General Relativity: Four Interior Metric Solutions...

[Orion1]

In Einstein's theory of general relativity, the interior metric or interior fluid solution, is an exact solution to the Einstein field equations and Einstein-Maxwell equations that describes the gravitational field and the space-time geometry in the interior of a non-rotating or rotating neutral or charged spherically symmetric body of mass M, which consists of an incompressible fluid and constant density throughout the body and has zero pressure at the surface and that the electric charge and angular momentum of the mass may be zero or non-zero, and the universal cosmological constant is zero. For a non-zero charged mass, the metric takes into account the Einstein-Maxwell field energy of an electromagnetic field within the space-time geometry. The space-time geometry is in Boyer-Lindquist coordinates.

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Reference:
Wikipedia - Four-gradient As a Jacobian matrix for the SR Minkowski metric tensor: (ref. 1)
https://en.wikipedia.org/wiki/Four-gradient#As_a_Jacobian_matrix_for_the_SR_Minkowski_metric_tensor
Wikipedia - Schwarzschild radius: (ref. 2)
https://en.wikipedia.org/wiki/Schwarzschild_radius
Wikipedia - Interior Schwarzschild metric - Other formulations: (ref. 3)
https://en.wikipedia.org/wiki/Interior_Schwarzschild_metric#Other_formulations
Austrian Reports on Gravitation - Interior Schwarzschild Solution And Free Fall - Rainer Burghardt: (ref. 4)
http://www.arg.or.at/Wpdf/WIff.pdf
Wikipedia - Interior Schwarzschild metric: (ref. 5)
https://en.wikipedia.org/wiki/Interior_Schwarzschild_metric#Mathematics
Wikipedia - Exterior Reissner-Nordstrom metric: (ref. 6)
https://en.wikipedia.org/wiki/Reissner–Nordström_metric#The_metric
 

Edited January 30, 2022 by Orion1
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