Defining a Singularity
In physics and mathematics, a singularity is a point where a certain quantity becomes infinite or undefined. In the context of gravity, it's a location in spacetime where the density of matter and the gravitational field are predicted to be infinite, causing the normal laws of physics to break down.
Section 2: Gravitational vs. Mathematical Singularities
The most famous type is the gravitational singularity, predicted by Einstein's theory of general relativity to exist at the center of black holes and at the beginning of the universe (the Big Bang). There are also mathematical singularities, which are points where a mathematical function or equation behaves erratically, such as approaching infinity or being undefined.
Section 3: A Black Hole Example
Imagine a massive star collapsing under its own gravity. General relativity predicts that all of its mass will be crushed into a point with zero volume. This point is a singularity. While the mass is finite, the density (mass divided by volume) becomes infinite, creating an unimaginably powerful gravitational pull.
Section 4: The Edge of Modern Physics
Singularities are critically important because they signal the limits of our current physical theories. General relativity works well for most of the universe, but it cannot describe the conditions at a singularity. This tells physicists that a more fundamental theory, like quantum gravity, is needed to understand these extreme phenomena.