Wonders of the Universe

INTO THE DARKNESS

The success of Einstein’s Theory of General Relativity is one of the greatest of human achievements, and in my view it will be remembered as such for as long as there is anything worth calling a civilisation. But there is a final twist to the story of gravitation, because Einstein’s remarkable theory predicts its own demise.

The collapse of a neutron star is prevented by neutron degeneracy pressure. Neutrons are fermions, as are electrons, but because they are more massive than electrons, they can be packed much more tightly together before the Pauli exclusion principle steps in once more and forbids further contraction. Another stable staging post against gravity should be provided by quark degeneracy pressure, because quarks too are fermions, but ultimately, if the star is too massive gravity will overwhelm even these fantastically dense objects. It is believed that the limit above which no known law of physics can intervene to stop gravity is around three times the mass of the Sun. This is known as the Tolman-Oppenheimer-Volkoff limit. For the remnants of stars with masses beyond this limit, gravity will win.

In 1915, only one month after Einstein published the Theory of General Relativity, the physicist Karl Schwarzschild found a solution to Einstein’s equations which is now known as the Schwarzschild metric. The Schwarzschild metric describes the structure of spacetime around a perfectly spherical object. There are two interesting features of Schwarzschild’s spacetime: one occurs at a particular distance from the object, known as the Schwarzschild radius, but for distances less than the Schwarzschild radius, space and time are distorted in such a way that the entire future of anything that falls in will point inwards. This sounds weird, but remember that space and time are mixed up together in Einstein’s theory. In more technical language, we say that the future light cones inside the Schwarzschild radius all point towards the centre. This means that, as inexorably as we here on Earth march into the future, if you were to cross the line defined by the Schwarzschild radius, you would inexorably march inwards towards the object that is bending spacetime. There would be no escape, not even for light itself, in the same way that you cannot escape your future. This surface, defined by the Schwarzschild radius surrounding the object, is known as the event horizon. But what has happened to the object itself? This is the second interesting feature of the Schwarzschild metric. Let’s first think about the Sun. If you asked what the Schwarszchild radius for a star with the mass of the Sun is, it would be 3 kilometres (1 mile). This is inside the Sun! So there is no problem here, because you can’t get that close to the Sun without actually being inside it, at which point all the mass outside you doesn’t count any more.

But what about an object like a collapsing neutron star, getting smaller and smaller and denser and denser? What if you could have an object that was dense enough to have the mass of the Sun and yet be physically smaller than the Schwarszchild radius? It seems that there are such objects in the Universe; the stars for which even neutron degeneracy pressure will not suffice to resist the force of gravity. These objects are called black holes. At the very centre of the black hole, at r=0, the Schwarzschild metric has another surprise in store; the spacetime curvature becomes infinite. In other words, the gravitational field becomes infinite. This is known as a singularity. In physical theories, the existence of singularities signals the edge of the applicability of the theory; in simple language, there must be more to it! This has led many physicists to search for a new theory of gravity. Quantum theories of gravity such as string theory may be able to avoid the appearance of singularities, by effectively setting a minimum distance scale below which spacetime does not behave in the manner described by Einstein’s equations.

Black holes are fascinating objects; we don’t understand them, and yet we know they exist. They are of immense importance…the physics that lies inside the event horizon is undoubtedly fundamental.

As yet, we do not know whether any of these current theories are correct, or even if they are on the road to being correct, but what we do know is that black holes exist. At the centre of our galaxy, and possibly every galaxy in the Universe, there is believed to be a supermassive black hole. Astronomers believe this because of precise measurements of the orbit of a star known as S2. This star orbits around the intense source of radio waves known as Sagittarius A^* that sits at the galactic centre. S2’s orbital period is just over 15 years, which makes it the fastest-known orbiting object, reaching speeds of up to 2 per cent of the speed of light. If the precise orbital path of an object is known, the mass of the thing it is orbiting can be calculated, and the mass of Sagittarius A^* is enormous – 4.1 million times the mass of our Sun. Since the star S2 has a closest approach to the object of only 17 light hours, it is known that Saggitarus A^* must be smaller than this, otherwise S2 would literally bump into it. The only known way of cramming 4.1 million times the mass of the Sun into a space less than 17 light hours across is as a black hole, which is why astronomers are so confident that a giant black hole sits at the centre of the Milky Way. These observations have recently been confirmed and refined by studying a further 27 stars, known as the S-stars, all with orbits taking them very close to Sagittarius A^*.

This artist’s impression helps us to visualise the mysterious objects in space that are black holes.

Black holes are fascinating objects; we don’t understand them, and yet we know they exist. They are of immense importance, because despite the fact that we will never encounter one directly, the physics that lies inside the event horizon is undoubtedly fundamental. These are objects that will require a new theory of gravity, indeed a new theory of space and time, to describe. One of the holy grails of observational astronomy is to find a pulsar orbiting around a black hole. Such a system surely exists somewhere, and to be able to observe the behaviour of one of these massive cosmic clocks in the intensely curved spacetime close to a black hole would surely test Einstein’s Theory of General Relativity to its limit. It may even, if we are lucky, reveal flaws that point us towards a new theory