Deriving Friedmann Equation from RW Metric - Blumfeld

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Discussion Overview

The discussion revolves around the derivation of the Friedmann equation from the Robertson-Walker (RW) metric, focusing on the relationship between the metric and the stress-energy tensor within the context of general relativity. Participants are seeking resources and clarifications regarding the derivation process and the specific components involved.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant requests resources for deriving the Friedmann equation from the RW metric, specifically looking for calculations of Christoffel symbols.
  • Another participant asserts that the Friedmann equation cannot be derived from the RW metric alone, stating it is a constraint derived from the Einstein field equations and requires the stress-energy tensor.
  • A suggestion is made to refer to "Relativity Demystified" by David McMahon, which includes a problem related to the RW metric and the Friedmann equations.
  • A follow-up question seeks clarification on the specific form of the stress-energy tensor used in the derivation, particularly asking if it is the diagonal form {-rho, p, p, p}.
  • The same participant inquires about websites that provide the derivation of the Friedmann equation as a constraint from Einstein's field equations.

Areas of Agreement / Disagreement

Participants express differing views on whether the Friedmann equation can be derived from the RW metric, with one asserting it is a constraint and another seeking derivation resources. The discussion remains unresolved regarding the specifics of the derivation process and the stress-energy tensor involved.

Contextual Notes

Participants have not reached consensus on the derivation process, and there are unresolved questions regarding the specific assumptions and forms of the stress-energy tensor that apply to the Friedmann equation.

blumfeld0
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Hi does anyone know a website or paper where the friedmann equation is derived from the robertson walker metric?
it should have the calculation of atleast a few of the christoffel symbols etc

thanks

blumfeld
 
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The Friedmann equation can't be derived from the RW metric. It is a constraint on that metric, which is derived from the GR field equations. In other words, you can't derive it wityout the stress-energy tensor.
 
You may be interested in reading Relativity Demystified by David McMahon. On page 161 the following problem is worked out: Consider the Robertson-Walker metric and suppose we take the Einstein equation with nonzero constant, find the Friedman equations.
 
Hello Thank you for the reply
So the friedmann equation is a constraint on the metric derived from the stress energy tensor
what specific stress energy tensor is used? just the diagonal
{-rho, p, p ,p }?
also are theere any websites that have the derivation of this constraint equation from einsteins field equations>?
i will also try to check out the book you recommended
thanks!
 

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