The mass of spacelike hypersurfaces in asymptotically anti-de Sitter space-times

Advances in Theoretical and Mathematical Physics

Volumn 5, Issue 4, 2001, Pages 1-49

  Chruściel, Piotr T ^a   Nagy, Gabriel ^a,b  

^a UNIVERSITÉ DE TOURS   (France)

^b ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551487240     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/atmp.2001.v5.n4.a3     Document Type: Article

References (33)

1. L.F. Abbott and S. Deser, Stability of gravity with a cosmological constant, Nucl. Phys. B195 (1982), 76-96.
2. A. Ashtekar and S. Das, Asymptotically anti-de Sitter space-times: Conserved quantities, Class. Quantum Grav. 17 (2000), L17-L30.
3. A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quantum Grav. 1 (1984), L39-L44.
4. V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999), 413-428.
5. R. Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math. 39 (1986), 661-693.
6. M. Berger, Géométrie, Nathan, Paris, 1990.
7. W. Boucher, G.W. Gibbons, and G.T. Horowitz, Uniqueness theorem for anti-de Sitter spacetime, Phys. Rev. D 30 (1984), 2447-2451.
8. C. Cadeau and E. Woolgar, New five dimensional black holes classified by horizon geometry, and a Bianchi VI braneworld, Class. Quantum Grav. (2001), 527-542.
9. D. Christodoulou and A. Shadi Tahvildar-Zadeh, On the regularity of spherically symmetric wave maps, Commun. Pure Appl. Math 46 (1993), 1041-1091.
10. P.T. Chruściel, On the relation between the Einstein and the Komar expressions for the energy of the gravitational field, Ann. Inst. H. Poincare 42 (1985), 267-282.
11. P.T. Chruściel, Boundary conditions at spatial infinity from a hamiltonian point of view, Topological Properties and Global Structure of Space-Time (P. Bergmann and V. de Sabbata, eds.), Plenum Press, New York, 1986, URL http://www.phys.univ-tours.fr/~piotr/scans, pp. 49-59.
12. P.T. Chruściel, On the invariant mass conjecture in general relativity, Commun. Math. Phys. 120 (1988), 233-248.
13. P.T. Chruściel and M. Herzlich, The mass of asymptotically hyperbolic Riemannian manifolds, (2001).
14. P.T. Chruściel and J. Jezierski, The Trautman-Bondi mass, in preparation.
15. P.T. Chruściel, J. Jezierski, and J. Kijowski, Hamiltonian field theory in the radiating regime, Lect. Notes in Physics, vol. m70, Springer, Berlin, Heidelberg, New York, 2001, URL http://www.phys.univ-tours.fr/~piotr/papers/hamiltonian_structure.
16. P.T. Chruściel and W. Simon, Towards the classification of static vacuum spacetimes with negative cosmological constant, Jour. Math. Phys. 42 (2001), 1779-1817.
17. V.I. Denisov and V.O. Solov'ev, Energy defined in general relativity on the basis of the traditional Hamiltonian approach has no physical meaning, Teoret. Mat. Fiz. 56 (1983), 301-314.
18. H. Friedrich, Einstein equations and conformal structure: Existence of anti-de-Sitter-type space-times, Jour. Geom. and Phys. 17 (1995), 125-184.
19. G.W. Gibbons, Gravitational entropy and the inverse mean curvature flow, Class. Quantum Grav. 16 (1999), 1677-1687.
20. G.W. Gibbons, S.W. Hawking, G.T. Horowitz, and M.J. Perry, Positive mass theorems for black holes, Commun. Math. Phys. 88 (1983), 295-308.
21. M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter spaces, Commun. Math. Phys. 98 (1985), 391-424.
22. G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D59 (1999), 026005 (12 pp.).
23. B. Julia and S. Silva, Currents and superpotentials in classical gauge theories. II: Global aspects and the example of affine gravity, Class. Quantum Grav. 17 (2000), 4733-4744.
24. J. Kánnár, Hyperboloidal initial data for the vacuum Einstein equations with cosmological constant, Class. Quantum Grav. 13 (1996), 3075-3084.
25. J. Kijowski, Unconstrained degrees of freedom of gravitational field and the positivity of gravitational energy, Gravitation, geometry and relativistic physics (Aussois, 1984), Springer, Berlin, 1984, pp. 40-50.
26. J. Kijowski, Asymptotic degrees of freedom and gravitational energy, Proceedings of Journees Relativistes 1983 (Bologna) (S. Benenti et al., ed.), Pitagora Editrice, 1985, pp. 205-211.
27. J. Kijowski, A simple derivation of canonical structure and quasi-local Hamiltonians in general relativity, Gen. Rel. Grav. 29 (1997), 307-343.
28. J. Kijowski and W.M. Tulczyjew, A symplectic framework for field theories, Lecture Notes in Physics, vol. 107, Springer, New York, Heidelberg, Berlin, 1979.
29. F. Kottler, Über die physikalischen Grundlagen der Einsteinschen Gravitationstheorie, Annalen der Physik 56 (1918), 401-462.
30. J. Lelong-Ferrand, Geometrical interpretations of scalar curvature and regularity of conformal homeomorphisms, Differ. Geom. Relativ., Vol. Honour A. Lichnerowicz 60th Birthday, 1976, pp. 91-105.
31. A. Magnon, On Komar integrals in asymptotically anti-de Sitter space-times, Jour. Math. Phys. 26 (1985), 3112-3117.
32. R.M. Wald and A. Zoupas, A general definition of "conserved quantities" in general relativity and other theories of gravity, Phys. Rev. D61 (2000), 084027 (16 pp.).
33. X. Wang, Mass for asymptotically hyperbolic manifolds, Jour. Diff. Geom. 57 (2001), 273-299.