Abstract
Some aspects of the theory of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology.
Meinhardt, R
[1]
- Chile Univ., Santiago. Departamento de Fisica
Citation Formats
Meinhardt, R.
Axially symmetric stationary black-hole states of the Einstein gravitational theory.
Italy: N. p.,
1976.
Web.
Meinhardt, R.
Axially symmetric stationary black-hole states of the Einstein gravitational theory.
Italy.
Meinhardt, R.
1976.
"Axially symmetric stationary black-hole states of the Einstein gravitational theory."
Italy.
@misc{etde_7280783,
title = {Axially symmetric stationary black-hole states of the Einstein gravitational theory}
author = {Meinhardt, R}
abstractNote = {Some aspects of the theory of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology.}
journal = []
volume = {6:3}
journal type = {AC}
place = {Italy}
year = {1976}
month = {Jan}
}
title = {Axially symmetric stationary black-hole states of the Einstein gravitational theory}
author = {Meinhardt, R}
abstractNote = {Some aspects of the theory of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology.}
journal = []
volume = {6:3}
journal type = {AC}
place = {Italy}
year = {1976}
month = {Jan}
}