From supernovas to black holes to hawking radiation
Generally speaking, when stars of lesser mass than the huge examples described on the previous pages go supernova, they collapse under the force of their own gravity to become black holes, only a fraction of their former size and of immense density.
Black holes are described as 'black' because they cannot emit light and 'holes' because anything that gets too close falls into them, apparently never to return, although that is now a matter of some dispute, as we shall see. Brian Greene explains: “After a star has burned all its nuclear fuel through billions of years of atomic fusion, it no longer has the strength – the outward-directed pressure – to withstand the enormous inward force of gravity. Under a broad spectrum of conditions, this results in a cataclysmic implosion of the star’s enormous mass; it violently collapses under its own tremendous weight”[1]. To gain some idea of the densities involved, it has been said that if our sun were to become a black hole, it would fit comfortably within upper Manhattan and for something the size of the earth to become a black hole, it would need to be crushed into a sphere with a radius of less than half an inch[2].
No one has ever seen a black hole (well, not until recently when a supermassive black hole was observed at the centre of M87, a neighbouring galaxy to our own Milky Way, courtesy the Event Horizon Telescope) because not even light can escape its immense gravitational pull, but its presence can often be detected by observing what is going on around it, for example a planet or similar phenomenon outside its gravitational reach orbiting what appears to be nothing, or the apparently anomalous behaviour of dust and gas just outside the black hole’s ‘event horizon’, the point at which things are sucked into its vortex.
Black holes do emit radiation – a phenomenon known as Hawking radiation after the physicist who provided the theoretical basis for its existence in 1975 - and as they do so their mass slowly decreases and it evaporates. However, the process is prodigiously long – longer than the age of the universe in some instances for larger black holes[3] Hawking went on to assert that black holes must also destroy information, a position from which he subsequently recanted. Smaller micro black holes are predicted to be larger net emitters of radiation than larger black holes, and to shrink and dissipate faster. Under this theory, black holes are not totally “black” because the vacuum of the imploding star lets out very tiny amounts of matter and energy in the form of photons, neutrinos and other subparticles.
The reasoning process leading to the discovery of Hawking radiation went something like this[4]:
- If general relativity is correct and the energy density is positive, the surface area of the black hole’s event horizon, its boundary, should always increase when additional matter or radiation falls into it, but when analysed in accordance with quantum mechanical principles, black holes still seem to be emitting particles at a steady rate, even after one has stopped spinning. [5],[6]
- How was one to reconcile general relativity – the theory of the very large – with quantum theory – the theory of the very small? Hawking reasoned that Quantum Physics, and in particular the Uncertainty Principle, could explain why black holes were radiating particles, and in particular virtual particles, which were basically particles of matter and anti-matter which are constantly being created and destroyed immediately.
- According to quantum mechanical principles, the whole of space is filled with pairs of virtual particles and antiparticles that are constantly materialising in pairs, separating and then coming together again, and annihilating each other.
- What happens is that right at the event horizon, because of the massive force of the black hole, one member of a pair of virtual particles may fall into the hole, leaving the other member without a partner with which to engage in mutual annihilation. The forsaken particle or antiparticle may fall into the black hole after its partner, but it may also escape to infinity, where it appears to be radiation emitted by the black hole[5]. In fact, they are not actually coming out of the event horizon, they are actually being created right at the side of the event horizon and to an outside observer, they are seemingly shooting out.
- Hawking then demonstrated that a black hole has entropy, that part of thermodynamics which basically states that everything must release heat (unless it is at absolute zero) including, and contrary to the conventionally accepted wisdom, black holes. A black hole can radiate, and it radiates as though it is hot, though not very hot, just mildly warm, the heavier the hole, the lower its temperature.
- This means that somewhere inside or around the black hole there is enormous randomness. Hawking deduced that the amount of entropy (the logarithm of the hole’s amount of randomness) is proportional to the hole’s surface area: the more virtual particle pairs there are, the smaller the black hole will become, which is why the phenomenon is also called Black Hole Evaporation.
- When matter and anti-matter collide and self-annihilate, they release energy taken from taken from the black hole’s potential gravitational energy. It doesn’t matter if it is the anti-matter or the matter that escapes, because the energy used to create that particle was energy from the black hole, which essentially means that the Black Hole is losing energy and therefore losing mass.
- If it’s a smaller black hole, then it will actually be radiating more than it is absorbing, which in turn implies that over time, the black hole will get smaller and smaller until eventually it just disappears. That means that, contrary to what general relativity says, if the black hole is small enough to start with, it will get smaller and smaller and smaller until it is gone completely.
