Lecture 15 General Relativity and Curved Space

Key Concepts:

Space and Time

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.

The shortest path in a curved space may not necessarily be a "straight line".

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

	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.
	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 = 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.