Course Materials 

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Introduction

• Course Introduction PDF (1/27/21)
• Lorentz Transformations and Minkowski Diagrams (1/26/21)
• Subrahmanyan Chandrasekhar  Biography, Google Doodle
• Midterm Exam Topics
• New BH Image March 26 (14:44)
  • https://physicsworld.com/a/new-black-hole-image-reveals-magnetic-fields/
  • an observational paper and a theory paper,
• Falling Into A Black Hole - A Guided Experience (15:43)
• Final Exam Topics - New/ Last updated 4/22/21 at 12:30 PM

Special Relativity

• Dr. Herman's Notes
  • Figures from Minkowski diagram paper
    • Boost Axes,
    • Simultaneous Events in S
    • Time Dilation, fixed in S
    • Length Contraction, fixed in S
    • Time Dilation, fixed in S'
    • Length Contraction, fixed in S'
  • Train Problem
  • Boost Grids, Pics: beta = #/c - 1, 2, 3, 4, 5, 6, 7, 8, 9
• Brehme's Paper, Spactime Diagram Software
• Relativity Notes 
• Relativity Lecture Notes - with problems
• Think Like Einstein
• How Did Einstein Discover Relativity?
• Dummies guide to Special Relativity
• "On the Electrodynamics of Moving Bodies"
• Harris Notes

Four Vectors, Lagrangians, and Geodesics

• Four Vectors - at HyperPhysics or Wikipedia
• Basic Lagrangian Mechanics
• The Geodesic Equation -
• Derivation of Geodesic Equation - Derivation Handout
• Geodesics on a Sphere
• Christoffel Symbol Computation in Maple Christoffel.mws
• Wormhole Geodesic Computation and Handout - Handout
• Other Packages:
  • Sage Math
  • Maxima - Example, and ctensor example
  • Christoffel Symbols and Geodesic Equation - Mathematica

Schwarzschild Solution

• Schwarzschild Metric
• S. M. Carroll's Notes
• P. K. Townsend's Notes
• Eddington-Finkelstein coordinates (49:23)
• Maple Worksheets
  • Eddington-Finkelstein
  • Schwarz.mws,
  • Precession.mws (PDF Version)
• Geodesic Problem
• Penrose Diagrams Handout
• Lecture 23: Penrose Diagrams (1:28:01)
• Classical tests Handout
• Gravitational Collapse Physics Unsimplified (56:37)

Images of Black Holes

• Gravitational Lensing
  • Twin Quasar
  • Einstein Ring
  • Supernova Einstein Cross
  • The Strange Universe of Gravitational Lensing (13:31)
• Inside the black hole image that made history TED Talk (11:29)
• First Image of a Black Hole (5:28)
• Press Conference (52:36)
• Q&A with 2020 Nobel laureate Roger Penrose (27:38)
• Interactive visualization of a thin disk around a Schwarzschild black hole by  Thomas Müller
• Observing the shadow paper
• Null Geodesics Code - Papers 1, 2
• DNEG Gravitational Lensing Videos - or
  at IOP https://iopscience.iop.org/article/10.1088/0264-9381/32/6/065001/data

Kerr Solution

• Kerr BH Handout - New
• Ergosphere - Maple
• Roy Kerr – Rotating black holes (1:17:37)
• Lecture on Rotating Black Holes - Flournoy (1:06:58)
• Kerr-Newman Metric Review
• The Kerr metric, Teukolsky, 2015
• A Brief Introduction, Visser, 2008
• How Black Holes Spin Space Time (13:58)
• Building Gargantua - Part of Video (2.5 min)
• Honors Projects - Black Holes
• Measurement of Kerr Spin paper
• Spherical Photon Orbits, and Near Kerr naked singularities

Black Hole Thermodynamics

• Wald's Recollections
• Bekenstein's first papers 1, 2
• The Four Laws of Black Hole Mechanics
• Susskind on The Black Hole Wars
• Black Holes and the Structure of Spacetime by Juan Maldacena
• The Holographic Universe Explained
• "The Most Famous Paradox in Physics Nears Its End"
• Hawking and the information paradox
• Is The Universe a Hologram? (15:59)

Wormholes and Time Travel

• Wikipedia entry,
• Humanly Traversable Wormholes - Phys. Rev. D 2021
• Wormholes Open for Transport
• Wormholes, Time Machines, and the Weak Energy Condition
• Wormholes in spacetime and their use for interstellar travel: A tool for teaching
  general relativity
• The Meaning of Einstein's Equation
• Einstein's Equation -  PPT
• Einstein Field Equations for Beginners - YouTube Video
• Wormholes Untangle a Black Hole Paradox - article about ER = EPR and AMPS paper
• Cool horizons for entangled black holes
• The Holographic Universe Explained - (18:23)
• White Holes (13:26)

Other Links

• Professor Kip Thorne - Nonlinear Dynamics of Curved Spacetime 2015 (1:20:41)
• Kip S. Thorne - Geometrodynamics: 2019 (1:57:49)
• Black Hole Shadow
• Orbiting Photons
• Three types of singularities
• What goes on inside a black hole
• Gravitational Waves
  • Overview of gravitational waves and detectors (1:06:00)
  • LIGO Detections

  • Dr. Herman's

    • Gravitational Waves Derivation

    • Gravitational Waves Talk

    • When Black Holes Collide

• The Most Massive Black Hole Merger is 'Impossible' (20:26)

General Relativity

• Sean M. Carroll's Notes
• Physics Unsimplified

Handouts

• Minkowski Diagrams Paper
• Euler Equations and Geodesics
• Derivation of Geodesic Equation
• Wormhole Geodesic Computation and Handout
• Morris and Thorne paper

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