**Duration:** 21 weeks.

**Number of lectures per week:** 3

**Assessment:**

**End-of-year Examination:** One 3-hour examination

**Description: **This course gives an introduction to relativity and
cosmology.

**General Relativity** *Mathematical background* tensors,
covariant derivatives, geodesics, Killing's equation, the Riemann
tensor, physical meaning of the Riemann tensor. *The Einstein
equation and general relativity* the Einstein equation, the
cosmological constant, the weak field limit, the Schwartzschild
geometry, the bending of light by the sun and the perihelion of
Mercury. *Field theory methods* the Einstein-Hilbert action and
the vacuum Einstein equations, the introduction of matter and the
unified action.

**Cosmology** *Introduction* description of the universe, the
assumptions of cosmology, Obler's paradox. *Robertson-Walker
metric* the Robertson-Walker metric, the RW-Freidman equations and
their solutions for a dust universe and for a flat radiation universe,
discussion of mixtures, the age of the universe, the flatness
problem. *The cosmological constant* including the cosmological
constant, de Sitter space, cosmological evolution, the age of the
universe. the Hubble law for red-shift, *q*. *Inflation* the
inflaton, slow-roll inflation.

**Special Topics** *Gravitational radiation* the linearized
Einstein equations, the harmonic gauge, plane waves, counting the
polarizations for plane waves. *Kaluza Klein theory* Kaluza-Klein
theory, reducing general relativity on Kaluza-Klein space-time to
four-dimensions, momentum as charge, vacuum solutions.

Apr 9, 2003

File translated from T

On 9 Apr 2003, 14:02.