Outline Black Holes Schwartzchild radius River Model of a Black Hole Light in orbit Tidal forces
Black Holes
Black Holes What happens as the star shrinks / its mass increases? How much can spacetime be distorted by a very massive object? Remember: in a Newtonian black hole, the escape speed simply exceeds the speed of light => Can gravity warp spacetime to the point where even light cannot escape it s grip? That, then, would be a black hole.
Black Holes A Black Hole is a collapsed region of space Gravity curves space so much that close enough in light is bent so much it always falls in If you get close enough to a blakc hole, you can never get back out
Black Holes
Black Holes Time flows more slowly near a massive object, space is stretched out (circumference < 2πR) Critical: the ratio of circumference/mass of the object. If this ratio is small, GR effects are large (i.e., more mass within same region or same mass within smaller region) 1) massive 2) small??????
GR predicts: If mass is contained in a circumference smaller than a certain size critical circumference gravitational constant space time within and around that mass concentration qualitatively changes. A far away observer would locate this critical surface at a radius Schwarzschild radius The Schwarzschild Radius mass speed of light Gravitational time dilation becomes infinite as one approaches the critical surface.
How big does a BH need to be to R s = 3 (M/M ) km float?
Black Holes To a stationary oberserver far away, time flow at the critical surface (at R S ) is slowed down infinitely. Light emitted close to the critical surface is severely red-shifted (the frequency is lower) and at the critical surface, the redshift is infinite. From inside this region no information can escape red-shifted red-shifted into oblivion
Event Horizon Inside the critical surface, spacetime is so warped that objects cannot move outward at all, not even light. => Events inside the critical surface can never affect the region outside the critical surface, since no information about them can escape gravity. => We call this surface the event horizon because it shields the outside completely from any events on the inside.
Black Holes Critical distinction to the Newtonian black hole: Newton Einstein Nothing ever leaves the horizon of a GR black hole. Lots of questions What happens to matter falling in? What happens at the center? Can we observe black holes anyway? And much, much more
River Model of a Black Hole
River Model of a Black Hole
River Model of a Black Hole
Tides near a Black Hole
What would happen if you fell into a Black Hole the mass of the Sun? Recall that force of gravity is F = GMm / R 2
What would happen if you fell into a Black Hole the mass of the Sun? Recall that force of gravity is F = GMm / R 2 But, if you fall feet first, your head is farther away than your feet, so F 2 = GMm / (R+r) 2
What would happen if you fell into a Black Hole the mass of the Sun? Recall that force of gravity is F = GMm / R 2 But, if you fall feet first, your head is farther away than your feet, so F 2 = GMm / (R+r) 2 This force will try to stretch you How close can you get before this is a problem?
What would happen if you fell into a Black Hole the mass of the Sun? How close can you get before you get pulled apart? Difference in force, if r << R F - F 2 = df = GMm (1/R 2 1/(R-r) 2 )
What would happen if you fell into a Black Hole the mass of the Sun? How close can you get before you get pulled apart? Difference in force, if r << R F - F 2 = df = GMm (1/R 2 1/(R-r) 2 ) Difference in force, if r << R df = 2GMm r / R 3
What would happen if you fell into a Black Hole the mass of the Sun? How close can you get before you get pulled apart? Difference in force, if r << R F - F 2 = df = GMm (1/R 2 1/(R-r) 2 ) Difference in force, if r << R df = 2GMm r / R 3 Rearrange, R 3 = 2GMm r / df
What would happen if you fell into a Black Hole the mass of the Sun? R = (2GMm r / df) 1/3 M = 2*10 30 kg, G = 6.673*10-11 r = 1m, m = 40kg
What would happen if you fell into a Black Hole the mass of the Sun? R = (2GMm r / df) 1/3 M = 2*10 30 kg, G = 6.673*10-11 r = 1m, m = 40kg How much stretching force to kill you?
What would happen if you fell into a Black Hole the mass of the Sun? R = (2GMm r / df) 1/3 M = 2*10 30 kg, G = 6.673*10-11 r = 1m, m = 40kg How much stretching force to kill you? df ~ 1000 kg * 10 m/s 2 ~ 10,000 Plug in numbers, get R death ~ 800 km
What would happen if you fell into a Black Hole the mass of the Sun? R death ~ 800 km Schwarzschild radius R S = 3km for Solar mass BH So you die before you get close You also get squeezed from the sides Called spaghetti-fication
What about a bigger Black Hole? R death = (2GMm r / df) 1/3 R death ~ 800 km * (M/M sun ) 1/3 Schwarzschild radius R S = 2GM/c 2 R S = 3km * (M/M sun ) For Milky way center, M = 4 million M sun R death ~ 130,000 km, R S = 12 million km You survive! (sort of)
sketch What would happen if you observed Brian fall into a black hole???
What would happen if you observed Brian fall into a black hole??? His infall would appear to slow down due to the high gravity. From your point of view, he would stay at the event horizon forever. He would look redder due to gravitational redshift. He would be highly stretched from his perspective due to tidal forces (unpleasant!) sketch But for him time will not run slowly, he ll be dragged into the singularity point quickly.