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# have any predictions of general relativity other than the swarzchild solution ever been tested experimentally?

the swarzchild solution models a spherically symmetric space-time curvature in a vacuum, with the stress tensor describing the surrounding mass and energy distributions set to zero. but what happens when you have matter and energy distributions outside the spherical mass so the stress tensor no longer vanishes? how do we know the stress tensors are correct and correctly describe how space-time curves? einstein had to guess at what to put on the right side of his field equations, but was his guess correct? what if you only have electromagnetic energy and no mass distributions? has it ever been tested experimentally?

### 7 Answers

- goringLv 611 months ago
Newton was first to indicate that the mass of the Earth can be viewed as its mass volume to be concentrated as one lump at the center of the Earth.There are discrepancies on calculating the reduced volume and the Schwartzschild diameter. How ever it indicates that the actual mass volume of the massive space of the Universe is a lot smaller than we think.

- Tom SLv 711 months ago
Yes, many either experiments or observations:. https://en.m.wikipedia.org/wiki/Tests_of_special_r... ..... https://www.google.com/amp/s/www.space.com/amp/410...

- Anonymous11 months ago
Nobody knows how gravity works, there are some basic common sense ideas or laws, to me they can't even agree upon those. I think that even Einstein admitted he wasn't really that smart, and 99.99% of people aren't as smart as him. He thought that people were quite retarded.

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- Anonymous11 months ago
The Schwarzchild Radius is just the Escape Velocity equation with the "v" replaced by "c". You didn't even need General Relativity for that.

Escape velocity:

v = sqrt((2 G m)/r) |

v | speed

m | mass

r | radius

G | Newtonian gravitational constant (≈ 6.674×10^-11 m^3/(kg s^2))

Schwarzchild Radius:

r = (2 G M)/c^2 |

r | event horizon radius

M | mass

G | Newtonian gravitational constant (≈ 6.674×10^-11 m^3/(kg s^2))

c | speed of light (≈ 2.998×10^8 m/s)

Rearrange them, and they are the same equation.

- nebLv 711 months ago
Yes, several aspects of general relativity have been experimentally verified such as frame dragging from rotating gravitational sources and the recently discovered gravitational waves.

The Schwarzschild solution is a vacuum solution. There is no stress-energy tensor defined anywhere in the solution. That is what makes the Schwarzschild solution so simple. Schwarzschild black holes likely don’t physically exist since they are modeled as eternal, static solutions with no angular momentum.

The equations of general relativity are impossible to solve in the general case. The known exact solutions are all simplifications. What makes difficult solutions even more difficult is trying to model a matter/energy distribution where the stress-energy tensor is zero at some points and non-zero at other points. You essentially have a vacuum solution and a non-vacuum solution that have to be smoothly blended.

As for the stress-energy tensor itself, the Levi-Civita connection imposes a requirement for a rank 2 symmetric tensor as the source of gravity. It is not a big stretch to extend the energy-momentum 4-vector from special relativity to a stress energy tensor.

Now, are there other possible sources other than a symmetric stress-energy tensor? The answer to that is yes. If we modify General Relativity to allow a non-symmetric connection (introduces a spacetime torsion), we can then have a non-symmetric stress-energy tensor. The Einstein-Cartan modification does that. It postulates a torsion tensor that models quantum spins. Difficult to test because only a non-vacuum torsion will behave differently than vanilla relativity.

As for electromagnetism, yes there is a stress-energy tensor for electromagnetism. Testing would be difficult since the energy-momentum density of electromagnetic fields is so small.

Anything that possess energy-momentum in any form will gravitate.

- daniel gLv 711 months ago
The scientist that went to a black hole to do experiments have not been heard from since.

As for Einstein, he hasn't been proven wrong yet.

As for electromagnetic energy, it must come from some form of mass even if minuscule like an atom.