Jorge
Pullin
The graphics from Pullin's
talk are here in seven web pages. Click on the indicated subject to go to the relevant
page. You can also download a
PDF version.
**pg. 1**
Pullin began the workshop with a succinct account of GR. He
pointed participants to more information in
Wikipedia, noting especially
Sean Carroll's
no-nonsense introduction, and then he
outlined his talk.
**pg. 2** He
gave a one-slide summary
of the special relativity needed to understand general relativity, and
then showed the essence of GR:
gravity is curvature of
spacetime and the spacetime
interval is the measure of "distance".
**pg. 3 **To describe
curved space you need tensors.
Trajectories are curves
parameterized by the proper time, and absent forces, these are straight
lines in spacetime. For vector algebra you need a metric; for vector
calculus you need the
covariant derivative.
**pg. 4 **
Einstein's equations
tell how matter curves spacetime. The curvature affects physics.
You need to know how curvature
shows up in the mathematics: Ricci tensor and curvature scalar.
Minimal coupling
relates physics to curved space; he shows the weak field metric outside
a sphere.
**pg. 5** There are
singularities in this metric. One is an
artifact of choice of coordinates; the other implies there are
black holes. In the weak field limit there is
an effective potential that accounts for the precession of the
perihelion of Mercury. This effective potential is an
"exterior" solution, not valid in
close.
**pg. 6 **The weak-field
metric implies there should be
gravity waves. The possibility of such waves can also be seen by
using Kruskal
coordinates and obtaining a wave equation. He then uses a Green's
function to obtain a
solution of this wave equation.
**pg. 7**
Summary: Gravity is the
deformation of geometry; Einstein's equations describe how geometry is
deformed; solutions of these equations describe well the effects of weak
fields and predict new phenomena for strong fields; the equations have
wave-like solutions, but the lowest contribution is quadrupolar.
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