# Spherically symmetric solutions in torsion bigravity

## TL;DR

This paper explores spherically symmetric solutions in a novel torsion bigravity theory, revealing differences from general relativity and bimetric gravity, especially in high-compactness star models, with implications for gravitational physics.

## Contribution

It introduces torsion bigravity as a geometric framework with unique properties, including a specific spectrum of excitations and distinct perturbative behavior compared to bimetric gravity.

## Key findings

- Spherically symmetric solutions have the same degrees of freedom as ghost-free bimetric gravity.
- No inverse powers of the spin-2 mass parameter appear at low orders in perturbation.
- High-compactness star models differ significantly from GR predictions.

## Abstract

We study spherically symmetric solutions in a four-parameter Einstein-Cartan-type class of theories. These theories include torsion, as well as the metric, as dynamical fields, and contain only two physical excitations (around flat spacetime): a massless spin-2 excitation and a massive spin-2 one (of mass $ m_2 \equiv \kappa$). They offer a geometric framework (which we propose to call "torsion bigravity") for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. We find that the spherically symmetric solutions of torsion bigravity theories exhibit several remarkable features: (i) they have the same number of degrees of freedom as their analogs in ghost-free bimetric gravity theories ( i.e. one less than in ghost-full bimetric gravity theories); (ii) in the limit of small mass for the spin-2 field ($ \kappa \to 0$), no inverse powers of $\kappa$ arise at the first two orders of perturbation theory (contrary to what happens in bimetric gravity where $1/\kappa^2$ factors arise at linear order, and $1/\kappa^4$ ones at quadratic order). We numerically construct a high-compactness (asymptotically flat) star model in torsion bigravity and show that its geometrical and physical properties are significantly different from those of a general relativistic star having the same observable Keplerian mass.