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Black Hole Image Simulation
Black Hole Embedded Diagram
Wormhole Embedded Diagram
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Table of Contents
1. Introduction
1.1 Notation
2. General Relativity and Tensor Calculus
2.1 Line Elements and the Metric Tensor
2.2 Euclidean Geometries and the Minkowski Spacetime
2.3 Deriving the Geodesic Equations
2.4 The Curvature Tensor
2.5 Einstein Tensor and the Energy Momentum Tensor
2.6 The Einstein Field Equations
3. Ray Tracing in the Schwarzschild Geometry
3.1 The Schwarzschild Metric
3.2 The Equations of Motion
3.3 Ray Tracing in the Schwarzschild Geometry
3.4 The Backwards Ray Tracing Algorithm
4. Schwarzschild Black Hole’s Appearances and Properties
4.1 Gravitational Lensing
4.2 Image Analysis and the Einstein Ring
4.3 The Impact Parameter and the Photon Sphere
4.4 Effective Potential
4.5 Singularities
5. Ray Tracing in Wormhole Geometries
5.1 Introduction to Wormholes
5.2 The Ellis Wormhole
5.3 The Three-Parameter Wormhole
5.4 Producing the Embedded Diagrams
5.5 Images of Wormholes
5.6 The Equations of Motion
5.7 Mapping a Point on the Camera to the Celestial Sphere
5.8 The Backwards Ray Tracing Algorithm
6. Wormhole’s Appearances and Properties
6.1 Altering the Wormhole’s Length
6.2 Altering the Wormhole’s Lensing Width
6.3 Traveling Through Interstellar’s Wormhole
6.4 Effective Potential
7. Conclusion
References