PH5011 General Relativity

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

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

Module Staff

TBC

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module provides an introduction to the theory of General Relativity. After laying the required foundations in mathematics and theoretical physics, it demonstrates how relativistic mechanics differs from non-relativistic mechanics. The module concludes with discussing observable effects of General Relativity and how they affect our understanding of nature and the Universe.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS PH3081 OR PASS PH3082 OR ( PASS MT2506 AND PASS MT2507 )

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral Re-assessment, capped at grade 7

Learning and teaching methods and delivery

Weekly contact

3 lectures or tutorials

Scheduled learning hours

30

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

120

The number of hours that students are expected to invest in independent study over the period of the module.

Additional information from school

Overview

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, cosmological redshift & Friedmann equations, Maxwell’s equations in GR, 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 https://www.st-andrews.ac.uk/physics-astronomy/students/ug/timetables-handbooks/.