Having previously posted a small article about the early universe, I would like to update and add some ideas relating to this concept. Here it is:
∞ = mc3
Infinity = mass multiplied by the speed of light (in a vacuum) cubed. i.e. 27,000 trillion.
Essentially, this equation describes the escape velocity of a Black Hole, where, ∞ is the Black Hole and mc3 is the escape velocity.
Infinity – This generally describes a region where spacetime curvature becomes infinite due to a gravitational singularity. Einstein’s Field equations suggest that in some areas of the universe matter and energy can become so compressed that they reach infinite density.
A more recent physicist working on the theory of black holes named Schwarzschild, described the gravitational field of a point mass and a spherical mass. He noticed that there was a peculiar behaviour at what is called a ‘Schwarzschild radius’, where the maths become singular – meaning some of the terms in Einstein’s equations become infinite. This region would have zero volume, yet, contain all the mass of a black hole, therefore, resulting in infinite density. Therefore, any discrete amount of mass given 0% volume would result in infinite density.
The above infinite density is usually found at the point of singularity within a black hole. Any object whose radius is smaller than its Schwarzschild radius is called a black hole. The Schwarzschild radius can be classified as the radius of a spherically symmetric non-rotating object. The Schwarzschild radius is proportional to the mass of an object, assuming that the object has a constant mass density. Whereas, the physical radius of an object is proportional to the cube root of its volume. Therefore, as the object accumulates matter at a given fixed density, its Schwarzschild radius will increase more quickly than its physical radius, therefore, forming a black hole.
The above proposed equation (∞ = mc3) demonstrates that Einstein’s General Theory of Relativity holds true. Scientists currently argue whether Einstein’s equations are accurate enough to work at a quantum level. This is because the maths suggest that there are regions of the universe that become infinite. However, this singularity is addressed and resolved in the above proposed equation.
Extrapolation – Another way to understand the relationship between the mass and density of a black hole is to know that the volume increases to the 3rd power of the physical radius i.e. volume is mathematically the physical radius cubed. This has parallels to the notion of light being cubed in relation to black holes. The parallels being that the volume as well as light would both be working to the 3rd power.
Light and its movement can contain several properties. Two of these properties could be its speed and direction of movement. Three-dimensional space can be classified as having three directions of travel i.e. length, breadth and height. Therefore, light can also be seen to travel through these three dimensions of space. Therefore, forming space itself and as a result volume.
This equation can not only be used to describe regions of singularity within the existing universe but can also be used to describe the early universe, whereby, mass and energy were compacted into a very dense area. Therefore, an infinity could be seen to start the universe’s initial expansion.
Therefore, having drawn out the main parallels between the volume of a black hole and light and its speed both increasing by cubed numbers, then, the main conclusion to be drawn is that light travelling at its speed cubed has enough power to overcome the gravitational singularity of the black hole and that it has the potential to escape this entity. Therefore, mass × speed of light cubed is the escape velocity from a gravitational singularity (region of infinity within a black hole).