# 8 Black Holes and General Relativity Stuff that warps your mind.

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8 Black Holes and General Relativity Stuff that warps your mind

8 Goals Why should time be affected by motion? Why should light be affected by gravity? Why should time be affected by gravity? What proof is there that they are?

8 Special Relativity 2 Main Postulates: 1. The speed of light is always c. Thou shalt not add your speed to the speed of light!

8 Special Relativity 2. Moving and non- accelerating reference frames are indistinguishable from one another. If it happens at rest, it must happen in (constant) motion. Are you moving, or are you at rest right now? At restConstant velocity

8 Time Dilation Tick! Tock! Tick! Tock! Compare

8 Moving clocks run slow Since: Compare S

8 How slow? Travel to Vega: Distance = 25 LY (7.5 pc) Time = Distance / velocity velocity = 0.999c Time Rest = 25 years Time Moving = 25 years x 0.04 = 1year! Copyright Lynette Cook, used with permission

8 How slow? Travel to Milky Way’s supermassive black hole: Distance = 28,000 LY (8.5 kpc) Time = Distance / velocity velocity = 0.999999c Time Rest = 28 thousand years Time Moving = 28 thousand years x 0.0014 = 40 yrs!

8 Twin Paradox Twins. One goes to Vega. One stays home. What happens? What does each see? How can one age, and the other not?

8 General Relativity 2 Main Postulates: 1. The speed of light is always c. Thou shalt not add your speed to the speed of light!

8 General Relativity 2. Accelerating reference frames are indistinguishable from a gravitational force. The Star Tours ride at Disneyland is awesome!

8 Gravity Bends Light

8 Is there Proof? Scientific Method: 1.Hypothesis: predict gravity bends light. 2.Test: The Sun has a lot of gravity and should deflect star light.

8 Solar Eclipse of 1919 Hard to see stars near the Sun. Can see stars near the Sun during an eclipse. Can predict time and position of Sun during eclipse years in advance. Measure the positions of stars 6 months before when they are up at night. During eclipse, measure their positions again. SOHO spacecraft Result: Theory of Relativity confirmed!

8 Gravitational Lensing If geometry right: gravity cause multiple images.

8 Einstein Lenses Copyright – J. Rhoads, WIYN Copyright – Charles R Evans (UNC) Einstein Ring Copyright – L. J. King (U. Manchester)

8 Copyright – A. Fruchter (STScI) Abell 2218

8 Space is Curved Einstein said to picture gravity as a warp in space. –Sagan : A “pucker” in fabric of space. Kepler’s Laws explained by movement around “puckers.” Everything moving is affected, regardless of mass.

8

8 Gravity makes time slow S F S F

8 Proof? GPS satellites use atomic clocks. Position determined by timing radio signals. In orbit F g = ¼ F g at Earth surface. Clock on satellite runs fast by 45  sec per day. D = v t D = c t  D = c  t  D = 3 x 10 5 km/s * 45 x 10 -6 s/day  D = 13.5 km/day