The issue of Branched Hamiltonian in F(T) Teleparallel Gravity

TL;DR

This paper discusses the Branched Hamiltonian issue in F(T) teleparallel gravity, highlighting its disadvantages compared to F(R) gravity and proposing F(R,T) gravity as a potential solution.

Contribution

It identifies the Branched Hamiltonian problem in F(T) gravity and suggests F(R,T) gravity as a way to overcome this issue.

Findings

F(T) gravity has a Branched Hamiltonian problem.

F(R,T) gravity can bypass the Branched Hamiltonian issue.

F(T) gravity's second order equations are not necessarily advantageous.

Abstract

As in the case of Lanczos-Lovelock gravity, the main advantage of F(T) gravity is said to be that it leads to second order field equations, while F(R) gravity theory leads to fourth order equations. We show that it is rather a disadvantage, since it leads to the unresolved issue of `Branched Hamiltonian'. The problem is bypassed in F(R,T) gravity theory.