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 $m_2\equiv \kappa$). 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.

arXiv comment28 pages, 3 figures

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Cited by in corpus (11)

• Metric-affine Geometries With Spherical Symmetry
• Extracting Bigravity from String Theory
• Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation
• Teleparallel bigravity
• Black holes in torsion bigravity
• Absence of a Vainshtein radius in torsion bigravity
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• Dynamical torsion gravity backgrounds
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• Black holes in the long-range limit of torsion bigravity
• Spherically symmetric perturbations of a Schwarzschild black hole in torsion bigravity