- #1
fox26
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The Schwarzschild solution of the Einstein Equation of GR is said to be the only time-independent matter-free solution of that equation. In this usage, does “matter-free solution” mean without matter everywhere
except at the singularity of the solution? I thought that the only solutions of the Einstein Eq. for a totally
matter-free universe were either just empty Minkowski space, or space-times that had only gravitational
waves in them. The S. solution is neither one. The universe of the S. solution supposedly is not totally
matter-, or at least mass-free, there is matter in the infinite-density singularity at the center of the S.
solution, or at least non-zero mass attributed to the black hole represented by the solution, a
non-rotating, uncharged black hole having non-zero mass, with R = 2Gm/c^2, R representing the
Schwarzschild radius of the black hole and m its mass. However, Stephen Hawking and
others have said that such a singularity isn’t really in the space-time of the S. solution. Are they wrong?
Doesn’t matter have to be in a space-time to contribute to the stress-energy tensor of the Einstein
equation applicable to that space-time? The problem of whether singularities could exist in a correct
GR-quantum theory is separate from this question.
I have other questions about GR, black holes, and gravitational collapse, which I will ask in later posts.
except at the singularity of the solution? I thought that the only solutions of the Einstein Eq. for a totally
matter-free universe were either just empty Minkowski space, or space-times that had only gravitational
waves in them. The S. solution is neither one. The universe of the S. solution supposedly is not totally
matter-, or at least mass-free, there is matter in the infinite-density singularity at the center of the S.
solution, or at least non-zero mass attributed to the black hole represented by the solution, a
non-rotating, uncharged black hole having non-zero mass, with R = 2Gm/c^2, R representing the
Schwarzschild radius of the black hole and m its mass. However, Stephen Hawking and
others have said that such a singularity isn’t really in the space-time of the S. solution. Are they wrong?
Doesn’t matter have to be in a space-time to contribute to the stress-energy tensor of the Einstein
equation applicable to that space-time? The problem of whether singularities could exist in a correct
GR-quantum theory is separate from this question.
I have other questions about GR, black holes, and gravitational collapse, which I will ask in later posts.
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