University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 11

Semester: 1

Availability restrictions: Normally only taken in the final year of an MPhys or MSci programme involving the School, or as part of MSc Astrophysics.

Planned timetable: 9.00 am Mon, Wed, Fri

This module covers: inertial frames, gravity, principle of equivalence, curvature of spacetime; basic techniques of tensor analysis; Riemannian spaces, metric tensor, raising and lowering of indices, Christoffel symbols, locally flat coordinates, covariant derivatives, geodesics, curvature tensor, Ricci tensor, Einstein tensor; fundamental postulates of general relativity: spacetime, geodesics, field equations, laws of physics in curved spacetime; distances, time intervals, speeds; reduction of equations of general relativity to Newtonian gravitational equations; Schwarzschild exterior solution, planetary motion, bending of light rays, time delays; observational tests of general relativity; Schwarzschild interior solution, gravitational collapse, black holes.

Relationship to other modules

Pre-requisite(s): Postgraduates: MSc Astrophysics students must discuss your prior learning with your adviser.. Before taking this module you must pass PH3081 or pass PH3082 or ( pass MT2506 and pass MT2507 )

Learning and teaching methods and delivery

Weekly contact: 3 lectures or tutorials.

Scheduled learning hours: 32

Guided independent study hours: 118

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 100%

As defined by QAA
Written examinations : 100%
Practical examinations : 0%
Coursework: 0%

Re-assessment: Oral Re-assessment, capped at grade 7

Personnel

Module coordinator: Dr M Dominik
Module teaching staff: Dr M Dominik
Module coordinator email md35@st-andrews.ac.uk

Additional information from school

The module provides an introduction to Einstein's theory of General Relativity. We lay the necessary grounds of differential geometry and tensor analysis with familiar concepts and non-relativistic mechanics before discussing the fundamental ideas behind Einstein’s theory. We show how Newton’s forces are being eliminated in favour of curvature of space-time, where matter and curvature are being related by Einstein’s gravitational field equations. We find Schwarzschild’s solution and discuss implications such as perihelion precession of planets, bending of light, gravitational redshift, time delay, black holes, and gravitational waves. Moreover, we show how General Relativity plays a role in current technology such as satellite navigation.

 

Aims & Objectives

The module should provide an introduction and applications to the theory of General Relativity, covering the following topics:

 

• the "need" for General Relativity and its historic evolution - fundamental principles of General Relativity
• the advanced mathematics required in order to apply the theory - derived predictions and their experimental tests
• application of general relativity in science and technology

 

Learning Outcomes

Students are expected to be able to

 

• understand the fundamental concepts of the theory of General Relativity
• practice tensor analysis to describe physical phenomena in curved space-time - derive the equations of motion from a given metric tensor
• compute the general-relativistic effects relevant to astronomy
• compute the effects of general relativity in modern technology

 

Synopsis

Curvilinear coordinates: basis and coordinates, reciprocal basis, metric, vector fields, tensor fields, coordinate transformations, affine connection;

Tensor analysis: covariant derivative, Riemann tensor, Einstein tensor;

Classical mechanics (review): principle of stationary action, Hamilton’s equations, Hamilton-Jacobi formalism;

Mechanics in curved space: equations of motion, embedding, geodesics, stationary paths, conserved quantities, Hamilton-Jacobi equation;

Special Relativity: Minkowski space, light cone, proper time, relativistic mechanics, energy-momentum tensor;

General Relativity: principles, Einstein’s field equations, cosmological constant, time and distance, synchronisation, Schwarzschild solution;

Consequences: relativistic Kepler problem, bending of light, gravitational redshift, time delay, satellite navigation, black holes, gravitational waves.

 

 

Recommended Books

Please view University online record: http://resourcelists.st-andrews.ac.uk/modules/ph5011.html

 

General Information

Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php.