Trip to a Black Hole I

by Robert J. Nemiroff 

Michigan Tech

Extraordinary Concepts in Physics Lecture 4

Physics X: About This Course

• Officially "Extraordinary Concepts in Physics"• Being taught for credit at Michigan Tech

o Light on math, heavy on concepts o Anyone anywhere is welcome

• No textbook requiredo Wikipedia, web links, and lectures onlyo Find all the lectures with Google at:

"Starship Asterisk" then "Physics X"  o http://bb.nightskylive.net/asterisk/viewforum.php?f=39

TRIP TO A BLACK HOLE: OVERVIEW

• Schwarzschild black hole onlyo It's the easiesto It's what I know best

 • Based partly on my paper:

o  "Visual distortions near a neutron star and black hole"o American Journal of Physics 1993, 61, 619

• And my web page:  o Virtual Trips to Black Holes and Neutron Stars

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

TRIP TO A BLACK HOLE: FAR AWAY

 • r -> infinity: space is "flat"

o all (1 - rs/r) terms go to 1. o gravity is Newtonian:  aN = GM/r2o  black holes attract the same as normal matter o curved universe NOT flat as r -> infinityo can see lensing effects with a telescope o orbiting the same as spinning in place

TRIP TO A BLACK HOLE: APPROACHING

• black hole appears blacko excludes evaporation effects

• blackness everywhere inside photon sphereo cannot see to the event horizon

• outside, average surface brightness unchangedo appears fuzzy as star images merge

• distant universe o speeds upo appears bluer

BACKGROUND: GRAVITATIONAL LENSING

• gravity bends light: "null geodesics"

GRAVITATIONAL LENSING: EINSTEIN RING

• Actual Einstein ring: APOD 2008 July 28

GRAVITATIONAL LENSING: EINSTEIN RING

• Detailed image of Einstein ring from AJP paper

TRIP TO A BLACK HOLE: ORBITING NEARBY

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

o One outside the ER, one insideo Observers also have two images

• Actually, an infinite number of images exist

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

o Appear reddero Clocks appear to run slower

TRIP TO A BLACK HOLE: ORBITING AT THE PHOTON SPHERE

TRIP TO A BLACK HOLE: ORBITING AT THE PHOTON SPHERE

• Everything below you is blacko because those light paths fall into the BH

• The whole sky appear above youo 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

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 

o its own infinite set of Einstein ringso its own redshift (or blueshift)

GRAVITATIONAL LENSING: EINSTEIN RING

• Einstein rings near a black hole