Our focus in Ep. 5, this episode, is black holes. We start by discussing the concept of escape velocity for satellites in Earth orbit, showing that the outcome of a launch depends on how much kinetic energy (energy of motion) the satellite had upon launch. We also recall that satellites that do end up orbiting gravitating bodies do so in elliptical orbits, in the Newtonian approximation. This helps explain why bodies launched with insufficient velocity come back to earth, like a thrown baseball. On the other hand, bodies launched with too much velocity get flung into outer space, having kinetic energy left over after they’ve climbed up and out of the earth’s gravitational well. Bodies launched with Goldilocks ‘just right’ speed are the ones that end up orbiting in ellipses. Along the way, we bust the myth that astronauts on the space shuttle don’t feel gravity – in fact they do, they’re just freefalling like the shuttle is as they orbit Earth. What they don’t feel is g-forces (an acceleration concept distinct from gravity itself).

We use the concepts of kinetic energy and gravitational potential energy to motivate a straightforward formula relating escape velocity to the mass of the big gravitating body, and to the distance from the centre of the body on launch. The closer in the satellite starts, the harder it is to escape the clutches of the big body’s gravity. The more massive that body, the harder it is to escape. We explain how the escape speed can even rise to the speed of light if you start out close enough to the centre of a gravitating body; this occurs at a radius called the Schwarzschild radius. This motivates the definition of a black hole as an object so dense it is physically contained within its own Schwarzschild radius. Another way of saying the same thing is that a black hole is a spacetime with such strong gravity that not even light can escape its clutches, if it falls in close enough to get caught by the black hole.

We next discuss the important features of the anatomy of black holes – horizons and singularities. The event horizon is defined as the surface of no return: if you cross it, you are fated to be drawn into the interior of the black hole and never come out again, ever. Physics behind the horizon may be interesting, but physicists there cannot communicate any of their results to the outside world because even photons are trapped inside the horizon! The singularity is a place, at the centre of a black hole, where the curvature of spacetime becomes formally infinite. That is a very nasty place indeed, because tidal forces – gravitational forces that stretch/squeeze perpendicular directions of a body (and which cause our ocean tides, incidentally) – are infinite at the singularity. So anything falling into the black hole singularity (everyone does, if they crossed the Schwarzschild radius) will be spaghettified in an untimely death. We mention en passant the deep problem of Einstein’s equations predicting curvature singularities; this motivates the need to develop “Gravity 3.0″: quantum gravity.

We next talk about how astronomers infer the existence of black holes, which are formed upon gravitational collapse when dead stars have run out of gas. The essence of their technique is to observe electromagnetic radiation emitted by particles in the accretion disk that forms around around the central black hole from gravitational attraction of nearby gas and dust, particles which can be heated to millions of degrees by friction in that disk. Redshift/blueshift of EM radiation is again the key idea. We also mention other clever methods used by astrophysicists and astronomers as well.

With the aid of a pretty poster from the Chandra web site at Harvard, we expand a little on stellar evolution for different kinds of stars. For instance, our Sun, after going through a red giant stage, will end up as a white dwarf star held up by electron Fermi degeneracy pressure (a concept we mentioned in episode 2 when introducing fermions). Bigger stars instead end up, after a spectacular supernova explosion, as neutron stars – which are held up by neutron Fermi degeneracy pressure. Even bigger ones, stars that started off at least ~5 or so times heavier than our Sun, eventually collapse in on themselves and form a black hole. In those cases, the stars are so heavy that no other force – not even electromagnetism, nor the weak nuclear force, nor the strong nuclear force – is able to prevent gravitational collapse!

There is a second interesting population of black holes in the universe. Black holes have also been discovered at the centre of most galaxies, dubbed supermassive black holes, with masses in the range of millions to a billion or so solar masses. Our own Milky Way galaxy has one of these. Supermassive black holes are important drivers of galactic evolution, and constitute a very active area of research in astrophysics. We finish with a Chandra picture of two active galaxies colliding, which includes a merger of supermassive black holes.

Here is a PDF of my slides from today. This is the narrated slideshow movie.