Stationary Universe in General Relativity and Lyra's Geometry

Abstract

The stationary universe solutions have been studied using the metrics of VAN STOCKUM (1937) and GODEL (1949) in a New ST theory (SAEZ and BALLESTER, 1985), general relativity with variable cosmological term (NARLIKAR eta]., 1991), Lyra's geometry (SEN, 1957) and Cosmic strings. It has been shown that the stationary universe has rigid rotation in ST theory. In the presence of variable cosmological term, there is non-rigid rotation in the presence of Zeldovich fluid for van Stockum metric. In Lyra's geometry the only solution is possible when the gauge function / 3 is variable and there is Zeldovich fluid. However, in the presence of cosmic strings, there is no solution with van Stockum or Godel metrics.

Gödel-type space–times in induced matter gravity theory

“…Owing to its striking properties, Gödel's model has a well-recognized importance and has to a certain extent motivated the investigations on rotating cosmological Gödel-type models and on causal anomalies in the framework of general relativity [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and other theories of gravitation. [53][54][55][56][57][58][59][60][61][62][63] Two recent articles have been concerned with five-dimensional Gödel-type space-times. First in Ref.…”