Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- 33 Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
- 34 Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
- 35 Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
- 36 Fermions and Dirac Spinors
- 37 The Dirac Equation and Its Solutions
- 38 General Relativity: Metric and General Coordinate Invariance
- 39 The Einstein Action and the Einstein Equation
- 40 Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
- 41 Nonperturbative Gravity: The Vacuum Schwarzschild Solution
- 42 Deflection of Light by the Sun and Comparison with General Relativity
- 43 Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
- 44 Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
- 45 Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
- 46 Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
- References
- Index
42 - Deflection of Light by the Sun and Comparison with General Relativity
from Part III - Other Spins or Statistics; General Relativity
Published online by Cambridge University Press: 04 March 2019
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- 33 Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
- 34 Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
- 35 Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
- 36 Fermions and Dirac Spinors
- 37 The Dirac Equation and Its Solutions
- 38 General Relativity: Metric and General Coordinate Invariance
- 39 The Einstein Action and the Einstein Equation
- 40 Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
- 41 Nonperturbative Gravity: The Vacuum Schwarzschild Solution
- 42 Deflection of Light by the Sun and Comparison with General Relativity
- 43 Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
- 44 Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
- 45 Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
- 46 Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
- References
- Index
Summary
We calculate “deflection of light by the Sun." First, we define a first-order action for a massless particle moving in a gravitational field, and then we calculate the motion of light on a geodesic as motion of light in a medium with a small, position-dependent index of refraction, giving the light deviation for small angles. Then we redo the calculation from the Hamilton–Jacobi formalism by first defining the Hamilton–Jacobi equation for light motion and then solving it. This gives the nonperturbative light deviation that matches the previous calculation at small angles. We end by comparison with the deflection of light by the Sun in special relativity, which is different by a factor of 2.
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- Classical Field Theory , pp. 396 - 404Publisher: Cambridge University PressPrint publication year: 2019