PH40137: Advanced general relativity
[Page last updated: 29 April 2025]
| Academic Year: | 2025/26 |
| Owning Department/School: | Department of Physics |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Masters UG & PG (FHEQ level 7) |
| Period: |
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| Assessment Summary: | EXOB 100% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | Before taking this module you must ( take PH10103 OR take PH32018 OR take PH20106 OR take PH20114 OR take PH20076 ) AND ( take PH20107 OR take MA20223 ) AND take AT LEAST 1 MODULE FROM {PH20016, PH32018, PH20076} |
| Learning Outcomes: |
After taking this unit the student should be able to:
show proficiency in calculations involving tensors (inner and outer products, contraction, parallel transport);
outline the basics of geometric/coordinate-free vector and tensor analysis;
perform covariant differentiation of tensor quantities in curved space, and discuss the foundations of differential geometry;
provide a physical explanation of the Einstein field equations;
show how the Schwarzschild, Kerr, and Friedman-Robertson-Walker metrics are exact solutions to the Einstein equations. |
| Synopsis: | Through this unit, you will develop a more mathematically rigorous understanding of general relativity, including deriving the Einstein field equations and exploring the black hole and cosmological solutions. |
| Content: | Vectors, one-forms and tensors. Vector spaces, manifolds and tangent spaces. Einstein summation convention. Curvilinear coordinates. Tensor operations, covariant differentiation. Review of special relativity, spacetime metric and geodesics. Local coordinates. Locally inertial frames. The Riemann tensor. The Bianchi identity, The Ricci tensor. Curvature scale. The Stress-energy tensor. Energy as the source of gravity. The dynamics of a pressure-less dust. Conservation laws. Perfect fluids. The Einstein field equations. The Einstein tensor. The cosmological constant. Interpreting the field equations. Killing Vectors. Schwarzschild and Kerr spacetimes. The Friedmann-Robertson-Walker metric. Cosmological dynamics. |
| Course availability: |
PH40137 is Compulsory on the following courses:Department of Physics
PH40137 is Optional on the following courses:Department of Physics
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Notes:
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