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PHY1483H F (Arts & Sci 483)Relativity Theory I

Course Title PHY1483H F (Arts & Sci 483)
Session fall
Year of Study 1st year
Time and Location This cross listed course is offered at together with PHY483F. For course schedule please see: PHY483F
Course Homepage Link to Course Homepage

A.W.  Peet
MP1118
416-978-3911

Homepage

Official Description


This cross listed course is offered at together with PHY483F. For course schedule please see
 https://www.physics.utoronto.ca/students/undergraduate-courses/current/phy483h1

Special relativity and tensors

 Galilean relativity and 3-vectors. Special relativity and 4-vectors. Relativistic particle. Electromagnetism. Constant relativistic acceleration.

Spacetime

Equivalence principle. Spacetime as curved manifold. Tensors in curved spacetime. Rules for tensor index gymnastics.

The covariant derivative

How basis vectors change: the affine connection. Covariant derivative and parallel transport. Geodesic equations.

Spacetime curvature

Curvature and Riemann tensor. Riemann normal coordinates and the Bianchi identity. Information in Riemann.

The physics of curvature

Geodesic deviation. Tidal forces. Taking the Newtonian limit.

The power of symmetry, and Einstein's equations

Lie derivatives. Killing tensors. Maximally symmetric spacetimes. Einstein's equations.

Black hole basics

Birkhoff's theorem and the Schwarzschild solution. TOV equation for a star. Geodesics of Schwarzschild. 

More advanced aspects of black holes

Causal structure of Schwarzschild. Reissner-Nordstrom black holes. Kerr black holes. The Penrose process.

Classic experimental tests of GR

Gravitational redshift. Planetary perihelion precession. Bending of light. Radar echoes. Geodesic precession of gyros. Accretion disks.

Gravitational waves

The wave equation for metric perturbations. Solving the linearized Einstein equations. Energy loss from gravitational radiation.

 ASSESSMENT

 Four homework assignments worth 10% each, midterm 20%, final exam 35%, tutorial participation 5%.

This cross listed course is offered at together with PHY483F. For course schedule please see: TBA

Textbook M.P. Hobson, G. Efstathiou, and A.N. Lasenby, General Relativity: An Introduction for Physicists (Cambridge, 2006).