[Richard777 (OP)]

Stress tensors represent pressure and shear. Total stress is the sum of pressure and shear.
Einstein rules may apply to total stress, giving the EFE.
If the Schwarzschild conditions are true, then the Schwarzschild metric is easily obtained from the EFE.
Can stress tensors give the EFE?

[PmbPhy]

-

Stress tensors represent pressure and shear. Total stress is the sum of pressure and shear.
Einstein rules may apply to total stress, giving the EFE.
If the Schwarzschild conditions are true, then the Schwarzschild metric is easily obtained from the EFE.
Can stress tensors give the EFE?

What does EFE stand for?

[jeffreyH]

Einstein field equations.

[PmbPhy]

-

Stress tensors represent pressure and shear. Total stress is the sum of pressure and shear.
Einstein rules may apply to total stress, giving the EFE.
If the Schwarzschild conditions are true, then the Schwarzschild metric is easily obtained from the EFE.
Can stress tensors give the EFE?

What does EFE stand for?

The stress tensor is part of the stress-energy-momentum (SEM) tensor and its the SEM tensor which appears as the source of gravity in the EFE.

[saspinski]

For a solid elastic body at rest, after setting the equations for the force equilibium and the generalized Hooke's law, we have 3 differential equations, linking the displacements and its derivatives to the body forces.
When the body forces results only from a gravitational field, that displacements can be a measure of the tidal forces of the field. 

[Thalias]

For a solid elastic body at rest, after setting the equations for the force equilibium and the generalized Hooke's law, we have 3 differential equations, linking the displacements and its derivatives to the body forces.
When the body forces results only from a gravitational field, that displacements can be a measure of the tidal forces of the field.

[puppypower]

Stress tensors represent pressure and shear. Total stress is the sum of pressure and shear.
Einstein rules may apply to total stress, giving the EFE.
If the Schwarzschild conditions are true, then the Schwarzschild metric is easily obtained from the EFE.
Can stress tensors give the EFE?

Einstein did not deal with pressure, sufficiently, since pressure will cause phase changes in matter that are universal, absolute and not reference dependent. For example, metallic iron boils at 2862 C, yet iron is a solid in the earth's core, where the temperature is twice this boiling temperature.

This is an example of the impact of pressure, on matter, that has nothing to do with space-time. It is based on distance, but not time; distance potential. One can form metallic iron, in the core of the earth, fast or slow, as long as the distances between atoms is correct. This phase change is also not dependent on space-time reference, since this same solid iron phase can be formed in any reference. We can form solid metallic iron at 5000C with a hot press, on the earth's surface, which does not contain sufficient mass or velocity to alter the space-time reference due to GR or SR.

Pressure is an example of distance potential that is not dependent on space-time reference. Pressure has the units force/d2, with the d2 or area also connected to the stress tensor. If we reduce pressure, surface tension and even shear stresses can form within stable phases that can exist at higher pressure. This tension has little to do with space-time but can be performed in all references.

Pressure is connected to the theorem of Einstein that states that the laws of physics are the same in all references. If you read between the lines, real laws of physics should not be reference dependent, since Einstein never said laws of  physics can also be relative. Therefore, laws outside of reality physics are reference dependent.

Your better off keeping the stress tensor as part of the laws of science that are independent of reference, since this is the gold standard from which tangible universal innovation can appear useful in all references. There is no reason to attach that wagon to a unicorn. It is better to keep it connected to energy conservation. According to Einstein, energy conservation needs to be the same in all references, since this is one of the few laws of physics. if it is relative it is not physics, but philosophy and fantasy; too shallow to be universal.

[yor_on]

stress tensors are needed to describe a 'whole universe'.