- Hawking found that the emission stemming from the black hole was exactly what was required to identify the area of the event horizon with the entropy of a black hole.
- This entropy, a measure of the disorder of a system, is summed up in this simple formula:
4Għ
which expresses the entropy in terms of the area of the horizon, and the three fundamental constants of nature, c, the speed of light, G, Newton’s constant of gravitation, and ħ, Planck’s constant. It is engraved on Hawking's memorial stone at Gonville and Caius College in Cambridge where he worked.
- The ten characters of the Hawking radiation equation which appears over his resting place in Westminster Cathedral (above) express his idea that black holes in the universe are not entirely black but emit a glow. In this equation the T stands for temperature; the ħ for Planck's constant which is used to understand parts of quantum mechanics; c stands for the speed of light; 8Pi helps us to grasp its spherical nature; G is Newton's constant to understand gravity; M stands for the mass of the black hole and k stand for Boltzmann's constant, which is the energy of gas particles.
- In the end result, the ‘Hawking temperature’ of a black hole and the consequent ‘Hawking radiation’ revealed profound connections between general relativity (black holes), thermodynamics (the physics of heat) and quantum physics (the creation of particles where before there were none)[6].
Along the way, Hawking claimed to have resolved a paradox that had been argued over for 30 years: how was it possible that the radiation left over from a shrinking black hole could carry all the information about what made the black hole: the information paradox? Originally, Hawking claimed that the information was lost (fullstop). His later view was that information (distinctions between things) might escape during the black hole's evaporation and finish up imprinted in two dimensional form around the black hole's event horizon: "so we can be sure of the past and predict the future", but as Kip Thorne points out, he did not actually prove that that was the case, so the question remains essentially unresolved.[6] In his posthumously published last book, he seemed to steer a middle path, saying the information was not actually lost, simply not returned in a useful way - "like burning an encyclopaedia but retaining the smoke and ashes".
Einstein never accepted black holes as physically real objects. He remained confused by the unphysical singularity at the event horizon and assumed that nature would prevent it somehow. He argued that conservation of angular momentum would cause particles in a collapsing object to stabilise in orbits of finite radius, making it impossible for an event horizon to form[7].
The discovery of intermediate black holes
Until recently astronomers had only observed black holes in two general sizes: "small" ones about the size of small cities called stellar black holes formed when a star collapses, and supermassive black holes that are millions, maybe billions, of times more massive than our sun and around which entire galaxies revolve. Something in between didn’t quite make sense.
Then, in May 2019, the LIGO and Virgo gravitational wave detectors picked up a signal described as a dull thud lasting one-tenth of a second that turned out to be the energy from two large stellar black holes crashing into each other some seven billion years ago. One was 66 times the mass of our sun and the other a husky 85 times the mass of the sun. The result of the merger was what may be described as an intermediate black hole, 142 times the mass of the sun. Lost in the collision was an enormous amount of energy in the form of a gravitational wave, and this was the signal picked up by the detectors. This was a indeed a first, the results being more fully described at The 'hushed thud' in May 2019
[1] Greene (2000), 339.
[2] Greene (2000), 80.
[3] Andrew Hamilton, http://casa.colorado.edu/~ajsh/hawk.html.
[4] This explanation is essentially an amalgam drawn from three sources; Kip Thorne’s Foreword to Hawking’s posthumous memoir Brief Answers to the Big Questions, John Murray 2018, London; Stephen Hawking’s Chapter in the same book, “Why we must ask the big questions”, and the site https://www.quora.com/What-is-Hawking-radiation (explanation of Unnikrishnan Menon).
[5] Hawking, Stephen. Brief Answers to the Big Questions, esp Ch 5 "What is inside a black hole" p 113; also (Kindle Locations 299-319). Hodder & Stoughton. Kindle Edition. Alternate references are from Kindle Locations 1174-1181.
[6] Kip Thorne Foreword, Hawking, Stephen. Brief Answers to the Big Questions: the final book from Stephen Hawking (Kindle Locations 103-121), Hodder & Stoughton. Kindle Edition, 16 October 2018. These issues are also comprehensively explored in Einstein and Hawking, Masters of the Universe, (2 Parts), (tells a brief history of relativity), BBC 2019, precis at https://in.mashable.com/science/10936/einstein-and-hawking-masters-of-our-universe-tells-a-brief-history-of-relativity
[7] Lawrence M Krauss, "What Einstein got wrong", Scientific American, Special Issue, 100 years of General Relativity, September 2015, 41 at 43.