Spacetime and Gravity (STG | SPA6308)

Year: 3 | Semester: A | Level: 6 | Credits: 15

Course organiser: Prof David Berman | Course deputy: Dr Matthew Buican

Synopsis:

This course presents the essential concepts of both special and general relativity. The emphasis is on the physical understanding of the theory and the mathematical development is kept simple, although more detailed treatments are included for those who wish to follow them; space-time diagrams being are used extensively. The course includes discussion of the big bang and black holes.

Aims:

The aim of this course is to teach the essential concepts of both special and general relativity, at a level of mathematics suitable to second and third year students. The student will also be taught basic facts about current models of the Universe and black holes.

Outcomes:

By the end of this course, a student would be expected to: understand and use space-time diagrams to describe events, inertial observers and simultaneity; know the Relativity Principle and use Lorentz transformations to prove time dilation, length contraction and the transformation of velocities; define the invariant interval, proper time, timelike, null, and spacelike intervals, and relate these to the light-cone and causality; know and use the definitions of four-vectors, the invariant scalar product, timelike, null and spacelike 4-vectors, 4-velocity, 4-momentum and 4-momentum conservation; be able to describe inertial and gravitational mass and the Equivalence Principle, with an understanding of the consequences of the EP: bending of light, gravitational redshift; know and describe basic features of curved spacetime: coordinates, the line element and the metric; know in words what the Einstein equation describes and what a geodesic is; be able to use the Schwarzschild line element to derive asymptotic flatness and the gravitational redshift; know and describe qualitatively the solar system tests of General Relativity: perihelion precession of Mercury and light bending by the Sun; know and describe in appropriate coordinates the main features of the Schwarzschild black hole: light cones, the event horizon and the curvature singularity; be able to describe the reasons for the use of Kruskal-Szekeres coordinates and draw the Penrose diagram for the Schwarzschild solution; be able to summarise using words and diagrams key features of the known universe: matter and radiation, the cosmic microwave background radiation, dark matter, the expansion of the Universe, the Hubble Law, the Big Bang plus be aware of the assumptions of spatial homogeneity and isotropy and the Cosmological Principle.

Recommended books:

Rindler, W.
Relativity: special, general and cosmological
Oxford University Press, (2001)
ISBN 0-19-850836-0

Hartle, J.B.
Gravity: an introduction to Einstein's general relativity
Addison-Wesley, (2003)
ISBN 0-8053-8662-9