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Geometric deformations of symmetric spacetimes with a string cloud
Phys. Rev. D 114, 044058 – Published 18 August, 2026
DOI: https://doi.org/10.1103/fph6-bf9k
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 -Einstein metrics admitting a deformation locally 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-Nordström-(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-Nordström-(A)dS black holes, the structure of Killing horizons is insensitive to the deformation.
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