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 this paper entitled The Kähler structure of asymptotic twistor space seems the Author has widely contribution generally to 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 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 to us "before being physicist you should be a mathematician"