»

Relativity

Staff members

Staff member Duty Term(s)
Prof Mike HobsonLecturer

The course contact is shown in bold.

Handouts

At present handouts are only available to visitors with a Raven password. The visibility of handouts depends on your permissions as you view this page: some may be restricted to staff and other supervisors.

If the lecturer or course contact has a private web page, listed under "Links" below, then the level of access to that page is determined by them, and not by the Physics Teaching System.

Pt II Relativity
 Examples sheet 1Part IIProblem sheet13/10/14 12:44:03
 Topic 1Part IIHandout10/10/14 13:03:41
 Topic 2Part IIHandout13/10/14 12:43:38
 Topic 3Part IIHandout17/10/14 12:15:32

Course description

(preview/print)

Relativity 2014-15
Prof Mike Hobson

Synopsis

Foundations of special relativity: Inertial frames, spacetime geometry, Lorentz transformations, spacetime diagrams, length contraction and time dilation, Minkowski line element, particle worldlines and proper time, Doppler effect, addition of velocities, acceleration and event horizons in special relativity.

Manifolds, coordinates and tensors: Concept of a manifold, curves and surfaces, coordinate transformations,  Riemannian geometry, instrinsic and extrinsic geometry, the metric tensor, lengths areas and volumes, local Cartesian coordinates, tangent spaces, pseudo-Riemannian geometry, scalar, vector and tensor fields,  basis vectors, raised and lowered indices, tangent vectors, the affine connection, covariant differentiation, intrinsic derivative, parallel transport, geodesics.

Minkowski spacetime and particle dynamics: Cartesian inertial coordinates, Lorentz transformations,  4-tensors and inertial bases, 4-vectors and the lightcone, 4-velocity, 4-acceleration, 4-momentum of massive and massless particles, relativistic mechanics, accelerating observers, arbitrary coordinate systems.

Electromagnetism: the electromagnetic force, the 4-current density, the electromagnetic field equations, the electromagnetic field tensor, the Lorentz gauge, electric and magnetic fields, invariants, electromagnetism in arbitrary coordinates.

The equivalence principle and spacetime curvature: Newtonian gravity, the equivalence principle, gravity as spacetime curvature, local inertial coordinates, observers in a curved spacetime, weak gravitational fields, intrinsic curvature, the curvature tensor, the Ricci tensor, parallel transport, geodesic deviation, tidal forces, minimal coupling procedure.

Gravitational field equations: the energy-momentum tensor, perfect fluids, relativistic fluid dynamics, the Einstein equations, the weak field limit, the cosmological constant, particle motion from the field equations.

Schwarzschild spacetime: static isotropic metrics, solution of empty-space field equations, Birkhoff’s theorem, gravitational redshift, trajectories of massive particles and photons. Singularities, radially infalling particles, event horizons, Eddington-Finkelstein coordinates,  gravitational collapse, tidal forces, Hawking radiation.

Experimental tests of general relativity:  precession of planetary orbits, the bending of light, radar echoes, accretion discs around compact objects, gyroscope precession.

Friedmann-Robertson-Walker spacetime: the cosmological principle, comoving coordinates, the maximally-symmetric 3-space, the FRW metric, geodesics, cosmological redshift, the cosmological field equations.

Kerr spacetime: the general stationary axisymmetric metric, the dragging of inertial frames, stationary limit surfaces, event horizons, the Kerr metric, structure of a rotating black hole, trajectories of massive particles and photons, Penrose process.

Linearised gravity and gravitational waves:  weak field metric, linearised field equations, Lorenz gauge, wave solutions of linearised field equations.

Topics in italics are non-examinable, and might be omitted.

BOOKS

General relativity: an introduction for physicists, Hobson M P, Efstathiou G P & Lasenby A N (CUP 2005). This covers all parts of the course.

Relativity: special, general and cosmological, Rindler W (OUP 2001). Good for the concepts and methods. Provides a lot of physical and geometrical insight.

Introducing Einstein's Relativity, d'Inverno R (OUP 1992). Provides a clear description covering most of the gravitation course material.

Gravity: an introduction to Einstein’s general relativity, Hartle J B (Addison Wesley 2003). A clear introduction that does not rely too much on tensor methods.

Spacetime and geometry, Carroll S M (Addison Wesley 2004). A very thorough, yet highly readable, introduction to general relativity and the associated mathematics

General theory of relativity, Dirac P A M (yes, that Dirac…!) (Princeton University Press 1996). A short and well-argued account of the mathematical and physical basis of general relativity. Probably only useful once you already understand the subject.

 

 


Other Links