Generalized Minkowski space with changing shape

TL;DR

This paper explores a generalized Minkowski space with a variable shape function, extending previous work on Minkowski products to model space-time-like structures with both deterministic and stochastic variants.

Contribution

It introduces a new model of Minkowski space with a changing shape function, including deterministic and random versions, broadening the mathematical framework for space-time structures.

Findings

Deterministic model can be defined with a shape function.

The model captures space-time-like properties.

Random variant introduces stochastic elements into the structure.

Abstract

In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could investigate a more general structure than a Riemannian manifold. Particularly interesting such a model when the negative direct component has dimension one and the model shows certain space-time character. We will discuss this case here. We give a deterministic and a non-deterministic (random) variant of a such a model. As we showed, the deterministic model can be defined also with a "shape function".