Classical Space-Times from the S Matrix

TL;DR

This paper demonstrates deriving classical space-times, like Schwarzschild, directly from the S-matrix without using Einstein's equations, employing on-shell techniques and revealing connections between gravity and Yang-Mills solutions.

Contribution

It introduces a method to obtain classical space-times from the S-matrix alone, bypassing the Einstein-Hilbert action, and extends the approach to Yang-Mills solutions, highlighting algebraic relations.

Findings

Derived Schwarzschild space-time from S-matrix as a series in G_N.

Showed that space-times can be obtained without Einstein-Hilbert action.

Linked gravity and Yang-Mills solutions via algebraic relations.

Abstract

We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in $G_N$. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space-time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space-times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang-Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently than the more traditional Feynman diagram approach.