Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ncimr...6..405m&link_type=abstract
Nuovo Cimento, Rivista, Serie 2, vol. 6, July-Sept. 1976, p. 405-447.
Astronomy and Astrophysics
Astrophysics
Astrophysics, Black Holes (Astronomy), Einstein Equations, Gravitation Theory, Space-Time Functions, Analytic Functions, Field Theory (Physics), Functional Analysis, Liapunov Functions, Numerical Stability, Relativity, Stellar Evolution, Topology, Transformations (Mathematics)
Scientific paper
Explicit vacuum solutions of Einstein's field equations are sought in a space-time admitting two isometries, an axially symmetric and a stationary isometry; the solutions are considered as candidates for black holes. The problem is approached using Ernst's equations, and essential use is made of Lichtenstein's theorem, stating that the equatorial plane z = 0 is a mirror symmetric plane for a homogeneous incompressible rotating fluid. A dynamical system is constructed. Liapunov stability of the solutions obtained is studied, and with the aid of multiple integrals in the calculus of variations, it is shown that the weakest causality condition (chronology) is a necessary condition for Liapunov stability. It is shown that the Kerr solution is Liapunov stable under a given topology.
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