Against geometry: Nonstandard general relativity

TL;DR

This paper proposes a class of nonstandard solutions to Einstein's equations that can explain arbitrary rotation curves without dark matter, challenging the geometric interpretation of general relativity.

Contribution

It introduces nonstandard vacuum solutions of Einstein's equations that embed Schwarzschild solutions and suggest a Minkowski space framework over the traditional geometric view.

Findings

Nonstandard solutions can reproduce arbitrary rotation curves.

Dark matter may be unnecessary if these solutions are physically valid.

General relativity can be viewed as a classical field theory in Minkowski space.

Abstract

We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed in the standard theory cannot be found. As a consequence general relativity is considered as a classical field theory in Minkowski space and not as a geometric theory in the sense of Einstein.