Constructing solutions to Einstein Field Equation

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SUMMARY

The discussion focuses on constructing solutions to the Einstein Field Equations (EFE), highlighting the challenges in finding exact solutions. Key metrics such as the Schwarzschild and Kerr metrics were mentioned as examples of solutions developed with specific goals. The conversation emphasizes the scarcity of physically relevant exact solutions since the EFE's inception nearly a century ago. Recommended resources include Wald's "General Relativity" and specific literature on the subject.

PREREQUISITES
  • Understanding of the Einstein Field Equations
  • Familiarity with general relativity concepts
  • Knowledge of the Schwarzschild and Kerr metrics
  • Basic mathematical skills in differential geometry
NEXT STEPS
  • Study Wald's "General Relativity," particularly Chapter 7
  • Research methods for constructing exact solutions to the EFE
  • Explore literature on the Schwarzschild and Kerr metrics
  • Investigate advanced mathematical techniques in differential geometry
USEFUL FOR

Physicists, mathematicians, and students of general relativity seeking to deepen their understanding of the Einstein Field Equations and their solutions.

NotASmurf
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The swartzchild metric, the kerr metric etc. where constructed with specific goals in mind, how does one go about doing that with goals in mind? Any help or comments appreciated. I don't expect a guide, I doubt one exists,
 
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Exact solutions of the Einstein field equations are notoriously difficult to find. In the almost 100 years since the EFE's discovery by Einstein, only a select few physically pertinent exact solutions have been found. There are whole books written on this subject (see e.g. https://www.amazon.com/dp/0521467020/?tag=pfamazon01-20), and there are several different methods worth trying. As an introduction, I might recommend Wald's "General Relativity" chapter 7.
 
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Thanks, useful and timeous as every matterwave.
 

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