Interpretation of intuitionistic solution of the vacuum Einstein equations in smooth topos

TL;DR

This paper explores how the interpretation of vacuum Einstein equations within smooth topos theory reveals that additional dimensions can influence gravitational fields, cosmological constants, and space-time signatures, offering a novel perspective in theoretical physics.

Contribution

It introduces a new approach to analyzing vacuum Einstein equations using intuitionistic topos theory, highlighting the role of additional dimensions and variable cosmological constants.

Findings

Infinitesimal weak gravitational fields can be strong in certain stages.

Cosmological constant varies with additional dimensions.

Space-time signature depends on vacuum density and cosmological constant.

Abstract

The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. In the article spherically symmetric solution of the vacuum Einstein equations in the Intuitionistic theory of Gravitation at different stages of smooth topos ${\bf Set}^{\bf L_{op}}$ is considered. Infinitesimal "weak" gravitational field can be strong at some stagies, for which we have the additional dimensions. For example, the cosmological constant is not constant with respect to additional dimensions. Signature of space-time metric can depend of density of vacuum and cosmological constant.