General Relativity is Einstein's theory of gravity. Instead of treating gravity as a force, it states that gravity is the result of the curvature of space. Mass causes space-time to be deformed; this deformation means that a "straight line" will appear to bend towards the mass.
The trampoline, with a grid
The Bowling ball
It is a little easier to envision if you leave out a dimension and think of space as two dimensional. Imagine you have a very large, sturdy trampoline, a bowling ball, paint, and some marbles. If you roll a marble across the trampoline, it will move in a straight line. Now imagine painting a line along the marble's course. Finally, put the bowling ball near the painted line. The line will curve towards the ball. The more the trampoline sags, the more the line will curve. Now bring it into three dimensions. Imagine a giant, 3D grid in deep space. A small object (small enough that its Newtonian gravity is negligible) travels along a grid line (it could technically follow any straight line, but we're positioning the grid for convenience). Now imagine that there was a massive object such as a planet or star in the center of this grid. The lines will bend towards the object. Those lines are only grid lines, however. They do not respond to the mass via an inverse square law and they are forced to return to the edges of the tramp. However, they do show the warping of the trampoline quite nicely. A more useful line here is the actual trajectory of the object, called a "worldline," whose warping is similar to that of the grid lines but not the same. In particular, worldlines do not bend away from the object as these grid lines do. The filters in my image editing program are designed to preserve certain properties of the image, in particular whether two objects intersect. Since actual general relativity doesn't preserve this, the grid is only useful for demonstrating the warping of space.

The grid lines are not only useless but are actually misleading. General relativity states that the worldlines are what Newton's First Law would refer to as "straight lines." This does not apply to the grid lines. An interesting consequence is that objects follow their trajectories due to inertia. On the other hand, potential energy is still considered a form of energy; in fact, it can be explained more simply. For example, suppose an object is floating (velocity is close to 0) in space nowhere near any massive objects. What is the total energy of this object? Since PE depends on a zero point, the question is ill defined and its answer could be any nonnegative number (ordinarily Newtonian PE can be negative if a poor zero point is chosen, but such a point does not appear to exist in this case). So under Newtonian gravity, there's no absolute scale of energy. Going back to the trampoline analogy however, we can devise such a system. The height of the trampoline above it's minimum possible height, measured at the point of the object including displacement due to the object itself, is clearly related to potential energy. Multiplying by the mass of the object and a conversion factor (a constant) should produce an absolute PE. Interestingly, there appears to be a maximum ratio of PE to mass, corresponding to a flat trampoline.

General relativity is actually very important for many reasons. Firstly, it is more accurate than Newtonian gravitation. According to Kepler's laws, the Earth orbits the Sun in an ellipse with the Sun at one focus. We've observed the other focus to move slowly around the Sun, but this is inconsistent with Newton's laws. However, it is consistent with general relativity. Secondly, special relativity doesn't make sense otherwise. Imagine there are a pair of twins named Bob and John. John gets on a spaceship at age 25 and goes at .5c (half the speed of light) while Bob remains on Earth. Also, John has a stopwatch which he keeps in front of the window, running. Bob has an identical stopwatch. When John returns, Bob should be older than him, assuming the trip lasted a significant amount of time. Let's examine both viewpoints, first using Newtonian gravity and then using general relativity. From Bob's reference frame, John is moving at .5c away. If Bob looks through a telescope into John's spaceship, he should see John's stopwatch moving more slowly than normal. But from John's reference frame, Bob's stopwatch appears to be slower. This can be resolved. Under Newtonian gravity, both are accelerating due to a force (Bob experiences gravity from the Earth and the Earth experiences gravity from the Sun; John must accelerate to turn around), which means their reference frames are not meaningful (accelerating reference frames cannot be handled the same way as inertial reference frames). That means that we have no easy way of determining who is right. But under general relativity, Bob isn't accelerating at all, so his reference frame is the valid one.

Black hole, with event horizon in green
A black hole arises when the deformation of spacetime is so great that no worldlines leave a particular region of space. The boundary surrounding this region is called the "event horizon." Since no worldlines leave that region, no object or particle can escape. A black hole also has something in the center called a "singularity." A singularity is a mass which physics is incapable of describing accurately. Mathematics suggests that the singularity would have infinite density, zero volume, and a very large but finite mass. It may be helpful to think of a black hole as a pit which is too steep to climb out of. Things can fall in, but they cannot get back out. The problem is the singularity. Neither Newtonian gravity nor general relativity can explain how such an object would behave. How can an object have infinite density? What happens when elementary particles strike it? It has zero volume, and supposedly so do elementary particles. Does that mean every elementary particle which strikes it simply stops at the singularity? How does the Pauli Exclusion Principle apply then? Is the particle converted to energy? What is the singularity made of? We don't know the answers to these questions. It has been suggested that some form of quantum gravity (mediated by gravitons) would solve these problems, but we don't have a working theory of quantum gravity.

General relativity was first described by Einstein alongside special relativity. As explained above, the two form a cohesive theory


Sonia Bansal - How does this apply to the average person?
Kevin - It is highly theoretical. Unless by "average person" you mean astronomer, Newtonian Gravity works fine for most practical purposes
Angad Sidhu - If singularity has a finite mass, can that mass be theroretically related to the mass of the star that had preceded the black hole?
Kevin - Yes. The mass of the object does not change when it goes from star to black hole. What changes is the volume and hence the density. The event horizon should be within the former radius of the star. Since objects can come closer to the singularity than they ever could to the star, the force of gravity is much stronger.
Robert Lopez - Is there any specific or more inclined region where a black hole will form? Are we in danger?!
Kevin - Black holes usually form from stars several times as massive as the sun. LHC probably won't make a black hole. We are probably not in danger from black holes at this time.
James Song- Why are miniscule versions of black holes not able to develop?
Kevin - A micro black hole would exude much greater Hawking Radiation and would decay much more rapidly than would a normal black hole.
Brandon Siegenfeld- If no particles or energy can leave a black hole can they decay, if so how?
Kevin - Particles which have entered the black hole cannot leave directly. However, energy from the black hole can spontaneously form particle-antiparticle pairs, and half the pair could fall into the black hole. See the Hawking Radiation link above.
Sam Edwards - In your example with Bob and John, what does general relativity do that Newtonian gravitation doesn't that makes Bob's reference frame valid?
Kevin - Bob's reference frame is the same as the Earth's reference frame. According to General Relativity, the Earth is moving in a straight line and the reason it appears to be moving in an ellipse is the curvature of space (space is curved so the straight line is bent into an ellipse).
Will Chan - Have there been practical applications of this theory? If so, what were they?
Kevin - General Relativity explains planetary precession around the sun and provides a more accurate picture of gravity to astronomers. Unfortunately, because General Relativity uses very complex equations, astronomers often make simplifying assumptions.
Greg Sturm - Aside from powerful telescopes, how do you detect a black hole? And what observations were made to determine that they could have an infinite mass?
Kevin - Black holes don't have infinite mass. That would imply infinite energy, which is problematic under current assumptions. You can detect a black hole by gravitational lensing: the black hole acts as a lens for passing light, creating a double image.
Douglas Chin - If one went back in time with a watch that was purposely set at the wrong time, would the watch fix itself?
Kevin - I'm sorry, I don't understand the question. Are you traveling to the "wrong time?" Are you going by wormhole or some other means? If you travel by wormhole to the "wrong time," the watch should still be set to the "wrong" time and hence should be right. Otherwise you need to be more specific.

Source: The information is based on Wikipedia's article on general relativity, but it is my own work and not cut-and-pasted
The images were made in The GIMP by me