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My understanding is that this tensor contains sources for spacetime curvature, analogous to how charge and current are sources for electric and magnetic fields. In other words, the elements of this tensor, such as mass density, are specified and used in the Einstein equation to solve for the metric.
In the derivation of the interior solution for a spherically symmetric static mass distribution, however, there appears the Tolman–Oppenheimer–Volkoff equation, a differential equation for the pressure of the material as a function of radial distance from the center. In other words, pressure is something to solve for rather than something that is specified (as the mass density is in this example). Any clarification would be helpful. Are the other elements specified or calculated?
In the derivation of the interior solution for a spherically symmetric static mass distribution, however, there appears the Tolman–Oppenheimer–Volkoff equation, a differential equation for the pressure of the material as a function of radial distance from the center. In other words, pressure is something to solve for rather than something that is specified (as the mass density is in this example). Any clarification would be helpful. Are the other elements specified or calculated?