Stability of gravity with a cosmological constant. (English) Zbl 0900.53033
Summary: The stability properties of Einstein theory with a cosmological constant \(\Lambda\) are investigated. For \(\Lambda > 0\), stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For \(\Lambda < 0\), stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressed for general field Hamiltonians. Stability for\(\Lambda < 0\) is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.
MSC:
| 83C40 | Gravitational energy and conservation laws; groups of motions |
Keywords:
Einstein theory with cosmological constant; semiclassical stability; asymptotically anti-de Sitter metricsReferences:
| [1] | Brill, D.; Deser, S., Ann. of Phys., 50, 548 (1968) |
| [2] | Grisaru, M., Phys. Lett., 73B, 207 (1978) |
| [3] | Schoen, P.; Yau, S. T., Phys. Rev. Lett., 43, 1457 (1979) |
| [4] | Witten, E., Comm. Math. Phys., 80, 381 (1981) · Zbl 1051.83532 |
| [5] | Gibbons, G. W.; Hawking, S. W., Phys. Rev., D10, 2738 (1977) |
| [6] | Coleman, S.; Callan, C. G., Phys. Rev., D16, 1762 (1977) |
| [7] | Perry, M. J., (Hawking, S. W.; Roček, M., Superspace and supergravity (1981)), Cambridge · Zbl 0465.53041 |
| [9] | Hawking, S. W.; Ellis, G. F.R., The large scale structure of space-time (1973), Cambridge · Zbl 0265.53054 |
| [10] | Deser, S., Gen. Rel. Grav., 8, 573 (1977) |
| [11] | Townsend, P., Phys. Rev., D15, 2802 (1977) |
| [12] | Deser, S.; Zumino, B., Phys. Rev. Lett., 38, 1433 (1977) |
| [13] | Kihara, M.; Nariai, H., RRK 81-9 (1981), Hiroshima preprint |
| [14] | Arnowitt, R.; Deser, S.; Misner, C., (Witten, L., Gravitation an introduction to current research (1962), Wiley: Wiley New York) · Zbl 0115.43103 |
| [15] | Nariai, H.; Kimura, T., Prog. Theor. Phys., 28, 529 (1962) · Zbl 0105.21404 |
| [16] | Deser, S., Ann. Inst. Henri Poincaré, 7, 149 (1967) · Zbl 0155.32801 |
| [17] | Brill, D.; Deser, S., Comm. Math. Phys., 32, 291 (1973) · Zbl 0263.53042 |
| [18] | Gibbons, G. W.; Perry, M. J., (Proc. Roy. Soc., A358 (1978)), 467 |
| [19] | Schoen, P.; Yau, S. T., Phys. Rev. Lett., 42, 547 (1979) |
| [20] | Gürsey, F.; Lee, T. D., (Proc. Nat. Acad. Sci., 49 (1963)), 179 · Zbl 0113.21901 |
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