Black holes and relativity

Andrew Conway

Types of black hole

Type Typical Mass Typical Size
Supermassive 1,000,000 M 3,000,000 km
Intermediate 1000 M 3000 km
Stellar collapse 10 M 30 km
Primordial 10-7 M 0.3 mm

Black holes

Event horizon radius

M × 2.95 km

Concentration of mass

Dropping into the event horizon

Thought experiment: You are located many Schwarzschild radii away from a black hole, and you release an object with a blue flashing light on it from rest, so that it falls directly towards the black hole. You would observe:

Theory of black holes

Special Relativity

This theory was published in 1905 by Albert Einstein. It is based on two postulates:

  1. The laws of physics are the same to all observers travelling at constant speed relative to each other (often called inertial frames).
  2. The speed of light in a vacuum is measured to be the same by all observers.

The speed of light is denoted by c, and is 299,792,458 m/s. It is commonly approximated to 300,000 km/s.

It is the second postulate that allows us to predict the counter-intuitive effects that become noticeable for objects moving close to the speed of light.

Special relativity effects

The twin paradox

General relativity

The equivalence principle and mass

Newton's laws stated:

But why are those two masses equal?

Equivalence principle and orbits

Equivalence principle - in a lift!

If you were inside a lift (or some windowless, sealed container), there is no experiment you can do to distinguish between the following:

In all three cases you would feel weightless.

Gravity vs spacetime curvature

So, instead of the Earth, or a pea, or any object feeling a mysterious force of gravity that just happens to be proportional to its mass, we imagine that the motion of an object is influenced by the curvature of spacetime:


Rubber sheet analogy

Spacetime curvature

Source: Johnstone CC-BY SA 3.0

Curvature of space time

Mass tells spacetime how to curve and spacetime tells masses how to move.

Some General Relativity effects

Evidence for General Relativity

The theory is now very well supported by evidence:

Hawking radiation

Worm hole - schematic

Worm hole spacetime

Source: AllenMcC CC-BY SA 3.0

Worm hole