The equivalence principle and tensor analysis

General Relativity (Fall, 2012)

September 24, 2012

The principle of equivalence of gravity and acceleration, or gravitational and inertial mass is the fundamental basis of general relativity.   This was Einstein's key insight.  Professor Susskind begins the first lecture of the course with Einstein's derivation of this equivalence principle.  He then moves on to the mathematics of general relativity, including generalized coordinate transformations and tensor analysis.  This topic includes the important point that the determination as to whether a spatial geometry is flat (i.e. Euclidean) is equivalent in some respects to the determination of whether an object is in a gravitational field, or merely an accelerated reference frame.

  • The equivalence principle
  • Accelerated reference frames
  • Curvilinear coordinate transformations
  • Effect of gravity on light
  • Tidal forces
  • Euclidean geometry
  • Riemannian geometry
  • Metric tensor
  • Distance measurement in a curved geometry
  • Intrinsic geometry
  • Flat spacetime
  • Einstein summation convention
  • Covariant and contravariant vectors and tensors