Static Anisotropic Solutions in f(T) Theory

TL;DR

This paper derives new spherically symmetric solutions in f(T) gravity, including isotropic and anisotropic matter configurations, reconstructs the algebraic form of f(T), and explores a polytropic stellar model.

Contribution

It introduces novel solutions in f(T) theory for both isotropic and anisotropic fluids, and reconstructs specific f(T) functions for these cases.

Findings

New spherically symmetric solutions in f(T) gravity.

Reconstruction of algebraic f(T) functions for specific matter contents.

Analysis of a polytropic stellar model within f(T) framework.

Abstract

In a previously work, we undertook a static and anisotropic content in $f(T)$ theory and obtained new spherically symmetric solutions considering a constant torsion and some particular conditions for the pressure. In this paper, still in the framework of $f(T)$ theory, new spherically symmetric solutions are obtained, first considering the general case of an isotropic fluid and later the anisotropic content case in which the generalized conditions for the matter content are considered such that the energy density, the radial and tangential pressures depend on the algebraic $f(T)$ and its derivative $f_{T}(T)$. Moreover, we obtain the algebraic function $f(T)$ through the reconstruction method for two cases and also study a polytropic model for the stellar structure.