I have received an email this day  about Author Awarded 2020 [Nobel Prize in Physics](https://www.aip.org/science-news/nobel2020) such that the winners are:  **Roger Penrose**, **Reinhard Genzel** and **Andrea Ghez**. [Roger Penrose](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Roger_Penrose) is an English mathematical physicist he has made contributions to the mathematical physics of general relativity and cosmology. I have checked some of his works which related to mathematics I have got 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](https://doi.org/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:

>**Question**
What are contributions of Sir Roger Penrose the winner of Nobel prize 2020 to mathematics of general relativity like tensor and manifolds  ?

We may motivate this question adding a  nice question which it is pointed out in the comment by  Alexandre Eremenko below such that he asked: Is Sir Roger Penrose the first true mathematician to receive a Nobel prize in pysics? If the answer is yes then Sir Roger Penrose  would say  us "before being a physicist you should be a mathematician".