Einstein field equations

General Relativity (Fall, 2012)

November 26, 2012

Professor Susskind derives the Einstein field equations of general relativity.  Beginning with Newtonian gravitational fields, an analogy with the four-current, and the continuity equation, he develops the stress-energy tensor (also known as the energy momentum tensor).  Putting these concepts together and generalizing the Newtonian field equation leads to the definition of the Ricci tensor, the Einstein tensor, and ultimately the Einstein field equations.  These equations equate curvature of spacetime as expressed by the Einstein tensor, with the energy and momentum within that spacetime as expressed by the stress–energy tensor.

  • Newtonian gravitational field
  • Continuity equation
  • Stress–energy tensor (also known as the energy-momentum tensor)
  • Curvature scalar
  • Ricci tensor
  • Einstein tensor
  • Einstein field equations