Black Holes

General Relativity

However, before we discuss black holes, we must first debrief the underlying theory which gives rise to black holes: the theory of general relativity formulated by Albert Einstein. General relativity can get very complicated but its basic principles aren't very difficult to understand. However, relativistic mechanics, the physics that governs bodies like black holes and stars, highly differs from classical mechanics, the physics used to explain our everyday lives. This distinction often makes the concepts of relativity very confusing to those who haven't gotten much experience. Another thing to note that there is also special relativity, also formulated by Einstein, which is different from general relativity. While both theories have very much similar bases, they explain two different things. General relativity explains how gravity causes interactions in the universe and its effect on nature. On the other hand, special relativity explains relativity outside gravity, especially with regard to light and time.

One of the most important ideas of general relativity is that it doesn't define gravity as a force as Newton did. Newton explained gravity as the mutually attractive force between two masses. This holds true for objects on the scales and speeds of ordinary, everyday objects like cars and people. However, if we take this and apply it to stars, then it becomes clear that there's an issue with Newton's Law of Gravitation.

The theory of general relativity has two important postulates: the speed of light in a vacuum is constant and that the laws of physics don't change between reference frames(if those reference frames themselves don't accelerate or rotate).

Since light is massless, light travels at the fastest speed an object can achieve, literally known as the speed of light, denoted by c. The speed of the light in m/s is 299,792,458 m/s and is essentially the universal speed limit.

Spacetime

Einstein didn't explain gravity as a force. Instead, Einstein asserted that gravity is a bend in the fabric of spacetime. Before we get ahead of ourselves, we have to explain what spacetime is. Spacetime is basically our three spatial dimensions(height, width, depth) but it also includes a fourth dimension, which is time. It can be thought of on a simple level as 3D space with the inclusion of time.

Now, where general relativity gets interesting is the presence of mass. Concentrated mass(also known as energy thanks to the famous equation E=mc^2) curves the otherwise flat fabric of spacetime, creating the effect we call gravity. This might make one ask how mass can affect spacetime if everything in the entire universe together is of finite mass.

This where the term "concentrated" is important. If the mass is compact enough, it'll curve spacetime. If the mass is more spread out, then that won't happen as much. This can be thought of intuitively even in classical mechanics with Newton's Law of Gravitation(Equation 7 on the Science Reference Astronomy Equation Sheet). The mass of the body is important but its radius is also important. The mass of the Sun is huge but a neutron star's gravity is much stronger than the Sun's because neutron stars have extremely compact radii.

Since mass curves spacetime, affecting both space and time, other objects with mass will be affected by the curvature and fall into it. This is, in Einstein's words, why we as humans fall towards the Earth's center of mass. While Newton's laws can also explain this accurately, it isn't the case in many instances. Take Mercury's Orbit, for example. Mercury orbits the closest to our Sun, which is extremely massive(much beyond any ordinary object which can be explained by Newton's laws). Mercury's orbit is slightly different from what Newton's laws predict as the orbit follows general relativity a lot better. This is because the Sun has more of a curving than force effect on Mercury's orbit given the conditions of the orbit(how close it is and how massive the Sun is).

The reason for Einstein's explanation of mass and how it curves spacetime is important because according to Einstein, the curvature of spacetime bends light. For Newton, this wouldn't be the case because light is massless so it wouldn't experience the force of gravity in Newtonian mechanics. However, as observed from our own eyes through telescopes, when we view distant objects, their light can get bent by other bodies, hence demonstrating how curvatures in spacetime created by mass can curve light.

Black Holes