Regularization off(T)Gravity Theories and Local Lorentz Transformation

Gamal G L Nashed

doi:10.1155/2015/680457

Abstract

We regularized the field equations off(T)gravity theories such that the effect of local Lorentz transformation (LLT), in the case of spherical symmetry, is removed. A “general tetrad field,” with an arbitrary function of radial coordinate preserving spherical symmetry, is provided. We split that tetrad field into two matrices; the first represents a LLT, which contains an arbitrary function, and the second matrix represents a proper tetrad field which is a solution to the field equations off(T)gravitational theory (which are not invariant under LLT). This “general tetrad field” is then applied to the regularized field equations off(T). We show that the effect of the arbitrary function which is involved in the LLT invariably disappears.

Highlights

Amended gravitational theories have become very interesting due to their ability to provide an alternative framework for understanding the nature of dark energy
This is done through the modifications of the gravitational Lagrangian so as it renders an arbitrary function of its original argument, for instance, f(R) instead of Ricci scalar R in the Einstein-Hilbert action [1,2,3,4]
The idea is initially done by Einstein who had tried to make a unification between electromagnetism and gravity fields using absolute parallelism spacetime [5, 6]

Summary

Introduction

Amended gravitational theories have become very interesting due to their ability to provide an alternative framework for understanding the nature of dark energy This is done through the modifications of the gravitational Lagrangian so as it renders an arbitrary function of its original argument, for instance, f(R) instead of Ricci scalar R in the Einstein-Hilbert action [1,2,3,4]. The idea is initially done by Einstein who had tried to make a unification between electromagnetism and gravity fields using absolute parallelism spacetime [5, 6]. This goal was frustrated by the lack of a Schwarzschild solution.

Objectives

Conclusion