PenroseHawking

PenroseHawking refers to the body of work associated with Roger Penrose and Stephen Hawking on general relativity, gravitational collapse, black holes, and spacetime singularities. In common usage, the term is closely tied to the Penrose–Hawking singularity theorems, which collectively argue that under reasonable physical conditions spacetime cannot be geodesically complete.

The Penrose singularity theorem, introduced by Penrose in 1965, shows that if a spacetime contains a trapped surface formed by collapse, then geodesics cannot be extended in a smooth way, implying a singularity. The argument uses the focusing of geodesics, encapsulated by the Raychaudhuri equation, and certain energy conditions.

Hawking extended these ideas in the 1970s to cosmology, demonstrating that the expansion of the universe under similar assumptions would also lead to singularities. This broadened the scope from collapsing stars to the entire cosmos, reinforcing the view that singularities are a general feature of general relativity rather than isolated curiosities. The combined results are often referred to as the Penrose–Hawking singularity theorems and rely on global spacetime assumptions, such as causality conditions, and the existence of trapped surfaces or analogous conditions.

Impact and significance: The theorems provided foundational support for black hole physics and cosmology by showing that singularities are an expected outcome of Einstein’s equations under broad conditions. They do not describe the internal structure of singularities or the quantum nature of spacetime; addressing those questions has driven subsequent work in quantum gravity and related fields.

See also: Penrose–Hawking singularity theorems, Penrose diagram, Black hole, Hawking radiation, Quantum gravity.