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principle The of relativity No experiment can be done to determine which frame a reference is at rest and which is in motion at a constant velocity Equivalence principle Acceleration is the same as gravity Free-fall = constant velocity/flat spacetime Discussion If you shine a laser into the window of a rocket that is accelerating past you, draw the path of the laser as it would appear to those inside the rocket. Gravity bends light rays Light always takes the shortest path between two points. In a gravitational field, where spacetime is curved, light follows a geodesic, a curved path. Gravitational lens Discussion Explain why light bends in a gravitational field. Hint: How does a lens made of glass bend light? Gravity slows time Clocks tick more slowly in a gravitational field. Not the Same as SR time dilation Both clocks remain at rest relative to each other regardless of the acceleration. Both observers agree that the clock in front is ticking faster than the clock in back. Discussion If time moves more slowly on a star that has a higher surface gravity, how will this effect this the light we see emitted from the surface of the more massive star compared to that of the less massive star? Hint: Think about how the light is actually created. Gravitational redshift Summary Gravity is the same as acceleration 1)slows the passage of time 2) Bends the path of light 3) Causes light to be redshifted Dark stars a star that has an escape velocity greater than the speed of light. vesc GM = 2 R Schwarzschild radius The radius at which light cannot escape from a black hole. M RS = 3.0 km M Sun Mini-black holes? Earth becomes a black hole if squeezed down to a radius of 9 mm. Point of no return Because Special Relativity forbids matter being accelerated to the speed of light, nothing can get out after passing the Schwarzschild radius. Discussion The Schwarzschild radius is often called the event horizon. Why do you think that is? Gravitational Redshift Light emitted from a black hole's Schwarzschild radius becomes infinitely redshifted. Gravitational time dilation Gravity warps spacetime and causes clocks to tick slowly. As you get closer to the event horizon, clocks tick slower as viewed from flat spacetime. At the event horizon a clock would cease to tick. Frozen Stars Because time stops at the event horizon, matter dropped into a black hole will appear to be suspended just above the event horizon. Discussion If time stops at the event horizon then no matter can ever pass the event horizon and black holes can never form. Is this reasoning correct? Consider this situation from the perspective of the matter falling into the black hole. Does it see time slow? Why or why not? The event horizon is not a physical boundary Objects in free-fall feel no gravity or time dilation It will not notice it has passed the point of no return If Discussion time stops at the event horizon of a black hole, doesn't this mean that atoms in matter will not move and thus the temperature will reach absolute zero at the event horizon? Are black holes literally frozen? Discussion What would we need to do in order to get the time to stop for the matter? Three perspectives 1. View from flat spacetime far from event horizon 1. Scaffold view matter at rest with respect to the singularity near event horizon 1. Free-float view matter in free fall You have to feel the weight to slow time Discussion Is it possible for us to even see the matter at the event horizon? Why or why not? No frozen stars Things are not stuck on the event horizon of black holes. Instead, the light we receive for the rest of eternity is merely echoes from the past. Light that was emitted at the event horizon will just take an infinite amount of time to reach us. Discussion If we made a black hole out of iron, and another black hole out of marshmallows, do you think there is any way we could tell the difference? Spacetime is dragged along with a rotating black hole. On the ergosphere, spacetime is dragged along at the speed of light. Discussion What if the Sun suddenly collapsed into a black hole, how would this effect Earth's orbit? Black Holes don't suck Black holes don't suck up all matter in the Universe. At distances greater than three times the Schwarzschild radius the gravity of a black hole is the same as any other object with the same mass. Discussion Suppose you are locked in a closed room that is in free-fall. The equivalence principle tells us this is exactly the same as what other frame of reference? Discussion According to Newton, gravity is a force that depends on the distance between masses. According to Newton what are tidal forces? Discussion Suppose two probes with the same mass are sent to explore a black hole. The first is the size of a bus, while the second is only 10 cm across. In which case will the tidal forces be the greatest? Why? Discussion In the previous question does the mass of the probes matter? Explain. Discussion Suppose you are locked in a closed room where you do not feel your weight. This time I allow you to have two billiard balls. You place the balls side-by-side in front of you. If your closed room is moving at a constant velocity how will the balls move? Discussion Suppose you are locked in a closed room where you do not feel your weight. This time I allow you to have two billiard balls. You place the balls side-by-side in front of you. If your closed room is falling freely in a gravitational field how will the balls move? Discussion Suppose you place the balls on top of each other in front of you how will they move? In General Relativity Tidal forces are warped spacetime. Space is stretched in the radial direction and squeezed in the perpendicular direction.

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