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- W3198866514 abstract "General relativity field equations are a set of differential equations that can be solved for the metric tensor which defines curved space. They are derived from two physical assumptions that the speed of light is constant in any frame of reference that may be moving relative to one another and space is curved by the mass of physical bodies. Some other assumptions related to mathematics such as symmetry and continuity are also needed. First, the metric tensor is defined as a transformation from Euclidean space to curved space. The equation of geodesics describes the equations of motion of a particle within a gravitational field. The Riemann tensor and Ricci tensor are obtained by differentiation of the metric tensor with respect to an assumed coordinate system. The Einstein tensor scales the Riemann tensor proportional to the mass present. The mathematics use Einstein summation notation and are well defined in many sources. Since navigators use matrix notation, some of the key derivations are repeated in matrix notation. Also, a computer solution for the metric tensor and equations of motion is obtained by processing simulated data in an orbit determination filter thus bypassing the analytic solution obtained from the Einstein tensor." @default.
- W3198866514 created "2021-09-13" @default.
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- W3198866514 date "2021-01-01" @default.
- W3198866514 modified "2023-09-23" @default.
- W3198866514 title "Einstein Field Equations" @default.
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- W3198866514 doi "https://doi.org/10.1007/978-3-030-77546-9_1" @default.
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