Stochastic Einstein equations. (English) Zbl 1246.83166
Summary: Stochastic Einstein equations are considered when three-dimensional space metric \(\gamma_{ij}\) are stochastic functions. The probability density for the stochastic quantities is connected with Perelman’s entropy functional. As an example, the Friedman Universe is considered. It is shown that for the Friedman Universe the dynamical evolution is not changed. The connection between general relativity and Ricci flow is discussed.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83F05 | Relativistic cosmology |
| 83C45 | Quantization of the gravitational field |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 94A17 | Measures of information, entropy |
| 53Z05 | Applications of differential geometry to physics |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
References:
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| [4] | DOI: 10.1088/0264-9381/27/7/075012 · Zbl 1187.83055 · doi:10.1088/0264-9381/27/7/075012 |
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| [7] | Gardiner C., Handbook of Stochastic Methods (2009) · Zbl 1181.60001 |
| [8] | DOI: 10.1017/CBO9780511721465 · doi:10.1017/CBO9780511721465 |
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