Appears in collection : General relativity: a celebration of the 100th anniversary

https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-rogerpenrose.pdf Abstract. Up until recently, the applications of twistor theory to general relativity have been rather limited, applicable mainly to special solutions of the Einstein equations and to complex solutions which are anti-self-dual, these describing left-handed “non-linear gravitons”. Recently, however, a new approach—palatial twistor theory—has emerged which, though related to the earlier ambitwistor approach, is essentially different, bringing the quantum ideas of non-commutativity into the geometry. Though the (Einstein) space-times treated this way are still classical, the approach suggests a possible route to a quantum gravity theory.