This set of slides

1. This set of slides • This set of slides continues the late-in-life evolution and death of massive stars, stars > 8 solar masses. • It starts with Special and General Relativity which leads us into black holes. • The last part of this set covers black holes. • Units covered: 53 and 68.

2. Galilean Relativity • Galileo noted that the speed of a thrown object depends on how fast and in what direction the thrower is moving. • If the thrower is moving in the same direction as the throw, the projectile goes faster. • If the thrower is moving in the opposite direction, the projectile goes slower. • Velocities can add up!

3. The Michelson-Morley Experiment Water waves travel in water. Sound waves travel in air. What does light travel in? Aether! (Or not.) • In the 1880’s Michelson and Morley devised an experiment to detect the motion of the Earth through the aether – a universal “atmosphere”. • Light should move slower in the direction of the Earth’s motion through space. • Detected no difference in speed. A “null” result. • No aether, plus, the speed of light seemed to be a constant.

4. The Lorentz Factor • It was proposed that perhaps matter contracted while it was moving, reducing its length in the direction of motion. • The amount of contraction was described by the Lorentz factor. • At slow speeds, the effect is very small. • At speeds close to the speed of light, the effect is dramatic.

5. An Explanation. • Albert Einstein proposed that light did not behave “classically”. • Two postulates of Special Relativity: • The laws of physics are the same in every inertial reference frame. • The speed of light (in a vacuum) always has the same value, no matter how fast the source of light and observer are moving relative to each other. • These postulates mean: • There is NO experiment you can do in a constant-velocity (inertial) reference frame that would prove whether you are moving or not! • Traveling at, say, half the speed of light, and turning on a flashlight, the light from the flashlight will leave you at c, and anyone else measuring that light will also measure c, no matter their speed relative to you. • NOTHING can travel through space faster than the speed of light!

6. Einstein’s Insights • Starting from these assumptions, Einstein realized: • Length contracts in the direction of motion, by a fraction equal to the Lorentz factor. • Time stretches (dilates) as well, also by the Lorentz factor. • Mass increases with motion! • Moving clocks run slow. • Moving objects reduce their length in the direction of motion.

7. Einstein’s Special Relativity • Time dilation and length contraction depend on the observer. • To an observer on Earth, the spacecraft’s clock appears to run slow, and the ship looks shorter. • To an observer on the ship, the Earth appears to be moving in slow-motion, and its shape is distorted. • The passage of time and space are relative! • Space is a 4th Dimension!

8. Possibilities for Space Travel • Example: A spacecraft leaves Earth, heading for a star 70 light-years away, traveling at .99c. • To an observer on Earth, it takes the spacecraft just over 140 years to get to the star, and then back again. • To passengers on the ship, it only takes 20 years for the round-trip. • This means that high speed travel to the stars is possible, but comes at the cost of friends and family.

9. Time as a Dimension • We are accustomed to living in a 3-D world. We can move left and right, forward and backward, up and down. • Einstein suggests we live in a 4-dimensional world. Four dimensions of space-time. • A graphical example… • String theory suggests that we actually live in a 10 or 11 or maybe only 8-dimensional universe. • Doesn’t much matter to your day-to-day life but…

10. The velocity necessary to avoid being gravitationally pulled back to an object (the escape velocity) is: Note that as R decreases, the escape velocity increases. A white dwarf’s escape velocity is around 6000 km/s, ten times faster than the Sun’s. A white dwarf is around 100 times smaller than the Sun. Also recall that nothing can travel faster than the speed of light, c, or 3108 m/s. If a stellar core is compressed so much that its radius is smaller than: (the Schwarzschild radius) then nothing can escape from its gravitational force, including light! The core would become a black hole. The Escape Velocity Limit

11. Einstein’s Theory of General Relativity • Equivalence Principle: There is NO experiment that you can perform that can tell you whether an acceleration is due to gravitational force or an accelerating reference frame. • In other words, being stationary in a gravitational field is equivalent to being accelerated in a constant acceleration frame of reference. • If you are on a spacecraft and drop an apple… • A consequence of this: Gravity deflects light! (Which has no mass and thus Newton’s Law says won’t be affected.)

12. Einstein continued: Mass Warps Space • Mass warps space in its vicinity. • The larger the mass, the bigger “dent” it makes in space. • Objects gravitationally attracted to these objects can be seen as rolling “downhill” towards them. • If the mass is large enough, space can be so warped that objects entering it can never leave – a black hole is formed.

13. Black Holes • If a stellar core is massive enough, it will not stop collapsing when it becomes a neutron star. • The radius of the core continues to shrink, and density continues to increase. • Eventually the core is compressed to a single point, called a singularity. • NOTHING can escape from this black hole. Once something, including light, crosses the event horizon, escape is impossible.

14. If light cannot escape a black hole, how can we see one? You can’t! Directly. If a black hole is in orbit around a companion star, the black hole can pull material away from it. This material forms an accretion disk outside of the event horizon and heats to high temperatures. As the gas spirals into the black hole, it emits X-rays, which we can detect! Viewing a black hole

15. Light curves from a black hole binary system

16. General Relativity continued • Einstein predicted that not only space would be warped, but time would be affected as well. • The presence of mass slows down the passage of time, so clocks near a black hole will run slower than clocks more distant. • The warping of space has been demonstrated many times, including by observations of the orbit of Mercury. • The slowing of clocks has been demonstrated as well.

17. Gravitational Redshift • Photons traveling away from a massive object will experience a gravitational redshift. • Their frequency will be shifted toward the red end of the spectrum.

18. “Theory” of Relativity • Still today, it’s the “theory” of special or general relativity. • BUT, it’s the best model we have for gravity and space-time. • Our “common sense” isn’t enough to discount these ideas. • NO experiment done in over 100 years has shown either to be invalid. • In the future, something better might come along. Or we might discover some phenomena that doesn’t fit. • Already, used in DAILY life. GPS satellites MUST make corrections for both special relativity (satellites are moving at high speed) and general relativity (altitude effect on time) in order to find a position on Earth (your car for example!)

19. Falling Into a Black Hole • Time would slow (as seen by outside observers.) Falling person notices nothing, even crossing event horizon. • Light from falling person (to outside observers) becomes more and more redshifted. The person falling slowly disappears from view (to outside observers.) • The warping of space would eventually take its toll on matter. • Gravitational “tidal forces” would stretch matter out into longer and longer, thinner and thinner strands. • Eventually all things that characterize matter would be gone. No atoms, molecules, protons, neutrons, electrons… • Everything is compressed into an infinitely small point of infinite density (the singularity). • All that remains is mass (energy) and angular momentum…