I received an email today about the award of the 2020 Nobel Prize in Physics to **Roger Penrose**, **Reinhard Genzel** and **Andrea Ghez**. Roger Penrose receives one-half of the prize "for the discovery that black hole formation is a robust prediction of the general theory of relativity." Genzel and Ghez share one-half "for the discovery of a supermassive compact object at the centre of our galaxy". Roger Penrose is an English mathematical physicist who has made contributions to the mathematical physics of general relativity and cosmology. I have checked some of his works which relate to mathematics, and I have found the paper

- M. Ko, E. T. Newman, R. Penrose,
*The Kähler structure of asymptotic twistor space*, Journal of Mathematical Physics**18**(1977) 58–64, doi:10.1063/1.523151,

which seems to indicate Penrose has widely contributed generally to the mathematics of general relativity like tensors and manifolds. Now my question here is:

QuestionWhat are contributions of Sir Roger Penrose, the winner of the 2020 Nobel prize in physics, to the mathematics of general relativity, like tensors and manifolds?

We may motivate this question by adding a nice question which is pointed out in the comment by Alexandre Eremenko below where he asks: *Is Sir Roger Penrose the first true mathematician to receive a Nobel prize in physics?* If the answer is yes, then Sir Roger Penrose would say to us "before being a physicist you should be a mathematician". On the other hand, in my opinion the first mathematician to be awarded several physics prizes is the American mathematical and theoretical physicist Edward Witten. This seems to meet Sir Roger Penrose in his research such as cosmology and research in modern physics (Einstein general relativity).

**Related question**: Penrose’s singularity theorem