Einstein Field Equations with Exponential Metric

N. Perković, M. Stojić

Einstein’s equation, gravitational field, Exponential Metric.

In this paper, a procedure for determining Einstein’s equation withexponential metric is shown in the case of static, centrally symmetric, gravitational field. The procedure has been conducted by introducing a covariance four-vector forstatic, gravitational field that has its values A_µ  (0,0,0,Ф). A scalar potential Ф is determined for the relativistic case of how body mass depends on its position in a gravitational field. Exponential metric in default with a metric tensor g_(µν)has been used to determine the Einstein tensor G_(µν). The energy-momentum tensor was obtained using the flat space metric.