Course11510679368 lectures
Introduction to General Relativity
Prof. Shubho R. Roy and Prof. Arpan Bhattacharyya · IIT Hyderabad and IIT Gandhinagar
About
This is an intermediate-to-advanced course in Einstein's general relativity theory and its application to the universe at large scales (cosmology). The first part of the course is dedicated to elementary topics, such as a review of Newton’s non-relativistic theory of gravitation and special relativity. The second part aims to synthesize special relativity and Newton’s gravity consistently, thereby leading to general relativity as the (unique) relativistic theory of gravitation. The third part is dedicated to mathematical preliminaries such as differential geometry (tensor calculus) followed by Riemannian geometry culminating in the Einstein field equations and a few simple solutions of the Einstein field equations: gravitational waves and the Schwarzschild black hole. The final part of the course is dedicated to the application of general relativity to the large-scale structure of the universe - we will review the basics of standard Lambda CDM cosmology and if time permits, an introduction to inflationary cosmology.
Intended audience: Advanced Masters (Physics) Students, Beginning PhD students, Advanced Undergraduate Students (Physics/Engineering Physics)
Prerequisites: Maxwell Electrodynamics, Analytical Mechanics, Mathematical Methods for Physics/Engineering, Special Relativity
Lectures
Week 1
- Newton's Gravitation: Part-I
- Newton's Gravitation: Part-II
- Newton's Gravitation: Part-III
- Newton's Gravitation: Part-IV
- Newton's Gravitation: Tutorial-1
- Newton's Gravitation: Tutorial-2
Week 2
- Special Relativity Review
- Minkowski Spacetime
- Lorentz Group: Part-I
- Lorentz Group: Part-II
- Topology of Lorentz Group
- Lorentz Group: Tutorial
- Relativistic index/component notation
Week 3
- Tensor analysis-I
- Tensor analysis-II
- Tensor analysis-III
- Introduction to differential forms
- Exterior Calculus
- Differential Forms: Tutorial
Week 4
- Free Point Particle-I
- Free Point Particle-II
- Point Particle with interactions
- Tensor Fields
- Point Particle with interactions: Tutorial
Week 5
- Covariant equations for Fluid mechanics-I
- Covariant equations for Fluid mechanics-II
- Stress-Energy-Momentum Tensor: Tutorial
- Electrodynamics in Lorentz covariant form-I
- Electrodynamics in Lorentz covariant form-II
- Electrodynamics in Lorentz covariant form: Tutorial
Week 6
- Alternative route to Maxwell's equations from Electrostatics-I
- Alternative route to Maxwell's equations from Electrostatics-II
- Towards a Lorentz covariant formulation for Newton's gravitation-I
- Towards a Lorentz covariant formulation for Newton's gravitation-II
- Consistent coupling of gravity to matter-1
- Consistent coupling of gravity to matter-II
- Covariance vs Invariance principles
Week 7
- Mathematical Preliminaries-1: Basics of Point-Set Topology 1
- Mathematical Preliminaries-1: Basics of Point-Set Topology 2
- Mathematical Preliminaries-1: Basics of Differential Geometry-1
- Mathematical Preliminaries-1: Basics of Differential Geometry 2
- Mathematical Preliminaries-1: Calculus on manifolds 1
- Mathematical Preliminaries-1: Calculus on manifolds 2
Week 8
- Mathematical Preliminaries-II: Riemannian manifolds
- Mathematical Preliminaries-II: Riemannian Geometry
- Mathematical Preliminaries-II: Riemannian Geometry
- Mathematical Preliminaries-II: Riemannian Geometry
- Mathematical Preliminaries-II: Riemannian Geometry
Week 9
- Geodesic Deviation and the Riemann Curvature tensor
- Principle of Minimal Coupling
- Einstein Field Equations-I
- Einstein Field Equations-II
- Weak field limit: Linearized GR
- Gravitational Waves
Week 10
- Gravitational Radiation
- Schwarzschild Solution-I
- Schwarzschild Solution-II
- Schwarzschild Solution-III
Week 11
- Timelike geodesics in Schwarzschild geometry
- Precession of perihelion of planets
- Lightlike geodesics in Schwarzschild geometry
- Gravitational Deflection & Retardation of light
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Hyderabad and IIT Gandhinagar
- Department
- Physics
- Taught by
- Prof. Shubho R. Roy, Prof. Arpan Bhattacharyya
- Level
- Undergraduate
- Language
- English
- Subjects
- Physics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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