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Black Holes - No Need to Be Afraid! Transcript Black Holes - No need to be afraid! Transcript Date: Wednesday, 27 October 2010 - 12:00AM Location: Museum of London Gresham Lecture, Wednesday 27 October 2010 Black Holes – No need to be afraid! Professor Ian Morison Black Holes – do not deserve their bad press! Black holes seem to have a reputation for travelling through the galaxy “hovering up” stars and planets that stray into their path. It’s not like that. If our Sun were a black hole, we would continue to orbit just as we do now – we just would not have any heat or light. Even if a star were moving towards a massive black hole, it is far more likely to swing past – just like the fact very few comets hit the Sun but fly past to return again. So, if you are reassured, then perhaps we can consider…. What is a black Hole? If one projected a ball vertically from the equator of the Earth with increasing speed, there comes a point, when the speed reaches 11.2 km/sec, when the ball would not fall back to Earth but escape the Earth's gravitational pull. This is the Earth's escape velocity. If either the density of the Earth was greater (so its mass increases) or its radius smaller (or both) then the escape velocity would increase as Newton's formula for escape velocity shows: (0 is the escape velocity, M the mass of the object, r0 its radius and G the universal constant of gravitation.) If one naively used this formula into realms where relativistic formula would be needed, one could predict the mass and/or size of an object where the escape velocity would exceed the speed of light and thus nothing, not even light, could escape. The object would then be what is termed a black hole. Suppose that the density of the Earth was vastly increased but it was able to retain its present size so the escape velocity just reached the speed of light at the surface and so became a black hole. The surface of the Earth would then become what is termed the event horizon of the black hole. If the mass remained constant but the diameter of the Earth then reduced under the effects of the immense gravity, the region, whose diameter was the original diameter of the Earth and from which nothing could escape, would remain exactly the same size. The fundamental point is that the diameter of the event horizon bears no relationship to the size of the matter forming the black hole, only its mass. As we shall see, we believe that virtually all (if not all) of the interior of a black hole is empty space. Black holes have no specifically defined size or mass; until recently we had only found evidence for black holes in two circumstances. The first, with masses of many millions of solar masses, are found the heart of galaxies and are called super-massive black holes whilst the second are believed to result from the collapse of a giant star of perhaps 20 solar masses whose stellar core has a mass exceeding ~ 3 solar masses. This is the point at which we believe that neutron degeneracy pressure (which allows stellar cores in the range 1.4 to 3 solar masses to form neutron stars) can no longer prevent gravitational collapse. More recently evidence has been building for what are called intermediate mass black holes having a mass of perhaps 40,000 solar masses which have been found at the centre of what have in the past been classified as globular clusters. Omega Centauri is one such cluster, but the evidence of a black hole coupled with the fact that it contains many more young stars than globular clusters implies that, instead, it might be the remnant core of a dwarf galaxy whose outer stars have been stripped off by the gravitational effects of our own galaxy. The idea of a black hole can also be thought of in terms of Einstein’s General Theory of Relativity. This states that a massive body distorts the space around it making it curved so that light, for example, no longer travels in straight lines but curves round the location of the mass. A black hole is simply when the mass is so great that the curvature of space traps the light which can no longer escape. A Schwarzschild Black Hole In the simplest case in which the stellar remnant is not rotating, the spherical surface surrounding the remnant within which nothing can escape is called the event horizon which has a radius, called the Schwarzschild radius, given by 2 RS = 2 GM/c The interior of an event horizon is forever hidden from us, but Einstein's theories predict that at the centre of a non-rotating black hole is a singularity, a point of zero volume and infinite density where all of the black hole’s mass is located and where space-time is infinitely curved. This author does not like singularities; in his view they are where the laws of physics are inadequate to describe what is actually the case. We know that somehow, Einstein's classical theories of gravity must be combined with quantum theory and so relativity can almost certainly not predict what happens at the heart a black hole. Particle physics tells us that nucleons are thought to be composed of up quarks and down quarks. It is possible that at densities greater than those that can be supported by neutron degeneracy pressure, quark matter could occur - a degenerate gas of quarks. Quark-degenerate matter may occur in the cores of neutron stars and may also occur in hypothetical quark stars. Whether quark-degenerate matter can exist in these situations depends on the, poorly known, equations of state of both neutron-degenerate matter and quark-degenerate matter. Some theoreticians even believe that quarks might themselves be composed of more fundamental particles called preons and if so, preon-degenerate matter might occur at densities greater than that which can be supported by quark-degenerate matter. Could it be that the matter at the heart of a black hole is of one of these forms? Let’s just suppose that the matter at the heart of a 10 solar mass black hole was in the form of quark degenerate matter. How big might it be? The diameter of a 1.4 solar mass neutron star is ~20 km. Neutrons have a diameter of ~10-15 m and it is suspected that quarks have a diameter of ~10-18 m. As the volume goes as the cube of the diameter, the volume of a quark mass of 1.4 solar masses would be (103)3 smaller, that is 109 times smaller or 20,000 / 1,000,000,000 m in diameter = 0.0002 m = 0.02 mm! As the black hole would be ~7 times more massive, the quark mass would be ~ about 2 times larger or 0.04 mm. That is pretty small! [Note: I have never seen this calculation done, nor can I find any such thing on the web – so be warned it may be totally erroneous!] The more massive a black hole, the greater the size of the Schwarzschild radius: if one a black hole with a mass 10 times greater than another will have a radius ten times as large. A black hole of one solar mass would have a Schwarzschild radius of 3 kilometres, so a typical 10-solar-mass stellar black hole would have an event horizon whose radius was 30 kilometres. Kerr Black Holes There is a theorem, called the “no-hair” theorem that postulates that all black hole solutions of the Einstein- Maxwell equations of gravitation and electromagnetism are completely characterized by only three observable properties; their mass, electric charge, and angular momentum. Once matter has fallen into the event horizon all other information (the word "hair" is a metaphor for this) about the matter "disappears" and is permanently lost to external observers. [This is somewhat contentious, as the theorem violates the principle that if complete information about a physical system is known at one point in time then it should be possible to determine its state at any other time.] On the large scale matter is neutral, so it is not though that black holes would carry an electromagnetic charge but, on the other hand, the stars, dust and gas that might go to form a black hole have angular momentum – rotational energy - such as has a spinning star. Thus, in general black holes are though to be spinning. This makes them both much more interesting, but at the same time far more complex! The solutions for a rotating black hole were first solved by Roy Kerr in 1963 and are thus called Kerr Black Holes. The vast majority of black holes in the universe are initially though to be of this type, but there is a mechanism named after Roger Penrose that theoretically allows spinning black holes to lose angular momentum and so they might eventually turn into Schwarzschild Black Holes. Like a Schwarzschild black hole there is a singularity at its heart of a Kerr Black Hole surrounded by an event horizon, but beyond this is an egg shaped region of distorted space called the ergosphere caused by the spinning of the black hole, which "drags" the space around it. [This is called frame dragging and gives a way of observing that a black hole is rotating.] The boundary of the ergosphere and the normal space beyond is called the static limit.
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