Advanced Course in General Relativity - Lecture 2

Delve into the second lecture of an advanced course on general relativity, exploring effective equations for test particles, Newtonian theory, and relativistic orbits. Examine bound orbits, innermost stable circular orbits, and light trajectories in gravitational fields. Compare Newtonian and general relativistic approaches to orbital mechanics, discussing precision and typical velocities in the solar system. Investigate effective potentials, photon orbits, and the introduction of Kerr metric for stationary, axisymmetric spacetimes. Engage with concepts like gravitational radiation and static geometries through detailed explanations and Q&A sessions, enhancing understanding of advanced topics in general relativity.

Advanced course in general relativity Lecture - 2
Effective equations for a test particle
Newtonian theory
Restore epsilon to minus one
Newtonian case
GR case
Bound orbit
Innermost circular orbit
What is called innermost stable circular orbit radius?
What is the amount of precision compared to the Kepler problem in Newtonian theory?
Newtonian theory
What are the typical velocities in solar system?
Newtonian theory - Orbit is basically a conic section ellipse
Q&A
Analgesic equation
Light orbits
What is the effective potential?
Photon
Photon energies is lower than by L square by 2m
Q&A
Introduction of Karrdometric
What is the idea that fortune solution represents a static geometry?
Stationary; Axis symmetric
Coordinate system
What do you mean my gravitational radiation?
Q&A