Key Concepts:

1. What is equivalence principle?
2. What is spacetime?
3. What does curvature of spacetime mean?
4. How is gravity related to the curvature of spacetime?
5. What observational evidence exists for the curvature of spacetime?
6. What is a black hole?
7. How does a black hole form?
8. How does one "see" a black hole?
9. What is a supermassive Black hole?

Exam 2

Review of Relativity and Special Relativity

Equivalence Principle

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• The principle of relativity states that measurements of motion, time, and space make sense only when we describe whom or what they are being measured relative to -- there are no absolute answers.
• The same is true when one person or object is accelerating with respect to the other.
• Extending this general idea further, the equivalence principle states that
The effects of gravity are exactly equivalent to the effects of acceleration.
• Scientific ideas for artificial gravity utilize this concept.

Space and Time

• spacetime = 4-D combination of space and time


• The dimension of time is related to the dimension of space as distance = (time) x (speed of light).
• Space is different for different observers.
• Time is different for different observers.
• Spacetime is the same for everyone.

Spacetime Diagram

• A diagram showing the location of an object or event in the time versus space axis.
• worldline = a line in a spacetime diagram that traces the path of an object.
• event = a particular point along a worldline.
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• Quiz 17A: 4-D isn't bad...

Spacetime Curvature

• The geometry of spacetime may be either flat or curved.
• Spacetime may be locally flat but curved on large scales, like the surface of the earth.
• Spacetime may be locally curved although flat or flatter on larger scales, like a small bump on a road.
• What you "see" in three spatial dimension may not correctly reflect the spacetime geometry (see below).

flat geometry:

spherical geometry

saddle-shaped (hyperbolic) geometry

Light Takes the Shortest Path

But the shortest path in a curved space may not necessarily be a "straight line". It depends on the geometry of space.

A New View of Gravity

Mass (gravitational force) causes spacetime to curve, and the curvature of spacetime determines the paths of freely moving masses.

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If you are at rest in a box, the light passing through the box travel on a straight line. If you were uniformly accelerated, the light passing through your box should be deflected. The equivalence principle states that light should also be deflected if you are in a gravitational field.

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Tests of General Relativity

	Mercury's Orbit Mercury's orbit slowly precesses around the Sun. cannot be explained by Newton's law of gravity. Time runs slower and space is more curved on the part of Mercury's orbit that is nearer the Sun.
	Gravitational Lensing The curvature of space near a massive object (e.g. Sun) forces the light beam passing near it to bend, much like a lens. Changes in angular separation between stars were measured to change near the Sun during the solar eclipse in 1919 by Sir Arthur Eddington. Trajectories of light from distant stars or galaxies are bent by the gravitational field of a massive object located along the line-of-sight, producing multiple images or a ring of images (read Einstein's 1936 Science paper on gravitational lensing).
	Gravitational Waves The orbital periods of binary pulsars gradually decreases with time. Two massive stars orbiting each other closely and rapidly generate ripples of curvature in space (or gravitational waves). In 1974, Russell Hulse and Joseph Taylor (of UMass) measured the decreases in the orbital periods of binary pulsars and explained it to be a consequence of orbital energy loss through gravitational waves.

Hyperspace and Wormholes

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• hyperspace = any space with more than three dimensions.
• wormhole = a tunnel through hyperspace.
• interstellar/intergalactic travel through wormhole may be possible as it does not violate laws of nature.

What is a black hole?

A classical definition: if an object becomes compact enough, the escape speed from its surface becomes the speed of light Black hole radius (Schwarzschild Radius): Quiz 17B: black hole Earth Curved spacetime: Einstein's 1936 Science paper on gravitational lensing (and more details at Wikipedia) Gravitational Lensing by a BH A journey into a black hole FAQs on black holes

Quiz 17c: Extreme gravity

How does a black hole form?

How does one "see" a black hole?

• gravitational influences:
  • Doppler effects seen on a companion (also see animation)
  • watch objects around it travel at high speeds.
• accretion disk in X-ray: material flowing into a black hole forms a disk around it. This gas heats to 10 million K, emitting blackbody radiation in X-ray.
• X-ray sky from Rossi X-ray Timing Explorer satellite (here is the movie)
• Cygnus X-1: best candidate for a stellar mass black hole
• a movie of radio jet in SS433 from NRAO Very Long Baseline Array

• event horizon: outer boundary of a black hole, inside of which nothing can escape, including light
• Hawking radiation: radiation resulting from quantum physical process ("pair production") -- something does escape a BH, leading to a possibility that a BH can eventually evaporate!

Quiz 17D and Quiz 17E: An important reminder about gravity

Supermassive Black Holes in Galaxies

• See stars fly around the Milky Way center (by R. Genzel)
• Ionized gas is seen circling and falling toward the Milky Way center (see picture on the right side)
• The Milky Way's Heart of Darkness
• The Shadow of a Black Hole at the center of the MW

Reading assignment for next lecture: Units 70-73