Celebrating 100 years of the General Theory of Relativity
D. Indumathi, The Institute of Mathematical Sciences, Chennai

Constant observers
In 1905, Albert Einstein wrote about the Special Theory of Relativity where he stated that light travels at a speed of 3 lakh km per second. Not only does light require no medium for its transport, no other matter particle can travel faster than this speed.
This theory was only valid when the particles were not accelerating, but moving uniformly with respect to something called an inertial reference frame. As a result, he showed that the laws of physics are the same for all such frames. While doing so, he came up with the beautiful concept of unifying space and time into a single space-time continuum. However, he had a problem.

Accelerating observers
Forces and therefore acceleration, are a part of Nature and hence this theory could not apply to all cases. Ten years later, or 100 years ago, Einstein wrote his General Theory of Relativity (GR) which included acceleration. In it, he determined that massive objects cause a distortion in space-time, which is felt as gravity.
The gravity we feel on Earth, Einstein said, is nothing more than the curvature of spacetime caused by our planet's mass. That may sound exotic but straightforward, but it took Einstein eight years of intense thought to work out its particulars. Mathematically GR is very complex, which is one reason tests continue even today to verify its consequences.
Suppose you are jumping up and down in the center of a trampoline. Your weight would press down into the fabric, causing it to bulge out. So a ball rolled around the edge would spiral inward toward the centre. In a similar fashion, the gravity of a planet pulls at moons or other objects in space.
In this illustration by NASA, the effects of Earth's gravity can be seen warping spacetime in accordance with Einstein's theory of general relativity. NASA's Gravity Probe B spacecraft is also depicted; more about it later.

Fig 1 : <earth_distort>

The orbit of Mercury
One of the first tests for GR was proposed by Einstein himself: the orbit of Mercury was not a constant but varied over time, due to its precession. While Newton could explain the amount of precession for other planets, he failed to get complete agreement for Mercury. Einstein showed that the difference is due to the distortion of the space around our massive Sun; Mercury being the closest planet is affected more than others and the extent of the effect is about 10%, easily measurable.

Eddington and Solar Eclipse
One of the expectation of GR is that the gravitational field caused by a large mass should seem to bend light. So, as light passes close to very massive objects, its path should appear to shift. This is hard to see since the amount of bending is very small. Conversely, if the bending is sufficient for us to see it, then the object must be very massive, in fact, as massive as our Sun. So the best option is to look at how our Sun bends starlight.

Fig 2: <relativity_lightdemo>

Unfortunately, this natural experiment also has a problem: The Sun is so bright that it's difficult to see starlight passing anywhere near it! Exactly when we want to observe the starlight (when it's passing close to the sun) is the exact time that the starlight can't be seen! Unless, of course, you could "switch off" the Sun.

Fig 3 : <starlight>

This is exactly what Eddington did: he waited for a solar eclipse when the moon blocked light from the Sun; the date was May 19, 1919. He took photos of groups of stars positioned near the Sun when it was blocked and dim because of the eclipse. He compared them to similar photos taken at night — when the light of those stars would not pass close to the Sun before reaching us.

The photos revealed that the sun's gravity did indeed change the path of nearby starlight, as can be seen from the famous "negative" of the picture seen here. (The star positions are marked as faint dashes in the photo.) This experiment was a great boost for GR.

Fig 4: <1919_eclipse_negative>

Gravitational Lensing
There are now many more modern tests of GR. One of the most spectacular is gravitational lensing. These are similar to what Eddington did. Here, a star that is behind a dense galaxy suffers multiple refractions due to the matter in front of it. So the matter acts as a lens, bending the light rays. Einstein's Cross is a quasar in the Pegasus constellation. It is one of the best-known examples of gravitational lensing. The quasar is about 8,000 million light-years from Earth, and sits behind a galaxy that is 400 million light-years away. Four images of the quasar appear around the galaxy because the intense gravity of the galaxy bends the light coming from the quasar (see image taken by NASA's hubble Space Telescope).

Fig 5 : <einstein_cross>

Gravity Probe B
Though Earth has a much weaker gravity than the Sun, technological advances have made it possible to confirm its GR effects. Spinning gyroscopes were placed in orbit aboard NASA’s longest-running mission, Gravity Probe B.

It became one of the longest-running projects in NASA history, with results finally announced only in 2011. The goal of the experiment was to test two key predictions derived from GR: one, that spacetime should be warped (or distorted) around a massive body; and second, that a rotating body like the Earth will literally drag spacetime around with it as it spins. Both these effects were seen by Gravity Probe B (see picture above).

Gravitational Waves
In 1916, Einstein published a paper in which he predicted the existence of gravitational waves. These are disturbances in the fabric of spacetime caused by the acceleration of massive objects. Like ripples in a pond, they propagate outwards in all directions, though at the speed of light. In theory, cataclysmic events like the spiraling merger of two neutron stars or black holes should create such ripples in spacetime, and scientists should be able to detect those ripples when they sweep past Earth. These waves were indirectly observed in a binary pulsar over 50 years ago.
However, in September of 2015, a direct detection was made of the gravitational waves emitted by two colliding black holes nearly 1.3 billion light years away! The instrument LIGO and its discovery will go down in history as one of the greatest human scientific achievements: 100 years after Einstein predicted them, gravitational waves were found, behaving exactly as predicted by the General Theory of Relativity.

Fig6 <gravity_waves>

The picture shows a three-dimensional computer simulation of how two black holes merge. The simulations were done according to Einstein's theory of general relativity on the Columbia supercomputer at the NASA Ames Research Center.  This was the largest astrophysical calculation ever performed on a NASA supercomputer. (Picture courtesy of NASA/ESA).
References:
1. Illuminating relativity: Experimenting with the stars, http://undsci.berkeley.edu
2. Wikipedia on General relativity and its tests