Have you ever heard of black holes? I suspect that these days most people have (especially if you’re a fan of Star Trek!) but what are they exactly? In this blog, I’m going to describe what a black hole is, and why mathematicians are interested in them. However to fully understand what black holes are, I first of all need to explain what gravity is and so that’s where we shall start.
What is gravity?
You and I, the chair on which I’m sitting, the computer on which you’re reading this and indeed everything you can see around you is held to the floor because it is being pulled towards the centre of the Earth by the force we call gravity (this is what stops us floating off into space). And if I throw a ball upwards it will fall back down again because gravity pulls it back down. To beat gravity I have to travel very fast, and this is how space shuttles and rockets work – they travel fast enough to avoid being pulled back down to Earth.
Theoretically if I threw a ball upwards fast enough it would fly off into space – it’s just that I would have to throw it incredibly quickly! (If you study Mechanics 3 at A-level you’ll learn how to calculate exactly how quickly you would need to throw it at!)
How does this relate to black holes?
A black hole is a region of space in which gravity is so strong that it is impossible to escape from it no matter how fast you go. In particular, the gravity around a black hole is so strong that even light cannot escape from it – hence the name black hole; they appear black because no light is emitted from them. Black holes can occur when a massive star (one much bigger than our own Sun) collapses to form an incredibly dense region of space.
I have always been fascinated by the idea of black holes (not to mention white holes and worm holes, which I’ll explain more about in a later blog – this means my title is a bit of a cheat but I thought white holes and worm holes sounded more interesting than just black holes!) but
Representation of a black hole
Why are a mathematicians interested in black holes and objects in outer space?
The answer to this question is that one of the few ways we have to explore our universe is to use mathematics to probe the hidden mysteries of space. The universe is far too big for us to be able to see, hear or touch even a small fraction of what exists around us.
If seeing is believing, then Mathematics gives a deeper understanding!
Even if we can see something, such as a distant star or black hole, what does that really tell us? After all, if you stand on the cliffs at Dover (which is on the south coast of England) on a clear day you can see as far as France but all that tells you is that there is another country out there; it doesn’t tell you anything much about that country. Similarly, we can point a telescope towards space and see what there is to see, but that can only reveal a limited amount of information. For anything more meaningful we need to turn to mathematics.
Most modern physics works on a very simple principle. Physicists examine the world around us and from this they hope to deduce the laws of physics (such as Newton’s laws or Einstein’s field equations) which are usually expressed in the form of mathematical equations. Physicists then assume that these laws apply right throughout the universe, and this is where mathematicians step in. We can take the equations that physicists give us and play around with them to see what we find!
A good example of this is the discovery of black holes. The equations which form the basis of the fundamental laws of physics can be used to predict the existence of black holes, the properties of black holes and the circumstances under which they occur – even without actually ever seeing a black hole itself! Indeed, thanks to the use of mathematics, scientists and mathematicians have been aware of the possibility of black holes existing within our universe long before we were able to find any actual physical evidence of their presence!
The study of black holes, and indeed the universe in general, is part of the field of study known as Cosmology which is a branch of both mathematics and physics. As a mathematician I studied Cosmology at university, which is essentially an extension of the Mechanics modules I studied at A Level (such as Mechanics 3). And when you apply mathematics to the equations governing black holes you discover some interesting and very weird properties.
My personal favourite, which I was taught at university, is that inside a black hole time and space are swapped around – this means that time becomes space and space becomes time! And famously, the renowned theoretical physicist and mathematician Professor Stephen Hawking earned his PhD by proving that inside a black hole is a singularity – a point which has infinite density and at which the conventional laws of physics breakdown. Now take a moment to think about this. A black hole is black so we can barely see the black hole itself, let alone take a look at what’s happening inside it so how can we possibly know what’s inside a black hole? The answer is, of course, to rely on mathematics!
Dr John McDarby is a Mathematics teacher at Bellerbys London.
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