 General Relativity
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 Presentation
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Points to remember from special relativity (ep. 6)
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Minkowski's spacetime concept. Spacetime is 4-dimensional; in Minkowski's perspective, it's Euclidian ("flat"). In Euclidian geometry (named after Greek mathematician Euclid), parallel lines remain at a constant distance from each other.
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Time dilation, Lorentz contraction -- at high velocities
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Special relativity is called "special" because it's a special case, assumes gravity can be neglected.
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General Relativity is Einstein's attempt to generalize special relativity to include gravity. Really, gravity is so central to GR that its often treated as being Einstein's theory of gravity.
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History of GR
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1905 -- Einstein's SR papers
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1907 -- Einstein publishes an article on acceleration under special relativity. He puts forth what's now called the "equivalence principle" -- "there is no experiment a person could conduct in a small volume of space that would distinguish between a gravitational field and an equivalent uniform acceleration."
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Basically, an object in free fall is in inertial motion, and so for a freefalling observer the rules of special relativity must apply.
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In the process, Einstein also predicted the phenomenon of gravitational time dilation (since gravitational acceleration looks just like a uniform linear acceleration).
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 Thought experiment: two people, each in an elevator cab
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1911 -- Einstein publishes another article expanding on his 1907 article, in which he predicts additional effects such as the deflection of light by massive bodies.
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By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. After 3 years of work and a number of false starts, in November of 1915 Einstein published what are now known as the Einstein field equations (express curvature of spacetime as a function of mass & energy distribution).
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Once the field equations were published, the further development of GR became a problem of solving the field equations for various cases and interpreting the solutions.
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1916 -- Karl Schwarzschild discovers an exact solution for the case of spacetime surrounding a massive object (simplifying assumptions: spherically symmetric, non-spinning, uncharged).
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1922 -- Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe.
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1929 -- Edwin Hubble finds evidence for the idea that the universe is expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career".
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Progress in solving the field equations and understanding the solutions has been ongoing.
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General relativity unifies special relativity and Isaac Newton's law of universal gravitation with the insight that gravitation is not viewed as being due to a force (in the traditional sense) but rather a manifestation of curved spacetime, this curvature being produced by the presence of mass, energy, and momentum (or stress-energy) within it.
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The theory of general relativity is based on a set of fundamental priciples which guided its development:
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The general principle of relativity: the laws of physics must be the same for all observers (accelerated or not).
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The principle of general covariance: the laws of physics must take the same form in all coordinate systems.
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The principle that inertial motion is geodesic motion: the world lines of particles unaffected by physical forces are timelike or null geodesics of spacetime.
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The principle of local Lorentz invariance: the laws of special relativity apply locally for all inertial observers.
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Curvature of spacetime: this permits gravitational effects such as freefall to be described as a form of inertial motion.
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Spacetime curvature is created by stress-energy within the spacetime: this is described in general relativity by the Einstein Field Equations.
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The equivalence principle, which was the starting point for the development of general relativity, ended up being a consequence of the general principle of relativity and the principle that inertial motion is geodesic motion.
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Wrapup
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In weak gravity conditions, the curvature of spacetime is so small that Newton's law of gravity works just fine (and mathematically, it's dramatically easier to deal with). But in very strong gravitational fields, Newton's description of gravity becomes inadequate, and General Relativity must be used to mathematically describe the gravitational effects.
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Things that GR & Einstein's field equations predict (directly or indirectly):
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Equivalence of gravity and linear acceleration -- massive objects / strong gravitational fields bend light & cause time dilation. Seen in astronomical images, motion of planets very near stars (even in Mercury's orbit!)
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Black holes
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Big bang theory for expansion of universe
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The status of general relativity is mixed -- it's the best theory we've got for what it covers, but there are enough "rough edges" that there is a strong concensus that there's something beyond Einstein's theory yet to be found.
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A number of competitors to general relativity have been proposed over the years, but most of them have gone by the wayside as tests have eliminated the competing theories while leaving GR standing. String theory is still being discussed, but largely because nobody's found a way to test it. Some propose that the current fixation on dark matter and dark energy may actually just be another way of expressing missing factors in GR, but again, tests will be required to confirm or refute this.
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Sources and other links
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Relativity in a broad sense
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General Relativity
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