Spring 2003

GENERAL RELATIVITY AND GRAVITATION

(Physics 255)

The course is intended as an introduction to the theory of General Relativity. No prior knowledge of General Relativity will be assumed, but some knowledge of special relativity and vector analysis is required; undergraduate and first year graduate students require consent of the instructor. Topics to be covered will include:

Special Relativity, Lorentz Transformations, Vector and Tensors, Energy-Momentum Tensor, Spin Four-vector, Electrodynamics, Relativistic Hydrodynamics.

Principle of Equivalence, Equations of Motion in a General Gravitational Field, Metric Tensor and Affine Connection, Newtonian Limit, Time Dilation and Gravitational Red Shifts. Mach’s Principle and Anisotropy of Inertia.

Principle of General Covariance, Tensor Algebra and Tensor Analysis, Covariant Differentiation, Parallel Transport of a Vector, Fermi-Walker Transport, Energy-Momentum Tensor, Riemann Curvature Tensor, Gravitation versus Curvilinear Coordinates, Bianchi Identities, Geodesic Deviation.

Einstein's Equations, Cosmological Constant, Action Principle. Brans-Dicke Theory. Energy, Momentum and Angular Momentum of Gravitation. Positivity of the Energy.

Classical Tests of General Relativity. The Schwarzschild Solution, Deflection of Light by the Sun, Precession of the Perihelion of Mercury, Radar Echo Delay.

Black Holes, Horizons and Singularity-free Coordinate Systems. Post-Newtonian Approximation, Lense-Thirring Effect, Weak Field Expansion, Polarization States, Gauge Invariance, Quadrupole Radiation and Gravitational Waves. Gravitons.

Idealized Cosmologies and the Evolution of the Universe, Red-Shift versus Distance Relation, Robertson-Walker Metric, the Standard Cosmological Model, Density and Pressure of the Present Universe, Radiation Versus Matter Dominated Evolution. Cosmological Constant. The Very Early Universe.

Recommended Books:

Gravitation and Cosmology, by Steven Weinberg (John Wiley, 1972).

Gravitation, by C.W. Misner, K.S. Thorne and J.A. Wheeler (W. Freeman, 1971).

Lectures on Gravitation, by Richard Feynman (Addison Wesley, 1998).

Flat and Curved Space-Times, by G.F.R. Ellis and R.M. Williams (Oxford University Press, 1988).

Herbert W. Hamber, FRH 3172 hhamber@uci.edu