Investigation of anisotropic metric in multidimensional space-time and generation of additional dimensions by scalar field

TL;DR

This paper explores how scalar fields can induce anisotropic metrics and generate additional dimensions in higher-dimensional space-time, providing solutions to Einstein's equations and methods for metric renormalization.

Contribution

It demonstrates the equivalence of scalar fields to anisotropic metrics and introduces a novel idea of dimension generation by scalar fields in higher-dimensional space-time.

Findings

Scalar fields can produce anisotropic metrics in higher dimensions.

Derived expressions for scalar field energy density that generate extra dimensions.

Proposed a renormalization procedure for the higher-dimensional metric.

Abstract

Were investigated anisotropic metric of higher dimensional space-time with only cosmological term and scalar field. Showed, that presence of scalar field is equivalent to anisotropic metric in the multy dimensional space-time and proposed idea of dimensions generation by scalar field. Were solved Einstein's equations for higher dimensional space-time of Kazner's type and derived expressions for density of energy for scalar field, which generate additional dimensions, and proposed the procedure of renormalization of the metric.