Initial Data for General Relativity: EFE

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SUMMARY

The discussion focuses on the initial data requirements for solving the Einstein Field Equations (EFE) in general relativity (GR). It emphasizes the necessity of understanding the energy-momentum tensor and its coupling with the metric to determine the metric at later times. The Cauchy problem is highlighted as a critical topic, with references to chapter 10 of "General Relativity" by Wald and additional online resources for further reading. The conversation underscores the importance of foundational knowledge in GR to navigate the complexities of initial data.

PREREQUISITES
  • Understanding of Einstein Field Equations (EFE)
  • Familiarity with the energy-momentum tensor
  • Knowledge of the Cauchy problem in general relativity
  • Basic grasp of metric tensors and their role in GR
NEXT STEPS
  • Read chapter 10 of "General Relativity" by Wald for a comprehensive overview of the Cauchy problem
  • Explore the provided online resources on the Cauchy problem for additional insights
  • Study chapter 27 of Geroch's GR notes for further clarification on initial data
  • Investigate advanced texts on initial value problems in general relativity for deeper understanding
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on general relativity and the mathematical foundations of the Einstein Field Equations.

HomogenousCow
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I'm getting pretty lost with how initial data works in general relativity.
Assuming the energy momentum tensor is known (coupled with the metric somehow), what is initial data required to determine the metric at all later times?
 
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The initial value problem is an extremely standard topic in most (all?) advanced GR texts. You would benefit much more from a thorough reading of a chapter on the Cauchy problem from a GR text and subsequently asking more specific questions here. See for example chapter 10 of Wald. You can also find a lot of readings online on the Cauchy problem e.g.

http://www.icm2006.org/proceedings/Vol_III/contents/ICM_Vol_3_22.pdf

http://arxiv.org/pdf/gr-qc/0002074v1.pdf

http://projecteuclid.org/download/pdf_1/euclid.cmp/1103841822

See also chapter 27 of Geroch's GR notes: http://home.uchicago.edu/~geroch/Links_to_Notes.html
 
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