Solve Einstein Field Equation without Vacuum Solution

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Discussion Overview

The discussion revolves around solving the Einstein Field Equations (EFE) without relying on vacuum solutions, exploring various scenarios where non-zero stress-energy tensors are applicable. Participants consider both theoretical and practical approaches to addressing the EFE in general situations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about solving the EFE for general situations, suggesting the use of numerical methods and computational tools.
  • There is uncertainty expressed regarding the exclusive use of vacuum solutions, with participants questioning why non-zero stress-energy tensors cannot be utilized.
  • Examples are provided, such as the Oppenheimer-Snyder scenario of a collapsing ball of dust, which involves a non-zero stress-energy tensor.
  • Another example mentioned is the solutions that describe the universe as a whole, indicating contexts where non-vacuum solutions are relevant.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity or applicability of vacuum solutions versus non-zero stress-energy tensors, indicating multiple competing views remain on the topic.

Contextual Notes

Participants highlight the limitations of vacuum solutions in certain scenarios, but the discussion does not resolve the assumptions or conditions under which different approaches may be valid.

TimeRip496
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How to solve EFE without using the vacuum solution like how you did in schwarzschild metric?
 
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Do you mean, how to solve the EFE for a general situation? If that is what you mean, probably using numerical methods and a computer.

If you mean something else, please say what.
 
DEvens said:
Do you mean, how to solve the EFE for a general situation? If that is what you mean, probably using numerical methods and a computer.

If you mean something else, please say what.
I am not sure why can we just use the vacuum solution to solve EFE? Why can't we use a nom zero stress momentum tensor to solve?
 
TimeRip496 said:
I am not sure why can we just use the vacuum solution to solve EFE? Why can't we use a non zero stress momentum tensor to solve?

The space outside the surface of an object floating in space (like a star or a planet) is vacuum so the stress-energy tensor there is zero. Thus, if we want a solution to the field equations that applies there we set ##T## equal to zero.

In other problems, for example a ball of dust collapsing under its own gravitational attraction to form a star or planet (google for "Oppenheimer-Snyder"), we don't have a vacuum and the stress energy tensor is not zero. Then we have to solve the field equation for a non-zero stress-energy tensor.
 
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Nugatory said:
In other problems, for example a ball of dust collapsing under its own gravitational attraction to form a star or planet (google for "Oppenheimer-Snyder"), we don't have a vacuum and the stress energy tensor is not zero. Then we have to solve the field equation for a non-zero stress-energy tensor.

Another example is the solutions describing the universe as a whole.
 

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