Σημείο ισορροπίας αναιρετικό

Σημείο ισορροπίας αναιρετικό

Ακροβατείς στο όνειρο

πως γίνεται η κραυγή σου

της πόλης το μυστήριο

και ακούγεται η σιωπή

της αντοχής εφαλτήριο.

Ιφιγένεια Φ. Γεωργιάδου

John F. Nash, Jr., Princeton University: An Interesting Equation

This is the last recorded lecture held by Professor John Nash. The next day he gave the same lecture in Bergen. Two days after the lecture in Bergen, and three days after this lecture was recorded, Professor John Nash died in a tragic car accident on his way home from the Abel Celebrations.

This lecture was held at The University of Oslo, May 20, 2015 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.

Program for the Abel Lecture 2015:
1. "An Interesting Equation" by Abel Laureate John F. Nash, Jr., Princeton University
2. "Surely you're joking, Mr. Nash?" by Camillo De Lellis, University of Zürich
3. "Some remarks on Mathematics" by Abel Laureate Louis Nirenberg, Courant Institute, New York University
4. "Exploring the unknown, the work of Louis Nirenberg on Partial Differential Equations" by Tristan Rivière, ETH Zurich
5. "Soap Bubbles and Mathematics" a Science Lecture by Frank Morgan, Williams College, US

17:06

Lecture by John F. Nash Jr. - An Interesting Equation (PDF)

The equation that we have discovered is a 4th order covariant tensor partial differential equation applicable to the metric tensor of a space-time. It is simplest in form if written with the use of the Einstein G-tensor. Then it can take the form » math.princeton.edu

Is John Nash's "Interesting Equation" really interesting?

As recently mentioned in the news, before his passing, John Nash worked on general relativity. According to the linked article John Nash's work is available online from his webpage.

His work is summarized in this pdf of his lecture notes. One can see that he replaced Einstein's field equations in the vacuum with

□Gab+Gps(2Rpasb−12gabRps)=0.

Einstein's field equations for the vacuum read

Gab+λgab=0.$$G_{ab}+\lambda g_{ab}=0.$$

Nash's formula seems a lot more complicated, but my knowledge of general relativity ends here. Does anybody know whether similar modifications of Einstein's field equations have been considered in the literature? Is there any evidence that Nash's suggestion might be an interesting modification worth looking into more deeply?