Special Theory of Relativity (Space, Time, and Motion)

• Principle of relativity: All observers not acted on by forces experience the same laws (an assumption, and we also assume that they move with constant velocity).
• Constancy of speed of light: All observers measure the same speed for light (a fact!).
• Consequences: Time dilation and length contraction; Increase of effective mass with speed, E = mc²; Mixing of space and time, replaced by spacetime.
• What does this have to do with black holes? Special relativity works well as long as gravity can be considered as a very weak force, and if we only observe what happens in relatively small regions; But otherwise, you have to add spacetime curvature...

 General Theory of Relativity (Gravity)

• Equivalence Principle: Gravity affects all objects in the same way; it cannot be distinguished from what you feel when you are just accelerating. It is a fictitious force like the centrifugal one, why is why it affects everything the same way.
• Thought experiment: In a closed elevator, could you distinguish acceleration from gravity?
• What does this tell us? Spacetime is curved and objects in free fall don't follow straight line paths, this is the fictitious gravity; The real forces are the ones that make us deviate from free fall; Curvature of spacetime tells matter how to move.
• What causes the curvature? The global shape of spacetime may force it to be curved, plus matter/energy tells spacetime how to curve locally.

Light Bending

• The main idea: If gravity is caused by spacetime curvature and affects all objects the same way, it must affect light too (no matter what Newton's theory may say!).
• Have we seen this? Yes, from apparent shifts in the positions of stars when their light passes near a massive object, from images of distant galaxies seen through gravitational lenses, and from gravitational redshift of light from stars (the mass of Sirius B was measured this way!).
• Extreme situations: Curvature may cause light to be bent so much that it is trapped near the massive object, inside a region from which not even light can escape: A black hole.
• Other effects: If spacetime can be curved, we should be able to see other effects too...

 Gravitational Waves

• What are gravitational waves? Ripples in the fabric of spacetime.
• Do we know they are out there? Yes, we have indirect evidence from the fact that the binary pulsar is gradually losing energy.
• How can we detect them? Several interferometer detectors, such as LIGO and VIRGO, are now operational; (Also search by monitoring spacecraft such as Cassini); other detectors are being planned

Other Predictions

• On Earth: Gravity makes time slow down, and the GPS would not work if general relativity was not taken into account.
• Near Earth: The fabric of spacetime twists like a vortex around a rotating body, making both orbits and spins of objects wobble (by tiny amounts!). [Astronomers are seeing evidence for this in the flickering of X-rays coming from near massive black holes.]
• In the Solar System: Since gravity affects lengths and times, orbits don't have exactly the shape that Kepler and Newton predicted.
• Wormholes? If the shape of spacetime can change, there is the theoretical possibility of shortcuts to remote places, as well as time travel...
• Can the whole universe be curved? This is also a fact! It is also possible that there are small extra dimensions! See what we know about cosmology...