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
41 - Nonperturbative Gravity: The Vacuum Schwarzschild Solution
from Part III - Other Spins or Statistics; General Relativity
Published online by Cambridge University Press: 04 March 2019
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
Summary
The nonpeturbative Schwarzschild solution of the Einstein's equations in vacuum is found. We start with the Newtonian limit for gravity, and find the metric in terms of the Newton potential. We write an ansatz, and solve the equations of motion to find the solution. The Schwarzschild black hole and its event horizon are defined. Birkhoff's theorem for the uniqueness of the Schwarzschild solution is stated.
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- Classical Field Theory , pp. 389 - 395Publisher: Cambridge University PressPrint publication year: 2019