A variational principle for stationary, axisymmetric solutions of Einstein's equations

Classical and Quantum Gravity

Volumn 23, Issue 23, 2006, Pages

  Dain, Sergio ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846149674     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/23/23/016     Document Type: Article

References (21)

1. Ansorg M and Petroff D 2005 Black holes surrounded by uniformly rotating rings Phys. Rev. D 72 024019 (Preprint gr-qc/0505060)
2. Bardeen J M 1970 A variational principle for rotating stars in general relativity Astrophys. J. 162 71-95
3. Bartnik R and Isenberg J 2004 The constraint equations The Einstein Equations and Large Scale Behavior of Gravitational Fields ed P T Chruściel and H Friedrich (Basel: Birkhäuser) pp 1-38 (Preprint gr-qc/0405092)
4. Bartnik R A and Chruściel P T 2005 Boundary value problems for Dirac-type equations J. Reine Angew. Math. 579 13-73 (Preprint math.DG/0307278)
5. Brill D 1959 On the positive definite mass of the Bondi-Weber-Wheeler time-symmetric gravitational waves Ann. Phys. 7 466-83
6. Brill D and Lindquist R W 1963 Interaction energy in geometrostatics Phys. Rev. 131 471-476
7. Cantor M and Brill D 1981 The Laplacian on asymptotically flat manifolds and the specification of scalar curvature Compositio Mathematica 43 317-30
8. Carter B 1973 Black hole equilibrium states Black Holes/Les Astres Occlus (École d'Été Phys. Théor., Les Houches, 1972) (New York: Gordon and Breach) pp 57-214
9. Dain S, Lousto C O and Takahashi R 2002 New conformally flat initial data for spinning black holes Phys. Rev. D 65 104038 (Preprint gr-qc/0201062)
10. Ernst F J 1968 New formulation of the axially symmetric gravitational field problem Phys. Rev. 167 1175-9
11. Friedman J L and Mayer S 1982 Vacuum handles carrying angular momentum; electrovac handles carrying net charge J. Math. Phys. 23 109-15
12. Gibbons G W and Hull C M 1982 A Bogomolny bound for general relativity and solitons in N = 2 supergravity Phys. Lett. B 109 190-4
13. Gibbons G W, Hull C M and Warner N P 1983 The stability of gauged supergravity Nuclear Physics B 218 173-90
14. Hawking S W 1973 A variational principle for black holes Commun. Math. Phys. 33 323-34
15. Horowitz G T 1984 The positive energy theorem and its extensions Asymptotic Behavior of Mass and Spacetime Geometry (Corvallis, Oregon, 1983) (Lecture Notes in Physics vol 202) ed F J Flaherty (Berlin: Springer) pp 1-21
16. Horowitz G T 2005 Higher dimensional generalizations of the Kerr black hole Preprint gr-qc/0507080
17. Matzner R A and Misner C W 1967 Gravitational field equations for sources with axial symmetry and angular momentum Phys. Rev. 154 1229-32
18. Maxwell D 2005 Solutions of the Einstein constraint equations with apparent horizon boundaries Commun. Math. Phys. 253 561-83 (Preprint gr-qc/0307117)
19. Neugebauer G and Herold H 1992 Gravitational fields of rapidly rotating neutron stars: theoretical foundation Relatividtic Gravity Research (Lectures Notes in Physics vol 410) ed J Ehlers and G Schäfer (Berlin: Springer) pp 303-18
20. Szabados L B 2004 Quasi-local energy-momentum and angular momentum in GR: A review article Living Rev. Relativ. 7 http://www.livingreviews.org/lrr-2004-4 (cited on 8 August 2005)
21. Wald R M 1984 General Relativity (Chicago, IL: The University of Chicago Press)