Four-dimensional effective theory of gravity embeddable in a distorted Randall-Sundrum brane scenario

TL;DR

This paper develops a four-dimensional effective gravity theory inspired by five-dimensional Randall-Sundrum models, incorporating Weyl geometry, addressing singularities, and exploring implications for brane stabilization.

Contribution

It introduces a Weyl-integrable geometric framework for effective 4D gravity compatible with Randall-Sundrum scenarios, including singularity resolution and applications to cosmology and black holes.

Findings

Vanishing of spacetime singularities for certain parameter values.

Recovery of general relativity through conformal symmetry breaking.

Insights into brane stabilization mechanisms.

Abstract

We present an effective four-dimensional formulation of the laws of gravity that respects the main features of a higher (five)-dimensional scenario of Randall-Sundrum type. The geometrical structure of the theory is that of a Weyl-integrable configuration. Standard general relativity over Riemann geometry is recovered through breaking of conformal symmetry. The singularity problem is treated. The local problem in the case of the static, spherically-symmetric Schwarzschild metric and the cosmological issue, in the case of Friedmann-Robertson-Walker perfect fluid filled universe, are treated separately. Vanishing of the spacetime singularities for some values of the free parameter of the theory is achieved. The implications of the results obtained for brane stabilization in the higher-dimensional structure are briefly discussed.