Between 1965 and 1970, Penrose and Hawking proved a set of six singularity theorems together, all of which make varied assumptions and have different starting points.

Of course, this all begs the question, what is a 'singularity?' In some text books you may find that a singularity appears in a model when the null or timelike geodesics cannot be extended indefinitely; that is to say, if the paths of photons or particles with mass terminate at some finite time into the past. That tells us when a singularity appears but not what it really,

******Though, when a cosmologist refers to the "Penrose-Hawking Singularity theorem" they're probably referring to the sixth theorem, which was proven in 1969 in a famous paper titled "The singularities of gravitational collapse and cosmology". This is the most powerful formulation of the Penrose-Hawking theorem, and it's the one I'll talk about here.Of course, this all begs the question, what is a 'singularity?' In some text books you may find that a singularity appears in a model when the null or timelike geodesics cannot be extended indefinitely; that is to say, if the paths of photons or particles with mass terminate at some finite time into the past. That tells us when a singularity appears but not what it really,

*actually*is. This turns out to be a difficult task but in The La…