Collision-free gases in static space-times. (English) Zbl 0614.76128
The authors established relationships between the space-time geometry and the kinematics and dynamics of the gas under the following three assumptions: (1) The gas is a one-component collision-free without charge. (2) The space-time geometry is static and spherical symmetric. (3) The distribution function is invariant under the \(G_ 4\) of motions.
This paper is based on a previous paper by the authors [see the review above (Zbl 0614.76127)] in which the same problem was considered for spatially homogeneous and locally rotationally symmetric space-times.
This paper is based on a previous paper by the authors [see the review above (Zbl 0614.76127)] in which the same problem was considered for spatially homogeneous and locally rotationally symmetric space-times.
Reviewer: K.L.Duggal
MSC:
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 76N15 | Gas dynamics (general theory) |
Keywords:
Einstein-Liouville equations; perfect fluid; invariant Einstein-Maxwell- Liouville solutions; charged gas; invariant electromagnetic potential; Liouville’s equation; static space-times; self-gravitating gas; collision-free gases; static spherical symmetric spaces; groups of motion; space-time geometry; dynamics of the gas; distribution functionCitations:
Zbl 0614.76127References:
| [1] | DOI: 10.1086/149693 · doi:10.1086/149693 |
| [2] | DOI: 10.1086/160013 · doi:10.1086/160013 |
| [3] | DOI: 10.1063/1.526807 · doi:10.1063/1.526807 |
| [4] | DOI: 10.1063/1.526713 · Zbl 0614.76127 · doi:10.1063/1.526713 |
| [5] | DOI: 10.1063/1.1666736 · doi:10.1063/1.1666736 |
| [6] | Kimura M., Tensor 30 pp 27– (1976) |
| [7] | DOI: 10.1103/PhysRevD.26.1262 · doi:10.1103/PhysRevD.26.1262 |
| [8] | DOI: 10.1007/BF01877593 · Zbl 0221.35069 · doi:10.1007/BF01877593 |
| [9] | DOI: 10.1016/0003-4916(83)90024-6 · Zbl 0525.53041 · doi:10.1016/0003-4916(83)90024-6 |
| [10] | DOI: 10.1086/149850 · Zbl 0172.27802 · doi:10.1086/149850 |
| [11] | DOI: 10.1007/BF02898747 · doi:10.1007/BF02898747 |
| [12] | DOI: 10.1007/BF00759230 · Zbl 0524.53019 · doi:10.1007/BF00759230 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
