Andrew Conway

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 |

- Observational evidence for the existence of intermediate mass black holes is far from clear.
- Primordial black holes might have been formed in the early Universe.

- A black hole is an object which has all its mass inside its event horizon.
- The event horizon is a boundary within which nothing can escape, not even light.

- The simplest type of black hole is the Schwarzschild black hole.
- It is a non-rotating black hole that has a spherical event horizon.
- The radius of the event horizon is called the Schwarzschild radius and is proportional to the object's mass.
- If M is the mass in solar masses, then the radius is equal to:

M × 2.95 km

- At distances much larger than the event horizon, the gravity exerted by a black hole is the same as for any object of the same mass.
- For example, if we replaced the Sun with a black hole of equal mass, the Earth would carry on moving in exactly the same orbit.
- It is only when you get close to a black hole - within a few times its Schwarzschild radius - that unusual effects are noticed.

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:

- At first the object behaves as you'd intuitively expect.
- As it gets closer to the black hole, you notice the time between flashes lengthens.
- You also start to notice that the light is looking more red and less blue.
- The object then seems to dim and then vanish - it now emits only infrared radiation.
- At the moment it appears to reach the event horizon, the light (which had begun to emit only radio waves!) stops flashing all together.

- Black holes cannot be understood using the classic physics laid out by Newton's laws.
- Instead we must use Einstein's theory of General relativity.
- It is easiest to begin with Special relativity.

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

- The laws of physics are the same to all observers travelling at constant speed relative to each other (often called inertial frames).
- 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.

- Moving clocks tick more slowly.
- Moving objects are reduced in size along their direction of motion.
- If you view two spaceships moving in opposite directions at 0.9c, the occupants of each spaceship will see the other moving away at less than c.
- Time travel into the future is possible by travelling close to the speed of light.
- Two observers might not agree on length and time measurements, but cause and effect are always preserved.

- Two identical twins Jack and Jill are born on Earth.
- At age 20, Jill departs on a space ship to the nearest star (4 light years) travelling at 0.8c.
- It takes 5 years to cover this distance at 0.8c, so the round trip is 10 years.
- Jack is 30 when Jill returns; Jill is only 26. Time has passed at different rates for each twin.
- But, from Jill's point of view the Earth with Jack on it moves at 0.8c; why isn't Jack 4 years younger at the end? This is the paradox.
- The answer is that we have ignored acceleration and special relativity cannot be simply applied to this situation. But what is described above is accurate - Jill will be approximately 4 years younger on her return.

- General relativity deals not only with accelerating observers, but also with gravity.
- Einstein published it in 1916.
- It includes Special relativity as a special case.
- The postulates of special relativity are still held, but the equivalence principle is introduced.

Newton's laws stated:

- An accelerating object must be experiencing a force equal to the its acceleration multiplied by the object's
*inertial*mass. - The gravitational force on an object is proportional to its
*gravitational*mass. - The equivalence principle states that these two masses are the same.

But why are those two masses equal?

- If the Earth were replaced by a pea moving at exactly the same velocity, it would orbit exactly as the Earth does.
- The orbit of the Earth, or any object, does not depend on its own mass, nor on any other of its own properties.

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

- The lift is in free fall towards the Earth.
- The lift is in orbit around the Earth.
- The lift is in space, far from any large mass.

In all three cases you would feel weightless.

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:

- flat spacetime: objects move with constant velocity.
- curved spacetime: objects have their velocity changed, and follow certain curves dictated by the shape of spacetime.

- space: three dimensions - up/down, left/right, forward/back.
- time: one dimension - we can only move forward in time.
- But we live in a four dimensions, e.g. if I arrange to meet you at a particular place (specifying three co-ordinates), that is of no use if I fail to specify the time too.
- So, just as we have a point in space and a moment in time, we can talk of an event in spacetime, which is four dimensional.

Source: Johnstone CC-BY SA 3.0

- The rubber sheet analogy shows that spacetime is deformed by the presence of mass, and the curvature is greatest nearest the mass.
- Imagine flicking a marble onto the rubber sheet - given the correct velocity, and if there were no friction, the marble could be made to orbit. This extends the analogy to explain the orbit of planets.
- The situation can be pithily summarised as follows:

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

- At speeds much less than light and if you are many times the Schwarzschild radius away from a compact mass (black hole or neutron star), Newton's laws hold and our intuitive understanding applies - this corresponds to a nearly flat spacetime.
- If we are in a nearly flat spacetime region and observe an object close to a compact, massive object, we will see the effect of gravitational time dilation (clocks tick more slow) and the closely related phenomenon of red shift.
- The path that light takes, though not its speed, is affected by the curvature of spacetime, giving rise to gravitational lensing.

The theory is now very well supported by evidence:

- Positions of stars during a solar eclipse were observed to have their apparent positions altered by gravitational lensing.
- Discrepancies of Mercury's orbit that could not be accounted for by Newton's laws were explained by General relativity.
- Gravitational time dilation has been observed in atomic clocks in the Earth's gravitational field, and requires corrections to be made in GPS satellite signal processing.

- By applying quantum physics to a location just outside the event horizon, it can be shown that black holes do emit a tiny amount of energy.
- Unlike stars, the luminosity is inversely proportional to mass.
- Very low mass primordial black holes will emit significantly and will evaporate completely, becoming very luminous in their final moments.
- Larger black holes emit so little that they will absorb more energy, e.g. from cosmic rays, than they emit at present.

Source: AllenMcC CC-BY SA 3.0

- One region of spacetime is connected to another region of spacetime.
- This means that it might be possible to travel from one place in the Universe to another in short times without travelling faster than the speed of light.
- It may even possible to travel between times in this way, possibly even back in time.
- It remains to be seen if this is physically possible; quantum physics may prohibit it.