On 2/13/2025 9:11 PM, Alan Grayson wrote:
On Thursday, February 13, 2025 at 9:59:31 PM UTC-7 Brent Meeker wrote:
That's effectively the Schwarzschild solution unless the a star is
rotating very fast. You don't even have to make the assumption
that the mass is concentrated at the center, you just assume
spherical symmetry.
Brent
TY, but what's the first thing one must DO, who never heard of
Schwartzchild, to derive a geodesic path? AG
Schwarzschild first assumed spherical symmetry. Then using spherical
coordinates, Einstein's equations are greatly simplified and
Schwarzschild solved them for the metric. Incidentally, Einstein, when
he published his paper describing general relativity, Nov 25 1915, said
he thought that no exact solutions to the equations would ever be
found. Karl Schwarzschild, while fighting as an artillery officer in
WW1, found his solution on Dec 22 and sent it to Einstein.
https://www.einsteinrelativelyeasy.com/index.php/general-relativity/171-schwarzschild-metric-derivation
But lest you think it's easy to find an exact solution, the
cylindrically symmetric, rotating star, case wasn't found until Roy Kerr
did it in 1965 at University of Texas where I once played soccer against
him at the Relativity Dept picnic. It was Americans v. Foreigners.
Brent
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