisfy the additional restriction of vanishing at the bifurcation 2-sphere of the horizon. By employing a rarely considered discrete isometry of Kruskal spacetime and the causal propagation property of the present equation, this restriction is removed. This also makes it possible to prove boundedness exterior to the horizon of a spacetime representing the collapse to a black hole of a spherically symmetric compact star for solutions of the same equation having C0 (infinity) initial data on a Cauchy surface drawn prior to the collapse.

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