Quadratic and cubic spherically symmetric black holes in the modified teleparallel equivalent of general relativity: Energy and thermodynamics

TL;DR

This paper derives new spherically symmetric black hole solutions in modified teleparallel gravity with quadratic and cubic torsion terms, analyzing their energy, invariants, and thermodynamics, revealing weaker singularities and novel physical effects.

Contribution

It introduces and analyzes new black hole solutions in f(T) gravity with cubic torsion contributions, extending previous quadratic models and exploring their physical and thermodynamic properties.

Findings

Higher-order torsion weakens singularities compared to GR.

Thermodynamic quantities are affected by cubic torsion terms.

New black hole solutions depend on additional parameters nd eta.

Abstract

In \cite{Bahamonde:2019zea}, a spherically symmetric black hole (BH) was derived from the quadratic form of $f(T)$. Here we derive the associated energy, invariants of curvature, and torsion of this BH and demonstrate that the higher-order contribution of torsion renders the singularity weaker compared with the Schwarzschild BH of general relativity (GR). Moreover, we calculate the thermodynamic quantities and reveal the effect of the higher--order contribution on these quantities. Therefore, we derive a new spherically symmetric BH from the cubic form of $f(T)=T+\epsilon\Big[\frac{1}{2}\alpha T^2+\frac{1}{3}\beta T^3\Big]$, where $\epsilon<<1$, $\alpha$, and $\beta$ are constants. The new BH is characterized by the two constants $\alpha$ and $\beta$ in addition to $\epsilon$. At $\epsilon=0$ we return to GR. We study the physics of these new BH solutions via the same procedure that was applied for the quadratic BH. Moreover, we demonstrate that the contribution of the higher-order torsion, $\frac{1}{2}\alpha T^2+\frac{1}{3}\beta T^3$, may afford an interesting physics.