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# Trip to a Black Hole I by Robert J. Nemiroff Michigan Tech

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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

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"

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

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" 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

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

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 One outside the ER, one inside 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 Appear redder 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 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

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)

Gravitational Lensing: Einstein Ring
Einstein rings near a black hole

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