Measuring the Hubble Parameter
we have a lot of difficulties in measuring it
mainly because distance is not well determined
some methods: Cephids, Tully-Fisher
Geometry of the universe
critical density, r = 3Ho/8pG
Flat universe
expansion slows down almost to zero
Euclidean flat space, density = critical
Open universe
expansion runs away forever
saddle shaped space, density < critical
end in cold death
Closed universe
expansion stops, then collapses
spherical space, density > critical
end in hot death
Black Holes
After neutron stars get > 4.5 M_sun, collapses
Black Holes have event horizons, where escape velocity is c the speed of light
The Schwartzschild Radius: R = 2GM/c2
Not even light escapes Schwartzschild Radius
The bigger mass the BH contains, the larger its event horizon, the less dense it is at the event horizon
Strange things happen as you go towards a BH:
observer far away, sends explorer towards BH
|
Explorer |
Observer |
||
|---|---|---|---|
|
Time |
Event |
Time |
Event |
|
1 minute |
Send signal |
1 minute |
Receive signal |
|
2 minute |
Send signal |
2 minute |
Receive signal |
|
3 minute |
Send signal, dark spot appears in sky |
1 day |
Receive signal, explorer slows down |
|
4 minute |
Send signal, dark spot covers ½ sky, experience tidal forces |
2 years |
Receive faint signal, explorer almost still |
|
5 minute |
Send signal, crosses into event horizon, complete darkness, larger tidal forces |
¥ |
Never receive signal, explorer stationary |