Introduction to… General Relativity

The theory of General Relativity was developed by Albert Einstein in the early 1910s. It was a revolutionary, ground-breaking theory that changed the perception of the concepts of space and time that were held by physicists in 1916, the year the paper was published. It describes how gravity, the attracting force we all know so well, arises from the curvature of space. This introduction will try to explain the basic principles that underlie this theory.


Gravity in classical picture

If you think of a theory describing gravity, chances are you are thinking of Newton’s theory of gravity (probably accompanied by the famous story involving an apple…..); the force between two objects that have mass gets larger when the objects are heavier, and weaker when they are further apart. And this was the picture of gravity that was widely accepted until Einstein developed his theory of general relativity.


This theory describes gravity as something completely different; objects with mass cause spacetime* to curve, creating a force on any object in their vicinity. Think of a blanket with a ball in the middle, held up on the edges. The mass of the ball will make a dip in the blanket. Place a second ball on the sheet and it will move towards the first one, at the bottom of the dip. Something similar happens everywhere in space. However, now there is no sheet that is curved, but space itself.


*spacetime is the combination of three space dimensions and time, the fourth dimension. Einstein’s theory of relativity showed that time and space are related to each other, and one cannot be considered without the other


The bending of spacetime

This “bending of space” is a very abstract concept and difficult to visualize. Einstein came up with this idea when he was thinking of a lift. When you stand in a lift that is accelerating, you feel the floor of the lift push into your feet, and it feels like you are heavier than you usually are. Similarly, when you are in a fun ride going down a slope, or when the lift accelerates going down, you feel weightless as you are moving at exactly the same speed as the lift and your feet do not press down on the floor of the lift. This suggests that gravity can be mimicked by an acceleration upwards. If there is no gravity, the feeling of weight can be simulated by accelerating upwards, and when you are weightless there is either no gravity or you are in freefall. There is no way to distinguish between the two.


This observation might seem strange, but it is conceptually understandable from experience. However, it gets more complicated from here. Imagine a lift accelerating upwards. A person in the lift feels a force that resembles gravity, pulling them down. Now this person has a laser pointer, and shines a light on the other side of the lift. (See figure 1) There will be a time difference between the moment the person in the lift turns the laser pointer on and the moment the light reaches the other side of the lift. (This will be a split second, but let’s just imagine that the lift is very large) During this time, the lift is accelerating up, so the light will describe a curved trajectory and it hits the opposite side of the lift at a lower height than where the laser pointer is. Einstein concluded that gravity makes straight lines curve, and not even light can escape from it!

Figure 1: The thought experiment of an accelerating lift.

This was a revolutionary and completely new observation, because light is massless! Gravity was up to then always associated with massive objects only, but this thought experiment suggests gravity can also affect massless objects. This is because gravity changes spacetime, like the ball on the sheet mentioned earlier. Light follows straight lines in spacetime, but if it is spacetime itself that is curved, the light will follow a curved line instead. The curvature is caused by the mass of the object, and the heavier the mass the more curved spacetime will be. Moreover, from Einstein’s theory of special relativity, energy and mass are interchangeable; E=mc^2. So a very energetic object (for example when something is very hot) will curve spacetime more than when it’s cold. And even massless objects could curve spacetime.



This might sound like a very implausible and abstract theory. However, general relativity has predicted several effects that have been observed, the most recent one the occurrence of gravitational waves that was awarded with the Nobel Prize in Physics in 2017.


Gravitational lensing

As mentioned before, gravity also affects light, and will bend its trajectory. This has been observed in space, when there is a bright star very far away, that is obscured by a massive object. Instead of blocking out the light, multiple images of the star can be seen. This is because the object bends the light around it, acting as a lens. Sometimes the image of the star gets so much distorted that it can be seen as (part of) a ring. This is called an Einstein ring.


Figure 2: The action of a gravitational lens (Source: CFHTLenS)

Gravitational waves

Einstein’s theory also predicts that a very massive object (like a star or black hole) that rotates will emit gravitational waves, losing energy in the process. These waves cause slight distortions in space that can be measured. This was confirmed experimentally in 2016, when an experiment (called LIGO) observed a slight difference in length between two mirrors spaced 4 km apart. The change, however, was less than 10^-18 m! This feat was awarded the Nobel Prize in Physics in 2017.


Time dilation

Another effect of the bending of light by gravity is time dilation. Let’s measure the time it takes light to travel from A to B, and let’s call this distance x. Light always travels at the same speed; the light speed c. The time it will take to travel from A to B is thus x/c.

However, in the presence of a heavy object (M) the trajectory of the light is bent, and it will take longer for the light to go from A to B. It will travel along a path of length y. But light always travels at the speed of light, and the distance between A and B has not changed! The only solution is that the time runs slower near a heavy object. And this can be measured; clocks on Earth run slower than on satellites, that are orbiting the Earth at large distances, and GPS needs to correct for these differences. It is even predicted that on the surface of a black hole time will stop completely.

Figure 3: Curvature of space makes time runs slower