Course guide of General Relativity (26711C1)

Curso 2024/2025
Approval date: 11/06/2024

Grado (bachelor's degree)

Bachelor'S Degree in Physics




Relatividad y Teoría de Campos y Partículas


Relatividad General

Year of study




ECTS Credits


Course type

Elective course

Teaching staff


  • Bert Janssen . Grupo: B
  • Javier Antonio Olmedo Nieto. Grupo: A


  • Mar Bastero Gil Grupo: 1
  • Bert Janssen Grupo: 2

Timetable for tutorials

Bert Janssen

  • Monday de 10:00 a 12:00 (Despacho 21)
  • Tuesday de 10:00 a 12:00 (Despacho 21)
  • Friday de 11:00 a 13:00 (Despacho 21)

Javier Antonio Olmedo Nieto

  • Tuesday de 11:00 a 13:00 (Despacho 19)
  • Wednesday de 14:00 a 16:00 (Despacho 19)
  • Thursday de 11:00 a 13:00 (Despacho 19)

Mar Bastero Gil

  • Tuesday de 11:00 a 13:00 (Despacho 23)
  • Wednesday de 16:00 a 18:00 (Despacho 23)
  • Thursday de 16:00 a 18:00 (Despacho 23)

Prerequisites of recommendations

  • Métodos Matemáticos I, II, III
  • Análisis matemático I, II
  • Álgebra lineal y Geometría
  • Mecánica y Ondas
  • Electromagnetismo

Brief description of content (According to official validation report)

  • Review of Special Relativity
  • Bases of Differential Geometry
  • Einstein equations
  • Classical Tests of General Relativity
  • Exact solutions: black holes, gravitational waves and cosmological models

General and specific competences

General competences

  • CG01. Skills for analysis and synthesis
  • CG02. Organisational and planification skills
  • CG05. Skills for dealing with information
  • CG06. Problem solving skills
  • CG08. Critical thinking
  • CG09. Autonomous learning skills

Specific competences

  • CE01. Knowing and understanding the phenomena of the most important physical theories
  • CE02. Estimating the order of magnitud in order to interpret various phenomena
  • CE03. Knowing and understanding the mathematical methods necessary to describe physical phenomena
  • CE05. Modelling complex phenomena, translating a physical problem into mathematical language
  • CE09. Applying mathematical knowlegde in the general context of Physics

Objectives (Expressed as expected learning outcomes)

  • Knowledge of General Relativity as the modern theory of gravity
  • Comprehend the importance of symmetries in Physics and being able to apply them
  • Notions of geometry in curved space
  • Knowledge of the Einstein equations and its implications
  • Knowledge of black holes, gravitational waves and cosmological models

Detailed syllabus


  1. Special Relativity - Lorentz transformations
  2. Minkowski space; four-vectors; Lorentz group
  3. Relativistic mechanics and electromagnetism in covariant formulation
  4. Manifolds and general coordinate transformations
  5. Tensor calculus; affine connections; covariant derivative
  6. Curvature tensors; geodesics
  7. The Equivalence Principle
  8. The energy-momentum tensor
  9. The Einstein Equations
  10. Physics in curved space
  11. Classical tests of General Relativity
  12. Schwarzschild black hole: causal structure and interpretation
  13. Gravitational waves: linearised theory; gravitational waves as perturbations; detection
  14. Cosmological models: FWR metrics; cosmological solutions


  1. Problems and exercises of the theory
  2. Asistence in specialised seminars


Basic reading list

  • Bert Janssen, Teoría de la Relatividad General, Universidad de Granada, 2020
  • Bert Janssen, Gravitación y Geometría, Editorial Universidad de Granada, 2021.
  • R. D'Inverno, Introducing Einstein's Relativity, Oxford University Press, 1992.
  • S. Carroll, Spacetime and Geometry, Addison-Wesley, 2004.
  • S. Weinberg, Gravitation and cosmology, Wiley, 1972.

Complementary reading

  • C. Misner, K. Thorn, A. Wheeler, Gravitation, Freeman, 1973
  • R. Wald, General Relativity, Chicago University Press, 1984.
  • H. Stefani, General Relativity, Cambridge University Press, 1982.
  • B.F. Schutz, A first course in General Relativity, Cambridge University Press, 1985.
  • J. Hartle, Gravity, Addison-Wesley, 2003.
  • E. Poisson, A relativist's Toolkit, Cambridge University Press, 2004.
  • T.P. Cheng, Relativity, Gravitation and Cosmology, Oxford University Press, 200

Recommended links

Teaching methods

  • MD01. Theoretical classes

Assessment methods (Instruments, criteria and percentages)

Ordinary assessment session

Continuous evaluation:

  • Exercises to be handed in & tests (30%)
  • Final exam (70%).

In order to succed for this course, the student must obtain at least 50% of the score of the final exam.

Extraordinary assessment session

The extraordinary assessment session will consist of the same tests as the Unique Final Evaluation. The student will have the oportunity to obain 100% of the score.

Single final assessment

Final exam (100%)

Additional information

Información de interés para estudiantado con discapacidad y/o Necesidades Específicas de Apoyo Educativo (NEAE): Gestión de servicios y apoyos (