Wonders of the Universe - Brian Cox [81]
This coloured X-ray image shows the area around the supermassive black hole, known as Sagittarius A*, which sits at the centre of the Milky Way Galaxy.
NASA / SCIENCE PHOTO LIBRARY
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,