Channel: Andrew Dotson

Category: Education

Tags: oduriccigeneral relativitycalculuscurvatureequationsnmsumajorphysicsriemanndotsonmotivatingdegreepoissongradschooltensorphdandrewscalarfieldmetricgravitygradstudentderivationeinstein

Description: Today we use all the tools we've got in our back pocket to "derive" the Einstein Field Equations of general relativity. It's more of a motivation than a derivation, I suppose. This series is based off the book "Tensor Calculus for Physics" by Dwight Neuenschwander: amzn.to/3rEema3 Video relating metric to gravitational potential: youtube.com/watch?v=kIi-qcSBa4w&t=69s&ab_channel=AndrewDotson Video deriving contracted bianchi identity: youtube.com/watch?v=zmWLUex-hGM&ab_channel=AndrewDotson Deriving the Riemann Curvature Tensor: youtube.com/watch?v=L8ISLzDYl68&t=1331s&ab_channel=AndrewDotson Uniqueness of Riemann Curvature Tensor: vixra.org/pdf/1912.0357v1.pdf or physics.stackexchange.com/questions/315374/on-the-uniqueness-of-the-riemann-christoffel-tensor 0:00 Intro 1:40 Goal: Generalize Poissons Equation 4:40 Criteria for Field Equations 12:09 What Could They be in Terms of? 15:13 "Guessing" the Form of the EFE's 18:41 Finding the Coefficients 32:23 Writing Down Einsteins Equations 33:52 Important Interpretation 34:04 Conclusion