Geometric deformations of symmetric spacetimes with a string cloud

TL;DR

This paper introduces a deformation framework for symmetric solutions to Einstein's equations with string-cloud sources, unifying various cosmological and black hole models while preserving key geometric features.

Contribution

The authors develop a unified deformation approach for symmetric Einstein solutions with string clouds, applicable to cosmological and black hole spacetimes, preserving their core properties.

Findings

Deformation preserves the evolution of scale factors in cosmological models.

Killing horizon structures remain unchanged under the deformation.

Framework applies to FLRW, Kantowski-Sachs, Bianchi, and Reissner-Nordström-(A)dS spacetimes.

Abstract

We establish a deformation framework for highly symmetric solutions to the Einstein equations. In this framework, four-dimensional metrics are constructed from three-dimensional {\eta}-Einstein metrics admitting a deformation determined by a single function. Under this deformation, the resulting spacetime solves the Einstein equations with a string-cloud source. Within this framework , a wide range of symmetric spacetimes can be treated in a unified manner. These include FLRW, Kantowski-Sachs, and LRS Bianchi cosmological models (including Taub-NUT-(A)dS solutions), as well as Reissner-Nordstr\"om-(A)dS black holes admitting spherical, planar, or hyperbolic symmetry. In the cosmological setting, the deformation leaves the evolution equations for the scale factors unchanged, and hence the expansion history coincides with that of the corresponding undeformed models. For the deformed Reissner-Nordstr\"om-(A)dS black holes, the structure of Killing horizons is insensitive to the deformation.