Solution of the vacuum Einstein equations in Synthetic Differential Geometry of Kock-Lawvere

TL;DR

This paper presents a non-classical spherically symmetric solution to the vacuum Einstein equations using Synthetic Differential Geometry of Kock-Lawvere, demonstrating the application of topos-theoretic methods in general relativity.

Contribution

It introduces a novel solution to Einstein's equations within SDG, bridging topos theory and gravitational physics.

Findings

Non-classical spherically symmetric vacuum solution derived

Application of SDG to Einstein equations demonstrated

Shows potential of topos-theoretic approaches in relativity

Abstract

The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. It is known that topos-theoretic geometry can be successfully developed within the framework of Synthetic Differential Geometry of Kock-Lawvere (SDG), the models of which are serving the toposes, i.e. categories possessing many characteristics of traditional Theory of Sets. In the article by using ideas SDG, non-classical spherically symmetric solution of the vacuum Einstein equations is given.