Post on 06-Jan-2016
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• Imagine being an ant… living in 2D
• You would understand:
left, right, forward, backward,
but NOT up/down…
• How do you know your world is curved?
Curvature in 2D…
Curvature in 2D…
Curvature in 2D…
Geodesics
• To do geometry, we need a way to measure distances
• In flat space, the shortest distance between P1 and P2 is
a straight line
• In curved space, the ant follows a
• Geodesic: shortest line between P1 and P2
(the fewest possible ant steps)
P1 P2
ant
To the ant, the geodesic is a straight line,
i.e., the ant never has to turn
Curvature and Clocks (time)
I
If both ants walk at constant velocity and leave P1 at the same time, then the ants arrive at point P2 at different times – the top ant gets their “first”. If both ants record the time when they first reach P2 – their clocks are no longer synchronized
E = mc2
• Photons have an energy related mass and are affected by gravity.
• The geometric surface shape of the Universe is determined by the mass distribution
• Photons are therefore constrained to always travel on the surface of the Universe
• Space is flat where there is no mass and curved where there is mass.
Experimental Evidence for GR
• If mass is small / at large distances, curvature is weak
=> Newton’s laws are good approximation
• But: Detailed observations confirm GR
1) Orbital deviations for Mercury (perihelion precession)
Newton: Einstein:
Precession movieLightBend
2) Deflection of light
Experimental Evidence for GR
Experimental Evidence for GR
• 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
Black Holes
• To a stationary oberserver far away, time flow at the critical surface (at RS) 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 informationcan escape red-shifted
red-shifted intooblivion
Black Holes