Four Dimensional Elasticity: Is it General Relativity?
Keywords: four dimensional, elasticity, general relativity, space-time, gravitational, stress, metric
The purpose of this paper is to show that it is possible to describe the space-time as a four dimensional elastic medium. This, when unstressed, has a Eudlidean metric, when stressed however it may change its metric, acquire curvature and in general display features typical of the general relativistic space-time with and without gravitational interaction. In particular we shall see that under a uniaxial stress it is possible to recover the Minkowski metric, provided the elastic parameters of the medium satisfy appropriate but rather loose conditions. Similarly we shall show that a simple stress pattern produces the Friedman-Robertson-Walker universe.