Authors: Steven Kenneth Kauffmann
In 1915 Einstein adopted a new coordinate condition for his GR gravity theory, namely that the metric tensor's determinant always equals -1, its Minkowskian zero-gravity value. In his landmark November 18, 1915 paper, Einstein showed that applying this coordinate condition to the approximate calculation of the metric of a static point mass (the sun) results in agreement with the previously unaccounted-for part of Mercury's perihelion shift, and doubles the deflection of light by the sun's gravity from his previous calculation which didn't use this coordinate condition; a 1919 solar-eclipse expedition verified the doubled deflection. In January, 1916 Schwarzschild published the exact version of Einstein's new static point-mass metric; as expected, it slightly lengthens circular-orbit periods. In May 1916 Droste published a much simpler metric which violates the Einstein equation at an empty-space radius and fails to lengthen circular-orbit periods. In 1922 Friedmann tried fixing the metric's time-time component to unity, making it Galilean covariant instead of Lorentz covariant, and eliminating gravitational time dilation. We replace Friedmann's metric condition by Einstein's in the Oppenheimer-Snyder model; the resulting gravitational time dilation accommodates both the acceleration of the universe's expansion and its early inflation.
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