Heuristic Approach EFE: Why 10 DOF?

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Discussion Overview

The discussion revolves around the question of why 10 degrees of freedom (dof) are sought in the context of a symmetric two-index tensor, particularly in relation to General Relativity. Participants explore the implications of the metric's symmetry and the dimensionality of spacetime.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that the metric is symmetric, leading to 10 independent equations out of 16, which accounts for 6 degrees of freedom, with the remaining 4 degrees of freedom attributed to arbitrary coordinate transformations.
  • Others challenge this interpretation, arguing that the assertion regarding the relationship between independent equations and degrees of freedom is incorrect.
  • One participant notes that the number of equations is related to the four dimensions of spacetime in General Relativity.
  • Another participant requests specific references to support the claims made about the degrees of freedom.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views regarding the interpretation of the degrees of freedom and the implications of the metric's symmetry.

Contextual Notes

The discussion includes unresolved mathematical interpretations and assumptions about the relationship between equations and degrees of freedom, as well as the implications of coordinate transformations.

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TL;DR
Some sources state we seek 10 dof ( and so ofc this is a symmetric two index tensor.


My question is why we seek 10 dof in the first place ?


Many thanks
Some sources state we seek 10 dof ( and so ofc this is a symmetric two index tensor.My question is why we seek 10 dof in the first place ?Many thanks
 
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binbagsss said:
Some sources

What sources? Please give specific references.
 
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The number of equations is because in General Relativity there are four dimensions of spacetime.
 
The metric is symmetric, so there are only 10 independent equations out of 16. That accounts for 6 degrees of freedom. The remaining 4 degrees of freedom are to allow for arbitrary coordinate transformations.
 
Daverz said:
The metric is symmetric, so there are only 10 independent equations out of 16. That accounts for 6 degrees of freedom. The remaining 4 degrees of freedom are to allow for arbitrary coordinate transformations.

No, this is not correct. First, 10 independent equations does not account for 6 degrees of freedom. Second, 4 degrees of freedom is not enough to allow for arbitrary coordinate transformations.
 
In the absence of any references, this thread is closed.
 

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