Static Solutions with Spherical Symmetry in f(T) Theories

TL;DR

This paper investigates static, spherically symmetric solutions in f(T) gravity with Maxwell fields, highlighting the importance of frame choice and identifying conditions for solutions in specific frames.

Contribution

It demonstrates the sensitivity of f(T) solution reconstruction to frame choice and introduces a conformally Cartesian coordinate frame for analyzing solutions.

Findings

Solution existence depends on the chosen frame.

Limited class of f(T) models can be solved in the introduced frame.

Searching for solutions in general models remains an open challenge.

Abstract

The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and then we introduce a particular frame based on the conformally Cartesian coordinates. In this particular frame, the existence conditions of various solutions are presented. Our results imply that only a limited class of f(T) models can be solved in this frame. For more general models, the search for spherically symmetric static solutions is still an open and challenging problem, hopefully solvable in other frames.