A little bit about curvature singularities

If you have ever taken a science class in school, chances are you’ve heard of the following two concepts: black holes and the Big Bang Theory. Each of these concepts has given rise to a fundamental question that is yet to be answered by scientists. Regarding black holes: what could possibly be behind those big black voids? And as for the Big Bang Theory: what exactly existed prior to the big explosion? Our matter and energy must have come from something, somewhere.

An example of a curvature singularity.
In a black hole as such, spacetime is
curved infinitely and the singularity
lies in the center.

These two fundamental questions can be resolved by invoking the existence of spacetime singularities. A spacetime singularity (or gravitational singularity) is a spot where the curvature of spacetime and the quantities used to measure a gravitational field are infinite. Here, the classical laws of physics that we know and experience on a daily basis break down: gravity and matter behave in ways that we cannot predict.

It is believed that the center of a black hole contains a singularity, a single point that contains infinite mass in an infinitely small area. All the matter and energy that gets pulled into the black hole flows to this spot. The effects of gravity strengthen as you approach a black hole. At the singularity, gravity is infinite. The curvature of spacetime is therefore also infinite (since Einstein told us that gravity is the curve in spacetime).

The Big Bang Theory suggests that before the explosion, the beginning of our universe was itself a singularity. All of the matter and energy currently in our universe was concentrated in a space of zero volume. Since ρ = M/V, the density of our universe at that moment was infinite.

An example of a conical singularity.
Spacetime is flat, yet a singularity can
theoretically still exist.

Spacetime singularities can be thought of as both the end and the beginning of space and time. Before the Big Bang, everything was contained in one spot. When that exploded, space and time was created along with matter and energy. In this way, we can think of this singularity as the beginning. As for black holes, their singularities stretch time and space to the point where they rip the fabric of spacetime. In a sense, it is the end of space and time.

The type of singularity described above is fittingly named “curvature singularity.” Another type, dubbed the “conical singularity,” does not involve a curved space or gravity. In this situation, a flat space simply happens to have a hole (see Figure to the right). This type of singularity, however, has little physical importance. Astrophysicists are more interested in learning about curvature singularities as they are more relevant to black holes and the beginning of our universe.

There is much mystery surrounding spacetime singularities and, as a result, remain purely theoretical. Physicists have many interpretations of what a singularity is, or what it could be. However, physicists do generally agree that the term “singularity” refers to infinite quantities that are practically inconceivable to us today.

Sources:

Uggla, Claes. "Spacetime Singularities." Einstein Online. Web. 23 Apr. 2015.
"Singularities - Black Holes and Wormholes - The Physics of the Universe." Singularities - Black Holes and Wormholes - The Physics of the Universe. N.p., n.d. Web. 23 Apr. 2015.
Curiel, Erik. "Singularities and Black Holes." Stanford University. Stanford University, 29 June 2009. Web. 23 Apr. 2015.

- Sarah Shy