I have received an email this day about Author Awarded 2020 Nobel Prize in Physics such that the winners are: 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 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,

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".