Four-scalar model and spherically symmetric solution in f(T) theory

Document Type

Article

Publication Date

9-2025

Abstract

In this study, we explore the realization of spherically symmetric solutions in the context of modified teleparallel gravity, particularly in f(T) theory, where T denotes the torsion scalar. Traditional mimetic gravity and its extension using two scalar fields fail to reproduce general spherically symmetric spacetimes within f(T) gravity due to the requirement of a constant torsion scalar or a linear form of f(T), which restricts the theory to the teleparallel equivalent of general relativity (TEGR). To address this limitation, we propose a four-scalar field model that extends the two-scalar framework, allowing the construction of arbitrary spherically symmetric spacetimes. We show that this model eliminates ghost degrees of freedom through suitable constraints enforced by Lagrange multipliers. As a test of our procedure, we consider a specific form of a spherically symmetric spacetime and derive the associated four scalars, analyzing their behavior. Within the framework of a quadratic correction term, [Formula presented], our method demonstrates the ability to reconstruct physically relevant solutions with non-ghost scalar fields. These results underscore the broader applicability of scalar field models in constructing viable geometries within modified gravity theories, extending beyond the scope of standard formulations.

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