Announcements Exam 3 is Monday April 13. Will cover the rest of Chapter 4, all of Chapters 5, 6, 7 & 8. New Sample Questions that include Chapter 8 are posted. New links for General Relativity have been posted on the website. Check them out! No class Wednesday. I have a meeting at 3:30 that I have to attend.

General Relativity deals with geometry

Basic geometries Flat (Euclidian)Spherical Hyperbolic

The Metric is the formula for the distance between two points Euclidian geometry Spherical geometry Hyperbolic geometry

General Relativity uses Riemannian Geometry Riemannian geometries are locally flat. On a small enough scale they are Euclidian. On a larger scale, though, there is curvature. The mathematics of Riemannian geometry was worked out in the mid 1800’s by Georg Friedrich Bernhard Riemann

The Earth is a good example of a Riemannian Geometry

The metric for general relativity is the space-time interval The space-time interval for Special Relativity is for flat space so  =  = 1 and  = 0. The metric for curved space-time includes the spatial separation between the two events (  x) plus the temporal separation (  c 2  t 2 ) plus a cross term. The mathematics of General Relativity is all about finding  and . In four dimensional space (three spatial and one temporal) there will be 10 coefficients.

The Equations of General Relativity can look simple The left side is the geometry of space-time. The right side is the mass-energy distribution

The symbols R  and T  are short hand ways of writing differential equations  Is called a Christoffel symbol

When the whole thing is seen, it isn’t so simple anymore

There’s more

and more

But what does it all mean? Mass-energy tell space-time what it’s geometry must be. Any object that moves into that “region” of space-time then follows the trajectory given by the shortest space-time interval between two space-time points (two “events”). Watch Warped Space-time Demo video

Observational evidence for General Relativity: Light Bending Einstein’s Cross Watch Gravity Lensing video

More often, arcs result from gravitational lensing

General relativity says the binary pulsar should radiate gravity waves Watch Binary Pulsar, Binary Pulsar Merger and Neutron Star Merger videos

Observed Spin-down of the binary pulsar system

LIGO looks for gravity waves Watch YouTube video at LIGO Gravity Wave Observatory video

LIGO is a big Interferometer

Two interferometers were built to be sure they detect gravity waves and not passing trucks

LISA is an interferometer that will be built in space Watch LISA Gravity Wave Detector video