New problems in general relativity

The problem of strong gravitational fields in classical (h = 0) general relativity is discussed. Strong fields require complex space—time topology; they require investigation by the methods of Riemann geometry as a whole over the complete atlas of mappings. Static solutions may not exist; dynamic oscillatory configurations of matter arise. A crucial spherically symmetric self-similar solution is described. The physical consequences are enumerated: there is no gravitational grave for matter and energy — there are no black holes; energy can emerge during and after gravitational collapse. The theoretical conclusions are confirmed by observations. A physical singularity of the infinite-density type arises in solutions with high symmetry. The crucial solution in flat space is continuable at spatial infinity through the singularity with conservation of the arrow of time; continuation through the singularity — the Big Bang — also occurs for cosmological models.