Schwarzschild and Kerr Solutions of Einstein's Field Equation -- an introduction
arXiv:1503.02172 · doi:10.1142/S0218271815300062
Abstract
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.
96 pages, 17 figures, pdflatex. Invited review article. To appear in Wei-Tou Ni (editor) "One Hundred Years of General Relativity: Cosmology and Gravity," World Scientific, Singapore (2015)
References in corpus (20)
- The Confrontation between General Relativity and Experiment
- Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
- Phenomenology of the Lense-Thirring effect in the Solar System
- The Kerr spacetime: A brief introduction
- Myers-Perry black holes with scalar hair and a mass gap
- On the uniqueness of smooth, stationary black holes in vacuum
- Motion of spinning test bodies in Kerr spacetime
- Spin-torsion coupling and gravitational moments of Dirac fermions: theory and experimental bounds
- On the Gravitomagnetic Time Delay
- Clocks around Sgr A*
- Rigidly rotating ZAMO surfaces in the Kerr spacetime
- Discovering the Kerr and Kerr-Schild metrics
- Emergence of the Dirac Equation in the Solitonic Source of the Kerr Spinning Particle
- A space-time characterization of the Kerr-Newman metric
- Generalized gravitomagnetic clock effect
- Complex Structure of the Four-Dimensional Kerr Geometry: Stringy System, Kerr Theorem, and Calabi-Yau Twofold
- On the discovery of Birkhoff's theorem
- On non-disk geometry of r = 0 in Kerr-de Sitter and Kerr-Newman-de Sitter spacetimes
- Rigid Rotation and the Kerr Metric
- Race for the Kerr field
Cited by in corpus (13)
- Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
- Zero mass limit of Kerr spacetime is a wormhole
- Exact Solutions in Poincaré Gauge Gravity Theory
- Physically motivated ansatz for the Kerr spacetime
- Proposed method of combining continuum mechanics with Einstein Field Equations
- Painleve-Gullstrand coordinates versus Kerr spacetime geometry
- Gravitational lensing and shadow of charged black holes in the low-energy limit of string theory
- On the Kerr metric in a synchronous reference frame
- Hawking effect in an extremal Kerr black hole spacetime
- Rapid Spectral Parameter Prediction for Black Hole X-Ray Binaries using Physicalised Autoencoders
- Thermal radiation in curved spacetime using influence functional formalism
- Zero Mass limit of Kerr-MOG Black Hole Equals Wormhole
- A New Black Hole Solution In Dilaton Gravity Inspired By Power-Law Electrodynamics