Derivation of the Last Stable Circular Orbit at 6M.Taylor-Hulse Binary Neutron Star System.Relativistic Precession in the Weak-Field Limit.Keplers Third Law in the Schwarzschild Metric.Expand the Effective Potential in the Weak-Field Limit.Explain How these can be Numerically Integrated.Equations of Motion for a General Orbit.Compare Speeds and Energies for Bookkeeper and Shell Observers.Derive Analytic Results for Radial Motion.General Relativity and Black Holes (cont.) Derive the Full Expression for the Effective Potential.Use Euler Equations (for External Aging) in Connection with the Schwarzschild Metric to find Constants of the Motion E and L.The Differential Equations for G00 and G11.Symmetry Arguments for Why the Non-zero Components are Functions of Radius Only.Symmetry Arguments by Which 6 Schwarzschild Metric Tensor Components Vanish.Handout Defining Einstein Field Equations, Einstein Tensor, Stress-Energy Tensor, Curvature Scalar, Ricci Tensor, Christoffel Symbols, Riemann Curvature Tensor.Current S Status of Cosmology, Unsolved Puzzles.Acceleration Parameter as a Function of Scale Factor.Lookback Age as a Function of Z for Various Values of Omega m, Omega Lambda and Omega k.Relation between Scale Factor and Z from the Doppler Shift.Solutions for Various Combinations of Omega m, Omega Lambda and Omega k.Critical Closure Density Open, Closed, Flat Universes.Dynamical Equations for the Scale Factor a - Including Ordinary Matter, Dark Matter, and Dark Energy.Cosmological Redshifts and the Hubble Law.Analogy between the Metric Tensor and the Ordinary Potential, and between Einstein’s Field Equations and Poisson’s Equation.Relative Acceleration of Test Particles in Falling Elevator of Finite Size.Local Equivalence of Gravity and Acceleration.Strong and Weak Principles of Equivalence.The Equivalence Principle and General Relativity Magnetic Force due to Current-Bearing Wire.General Transformation Laws for E and B.Relativistic Invariant E 2 - p 2 for a Collection of Particles.Revisit the Relativistic Doppler Effect.Formal Transformation of E and P as a Four-Vector.Two Photons Producing an Electron/Positron Pair.Between Photon and Relativistic Particle.Absorption and Emission of Light Quanta.Relativistic Motion in a B Field, Lorentz Forceįurther Gedanken Experiments Relating to Mass-Energy Equivalence, Relativistic Momentum Relativistic Dynamics and Particle Physics (cont.) Atomic Mass Excesses, Semi-Empirical Binding Energy Equation.Kinetic Energy, Rest Energy, Equivalence of Mass-Energy.Relativistic Version of Work-Energy Theorem.Relativistic Relations between Force and Acceleration.Relativistic Momentum Inferred from Gedanken Experiment with Inelastic Collisions.Relativistic Dynamics and Particle Physics Optional Problems in the Use of the Calculus of Variations as Applied to Lagragian Mechanics and Other Problems in the Extremization of Path Integrals.Extremal Aging for Inertially Moving Clocks.The Euler-Lagrange Equations and Constants of the Motion.Short Discourse on the Calculus of Variations.Twin Paradox with Arbitrary Acceleration.Twin Paradox with Constant Velocity Plus a Reversal.Doppler Effect and Angle Transformation via Transformation of Phase of Plane Waves.Astrophysical Examples Relativistic and Superluminal Jets.Alternative Looks at Time Dilation and Length Contraction.Derivation of Lorentz-Einstein Transformations.First Discussion of Minkowski Diagrams, World Lines.Classical Wave Equations Transformation to Other Frames.Galilean Transformation, Inertial Reference Frames.Related Subjects Brief History of Physics.
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