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This rearrangement, which appears as equation (8) at the end of this section, will make very clear the limits imposed within the Schwarzschild metric by the conservation of momentum and energy.
Einstein was careful to show that the field equations, nevertheless, correspond to the conservation of momentum and energy [2, Equations 47a] and thus have a nexus to physical reality.
The Schwarzschild metric, as a solution to the field equations, also corresponds to the conservation of momentum and energy.
The conservation of momentum and energy, as expressed in the Schwarzschild metric, requires that the magnitude of the sum of the velocities is always equal to the constant c.
In the previous section, the Schwarzschild metric in (1) has been rearranged as (8) to provide a more concrete picture of the relationships necessary for conservation of momentum and energy.
4 Equation (8) and limits imposed by the conservation of momentum and energy
The arrangement of the Schwarzschild metric in (8) allows for a more concrete explanation of the limitations inherent in the Schwarzschild metric that necessarily result from the conservation of momentum and energy.
This section has shown that because of the conservation of momentum and energy--as expressed by the Schwarzschild metric arranged as in (8)--matter from space cannot cross the Schwarzschild radius R to get to a location where r < R.
According to the conservation of momentum and energy described by the Schwarzschild metric, see (8) and (15), a particle can never from space cross the Schwarzschild radius R of a compact mass M.
In the Schwarzschild metric, no reference frame can cross its critical radius because to do so would be a violation of the conservation of momentum and energy [4].
For a precise description of how in the Schwarzschild metric gravity affects time based on the conservation of momentum and energy, see [4, Eq.

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