1. 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.

2. General Relativity deals with geometry

3. Basic geometries Flat (Euclidian)Spherical Hyperbolic

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

5. 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

6. The Earth is a good example of a Riemannian Geometry

7. 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.

8. 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

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

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

11. There’s more

12. and more

13. 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

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

15. More often, arcs result from gravitational lensing

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

17. Observed Spin-down of the binary pulsar system

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

19. LIGO is a big Interferometer

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

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