String Theory has no Isotropic Solution for the Modified Einstein's Equations without the Dilaton

TL;DR

This paper proves that the modified Einstein's equations derived from string theory, without the dilaton, admit no static isotropic solutions, highlighting fundamental limitations of such models in describing isotropic spacetimes.

Contribution

It demonstrates that string theory modifications to Einstein's equations without the dilaton cannot produce static isotropic solutions, a novel no-go result in gravitational theory.

Findings

No static isotropic solutions exist for the modified equations.

Any isotropic solution must be static, leading to the conclusion of non-existence.

The proof includes the cosmological constant in the analysis.

Abstract

We investigate the modification to Einstein's vacuum field equations which is imposed by string theory when the dilaton field is ignored. Including the cosmological constant in all calculations, we prove that such a theory of gravity admits no static isotropic solution. We then show that any isotropic solution of the equations in question must necessarily be static, therefore proving that no isotropic solution exists for this stringy modification to gravity.