Penrose-Hawking singularity theorems for an application of the focusing theorem.

The latter approach has led to some important results, most notably the Penrose-Hawking singularity theorems.

It conflicts with the Penrose-Hawking singularity theorems, for a start; and then there are other difficulties.

This work was extended by Hawking to prove the Penrose-Hawking singularity theorems.

However, the Penrose-Hawking singularity theorems show that a singularity should exist for very general conditions.

The issue cannot be avoided, since according to the Penrose-Hawking singularity theorems, singularities are inevitable in physically reasonable situations.

The Penrose-Hawking singularity theorems require the existence of a singularity at the beginning of cosmic time.

The Penrose-Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities.

Gravitational singularity (Penrose-Hawking singularity theorems)

Other similar theorems were found later on by Hawking and Geroch (see Penrose-Hawking singularity theorems).

As a super theory, EMD violates the positivity condition in the Penrose-Hawking singularity theorems.

Shortly afterwards, Hawking showed that many cosmological solutions describing the Big Bang have singularities without scalar fields or other exotic matter (see Penrose-Hawking singularity theorems).

For the purposes of proving the Penrose-Hawking singularity theorems, a spacetime with a singularity is defined to be one that contains geodesics that cannot be extended in a smooth manner.

His most significant contribution is the eponymous Raychaudhuri's equation, which demonstrates that singularities arise inevitably in general relativity and is a key ingredient in the proofs of the Penrose-Hawking singularity theorems.