The Formula Behind Black Holes
- Pranav Siddineni
- Jul 29
- 2 min read
Updated: Aug 16
Imagine a region in space where the gravity is so incredibly strong that nothing, not even light, can escape. That's the essence of a black hole. It's not a "hole" in the traditional sense, but rather a concentration of an enormous amount of mass squeezed into a tiny, infinitely dense space. A black hole forms when a massive star reaches the end of its life, running out of fuel and collapsing under its own immense gravity.
Key Features:
Event Horizon: This is the final boundary around a black hole — the point of no return. Anything that crosses this boundary is trapped forever, as the escape velocity (the speed needed to escape the black hole's gravity) exceeds the speed of light.
Singularity: At the center of a black hole lies a singularity — a point where matter is crushed to infinite density, and space-time curvature becomes infinite. This is where the laws of physics, as currently understood, break down.
The Math Formula Behind a Black Hole
The math behind black holes comes from Albert Einstein's theory of general relativity. A key part of this is the Schwarzschild Radius, which mathematically defines the event horizon for a non-rotating black hole.
In essence, this equation shows that if an object were compressed into a sphere with a radius smaller than the Schwarzschild Radius, a black hole would form. For example, to make the earth a black hole, it would have to be compressed to around 8.87 millimeters in radius — the size of a marble!
Note that this equation represents a simplified model, as it describes a non-rotating, uncharged black hole. The spacetime around a rotating black hole is more complex and is described by the Kerr Metric.
Recent Math Research
Black holes are an active area of research in mathematics. Here are a couple of recent advances:
Infinity of Possible Shapes: A recent mathematical proof suggests that in higher dimensions (five and above), there could be an infinite number of possible black hole shapes.
Reflections on Light: New equations can precisely describe how light bends and reflects around black holes, allowing scientists to study their gravitational environment.
Mathematicians and physicists study black holes extensively through computer simulations (pairing it with observational data). Perhaps one day we will have the technology to actually visit and peek into a real one!
