Spherically symmetric solutions in torsion bigravity

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 m2 ≡ κ). 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 (κ → 0), no inverse powers of κ arise at the first two orders of perturbation theory (contrary to what happens in bimetric gravity where 1/κ 2 factors arise at linear order, and 1/κ 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.

Absence of a Vainshtein radius in torsion bigravity

“…It was pointed out in Ref. [3] (and will be confirmed below) that the massive spin-2 sector of torsion bigravity is similar to ghostfree massive gravity in that its general exterior spherically symmetric static solutions involve only two arbitrary constants, one of them describing an exponentially growing solution. When considering both the massive and the massless spin-2 sectors, torsion bigravity solutions involve (similarly to ghostfree bimetric gravity) three arbitrary integration constants, the third one corresponding to the Einsteinlike massless spin-2 sector, and describing a Schwarzschildlike mass.…”

“…The aim of the present paper is to study whether an analog of the Vainshtein mechanism is present within tor-sion bigravity [3]. Torsion bigravity is a geometric theory which generalizes the Einstein-Cartan theory by having, besides a dynamical metric, a propagating torsion.…”

“…The present work will study some of these issues within a new type of bigravity theory, dubbed "torsion bigravity", which has not yet been studied in detail. Torsion bigravity [3] is a geometric theory, involving both massless spin-2 and massive spin-2 excitations, whose basic fields are a metric and an independent connection. The massive spin-2 degrees of freedom are contained within the torsion of the independent connection.…”

“…2 Our counting of arbitrary constants here does not use any asymptotic boundary condition, i.e., it allows for exponentially growing solutions at infinity. 3 In our torsion bigravity discussion below, we will use the notation κ for m 2 .…”

“…It was defined in Ref. [3] as a special case of the multi-parameter class of ghost-free and tachyon-free theories with propagating torsion introduced in Refs. [21][22][23][24][25][26].…”