1. Trip to a Black Hole I by Robert J. Nemiroff Michigan Tech
Extraordinary Concepts in Physics
Lecture 4
Trip to a Black Hole I by
 Robert J. Nemiroff 
Michigan Tech

2. Physics X: About This Course
Officially "Extraordinary Concepts in Physics"
Being taught for credit at Michigan Tech
Light on math, heavy on concepts
Anyone anywhere is welcome
No textbook required
Wikipedia, web links, and lectures only
Find all the lectures with Google at:
"Starship Asterisk" then "Physics X" 

3. Trip to a Black Hole: Overview
Schwarzschild black hole only
It's the easiest
It's what I know best
Based partly on my paper:
 "Visual distortions near a neutron star and black hole"
American Journal of Physics 1993, 61, 619
And my web page:  
Virtual Trips to Black Holes and Neutron Stars

4. Trip to a Black Hole: Key Distances
r = infinity: space is flat: aN = GM/r2
Near the black hole: a = aN / (1 - rs/r)1/2
r = 3 rs: last stable orbit
r = 1.5 rs: photon sphere
r = rs: event horizon
r = rc: Compton radius
r = 0: GR singularity

5. Trip to a Black Hole: Far Away
r -> infinity: space is "flat"
all (1 - rs/r) terms go to 1.
gravity is Newtonian:  aN = GM/r2
 black holes attract the same as normal matter
curved universe NOT flat as r -> infinity
can see lensing effects with a telescope 
orbiting the same as spinning in place

6. Trip to a Black Hole: Approaching
black hole appears black
excludes evaporation effects
blackness everywhere inside photon sphere
cannot see to the event horizon
outside, average surface brightness unchanged
appears fuzzy as star images merge
distant universe 
speeds up
appears bluer

8. Background: Gravitational Lensing
gravity bends light: "null geodesics"

9. Gravitational Lensing: Einstein Ring
Actual Einstein ring: APOD 2008 July 28

10. Gravitational Lensing: Einstein Ring
Detailed image of Einstein ring from AJP paper

11. Trip to a Black Hole: Orbiting Nearby

12. Trip to a Black Hole: Orbiting at 10 rs
Stars CANNOT cross the Einstein ring
Einstein ring mapped point behind BH center
Einstein ring divides complete image sets
Angular speeds diverge at the Einstein ring
One can see oneself 
All stars have two discernible images
One outside the ER, one inside
Observers also have two images
Actually, an infinite number of images exist

13. Trip to a Black Hole: Orbiting at 10 rs
Distant stars appear slightly bluer
Distant clocks appear to run faster
This also occurs for stars that appear next to the black hole
Objects ACTUALLY nearer to the black hole
Appear redder
Clocks appear to run slower

14. Trip to a Black Hole: Orbiting at the Photon Sphere

15. Trip to a Black Hole: Orbiting at the Photon Sphere
Everything below you is black
because those light paths fall into the BH
The whole sky appear above you
because those light paths escape the BH
The Einstein ring appears above the horizon
Stars still CANNOT cross the Einstein ring
Stars still speed up near the Einstein ring

16. Trip to a Black Hole: Orbiting at the Photon Sphere
Other image sets between other Einstein rings
"The" Einstein ring actually "First Sky Einstein ring"
There are infinitely many Sky Einstein rings
Every radius from the BH has 
its own infinite set of Einstein rings
its own redshift (or blueshift)

17. Gravitational Lensing: Einstein Ring
Einstein rings near a black hole