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Black Holes and General

Relativity

Stuff that warps your mind

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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?

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Special Relativity2 Main Postulates:1. The speed of light is always c.

Thou shalt not add your speed to the speed of light!

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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 rest Constant velocity

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Time Dilation

Tick!

Tock!

Tick!

Tock!

c

distancetime

Compare

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Moving clocks run slow

• Since:

c

distancetime

Compare

S

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How slow?

Travel to Vega: Distance = 25 LY (7.5 pc)

Time = Distance / velocityvelocity = 0.999cTimeRest = 25 years

TimeMoving = 25 years x 0.04 = 1year!

2

RestMoving c

v1TimeTime

Copyright Lynette Cook, used with permission

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How slow?

Travel to Milky Way’s supermassive black hole:Distance = 28,000 LY (8.5 kpc)

Time = Distance / velocityvelocity = 0.999999cTimeRest = 28 thousand years

TimeMoving = 28 thousand years x 0.0014 = 40 yrs!

2

RestMoving c

v1TimeTime

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Twin Paradox

• Twins. One goes to Vega. One stays home.

• What happens?• What does each see?• How can one age, and the other not?

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General Relativity2 Main Postulates:1. The speed of light is always c.

Thou shalt not add your speed to the speed of light!

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General Relativity

2. Accelerating reference frames are indistinguishable from a gravitational force.

The Star Tours ride at Disneyland is awesome!

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Gravity Bends Light

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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.

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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!

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Gravitational Lensing

• If geometry right: gravity cause multiple images.

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Einstein Lenses

Copyright – J. Rhoads, WIYN

Copyright – Charles R Evans (UNC)

Einstein Ring

Copyright – L. J. King (U. Manchester)

8Copyright – A. Fruchter (STScI)

Abell 2218

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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.

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c

distancetime

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Gravity makes time slow

S

F

S

F

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Proof?

• GPS satellites use atomic clocks.• Position determined by timing radio

signals. • In orbit Fg = ¼ Fg at Earth surface.• Clock on satellite runs fast by 45 msec

per day.D = v tD = c tDD = cDtDD = 3 x 105 km/s * 45 x 10-6 s/dayDD = 13.5 km/day