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8.962

General Relativity

4-0-8 units · Graduate

The basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.

Spring 2020

Topics

  • Introduction and the Geometric Viewpoint on Physics
  • Introduction to Tensors
  • Tensors Continued
  • Volumes and Volume Elements; Conservation Laws
  • The Stress Energy Tensor and the Christoffel Symbol
  • The Principle of Equivalence
  • The Principle of Equivalence Continued; Parallel Transport
  • Lie Transport, Killing Vectors, Tensor Densities
  • Geodesics
  • Spacetime Curvature
  • More on Spacetime Curvature
  • The Einstein Field Equation
  • The Einstein Field Equation (Variant Derivation)
  • Linearized Gravity I: Principles and Static Limit
  • Linearized Gravity II: Dynamic Sources
  • Gravitational Radiation I
  • Gravitational Radiation II
  • Cosmology I
  • Cosmology II
  • Spherical Compact Sources I
  • Spherical Compact Sources II
  • Black Holes I
  • Black Holes II
  • Advanced Topics I (not video captured)
  • Advanced Topics II (not video captured)

Readings

  • Carroll, Sean M. Spacetime and Geometry: An Introduction to General Relativity . Cambridge University Press, 2019. ISBN: 9781108488396.
    Required
  • Misner, Charles W., Thorne, K. S., & Wheeler, J. A. Gravitation . Princeton University Press, 2017. ISBN: 9780691177793.
    Listed reading
  • Universally known as MTW. A nice reference once you already know GR thoroughly; not so great if you are studying it for the first time. Very good for certain important topics (e.g., spherically symmetric stars, black holes); a few readings will be assigned from this volume. Carrying this textbook around for several weeks is an excellent way to strengthen your lower back.
    Listed reading
  • Schutz, Bernard. A First Course in General Relativity . 2nd Edition. Cambridge University Press, 2009. ISBN: 9780521887052.
    Listed reading
  • Hartle, James B. Gravity: An Introduction to Einstein’s General Relativity . Harlow: Pearson, 2003. ISBN: 9780805386622.
    Listed reading
  • Weinberg, Steven. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity . Wiley India, 2008. ISBN: 9788126517558 .
    Listed reading
  • This textbook was originally published at almost the same time as MTW; as a consequence, several generations of GR students were educated using either MTW or Weinberg. Takes a rather different point of view, trying to avoid becoming enraptured by the notion of geometry. Instead, Weinberg presents GR, as much as possible, as a classical field theory like any other. Time has not been terribly kind to this viewpoint, so this text is now considered somewhat deprecated. Nonetheless, it is beautifully written and very clear. Worth knowing.
    Listed reading
  • Wald, Robert M. General Relativity . University of Chicago Press, 1984. ISBN: 9780226870335.
    Listed reading
  • Poisson, Eric. A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics . Cambridge University Press, 2008. ISBN: 9780521537803.
    Listed reading

Prerequisites & course information

Prereq: 8.07 , 18.03 , and 18.06 G (Spring) 4-0-8 units

Sources