# General relativity

The theory of general relativity does not restrict itself to frames of reference that are moving relative to each other at a constant velocity. In the general theory accelerated frames are considered, as are gravitational fields - in fact, it can be shown that the effects of acceleration and gravitational field are equivalent.

### General relativity theory predicts the following:

(a) that light bends in a gravitational field - light just grazing the surface of the Sun has been observed to be deviated by some 1.75 seconds of arc;
(b) that the perihelion of Mercury, (its nearest point to the Sun), shows precession;
(c) that physical processes such as the vibrations within an atom are slowed down in a high gravitational field, and therefore the light coming from the stars is reddened slightly.

## Gravitational lensing

Light is deflected in the intense gravitational fields near a massive body such as the Sun or a black hole. It is only with bodies of astronomical masses that the deflection is big enough to observe. The observation of a quasar showed more than one image – but each one had a near identical spectrum and the intensity was affected similarly – therefore the images came from the same object. (Figure 1)

In some cases a complete ring of images has been observed. The focal lengths of gravitational lenses are about 1025 m or a billion light years.

## Flat and curved space

The idea that light is bent due to gravitational attraction near a massive body can be looked at in another way. Einstein suggested that space itself is curved near a massive object and so although a beam of light appears to be curving due to gravitational attraction it is actually following the 'contours' of the curved space. It is rather like rolling a ball across a rubber sheet that has been pulled downwards at the centre to simulate curved space due to a massive object.

According to the general theory, if a very large triangle were to be surveyed near the Sun or other large astronomical body the angles would not add up to 180o, suggesting that space is curved in a gravitational field!

If space is actually curved, which way does it curve? Has space a positive curvature like the surface of the Earth and therefore a finite size? Or has it a negative curvature like the saddle between two mountain peaks?

## Time and General Relativity

One of the predictions of the General theory of Relativity is that time runs more slowly in gravitational fields – the greater the field strength the more slowly time passes. The effect can be explained by a thought experiment using two clocks in a rocket.

Consider first the two clocks, A and B in a rocket that is moving. Both clocks emit pulses of light at regular intervals and these are detected by an observer in the centre of the rocket.

If the rocket is moving at a constant velocity the observer in the rocket will see the pulses of light from each clock reach them at the same rate since the clocks and the observer are in the same inertial frame.

However if the rocket starts to accelerate the observer will see the pulses from clock A arrive more rapidly than block B. This happens because the observer is moving 'into' the pulses from A but away from those from B. (Figure 2(a))

As far as the observer is concerned clock B is now running slower than clock A.

Because of the principle of equivalence the behaviour of light in accelerated fields is the same as that in gravitational fields. Therefore in the gravitational frame (Figure 2(b)) the clock nearest the Earth (clock A) will run slower than clock B because it is in a stronger gravitational field.
(See: 16-19/Relativity/Text/Principle of equivalence)

Imagine two clocks – one at the top of a tower and the other at the bottom. If the time shown by both clocks could be read by an external observer the clock nearest the ground would beat slightly more slowly because it is in a field of higher gravitational intensity.

Pound and Rebka carried out such an experiment in 1960 using an atomic clock, basically the gamma emitter 57Fe, and the 22.6 m high Jefferson tower at Harvard University They first placed the source at the top of the tower and the detector at the bottom and then put the source at the bottom of the tower and the detector at the top.

They measured the frequency of the gamma rays emitted by the source in both positions. Those emitted by the source when placed at the top of the tower and detected at the bottom wee found to be slightly blue shifted and those emitted when the source was put at the bottom of the tower and the detector at the top were found to be slightly red shifted.

This result indicated a minute slowing of time in the slightly stronger field at the base of the tower. The difference was indeed very, very small – the ratio of the frequency shift to the original frequency being about 5x10-15!

The result of relativity and time at an atomic level is that the frequency of radiation from atoms is slowed down and so there is a gravitational red shift radially. Therefore the light coming from a person descending into a black hole in an intense gravitational field would be reddened. If they were to watched by an observer outside the event horizon for the black hole they would seem to be stretched out in the gravitational field (spagettification!) and become redder and redder as time for them slows down.