New scalar compact objects in Ricci-based gravity theories

Abstract

Taking advantage of a previously developed method, which allows to map solutions of General Relativity into a broad family of theories of gravity based on the Ricci tensor (Ricci-based gravities), we find new exact analytical scalar field solutions by mapping the free-field static, spherically symmetric solution of General Relativity (GR) into quadratic f (R) gravity and the Eddingtoninspired Born-Infeld gravity. The obtained solutions have some distinctive feature below the wouldbe Schwarzschild radius of a configuration with the same mass, though in this case no horizon is present. The compact objects found include wormholes, compact balls, shells of energy with no interior, and a new kind of object which acts as a kind of wormhole membrane. The latter object has Euclidean topology but connects antipodal points of its surface by transferring particles and null rays across its interior in virtually zero affine time. We point out the relevance of these results regarding the existence of compact scalar field objects beyond General Relativity that may effectively act as black hole mimickers. *

A generalized Weyl structure with arbitrary non-metricity

“…Once understood that disformal generalizations of a Weyl structure necessarily lead to abandoning the vectorial non-metricity postulate, let us consider two possible kinds of such generalizations: one relying on GL (N, R) as the symmetry group, and another kind of deformations which are present in the so-called Ricci-Based Gravity theories (RBGs), a broad class of metric-affine theories with projective symmetry recently considered in the literature [33,34,[50][51][52][53][54].…”

Metric-affine bumblebee gravity: classical aspects

“…Thus, from the original frame of the theory (RBG frame), these non-linear interactions appear encoded in the spacetime metric and are responsible for the non-vanishing nonmetricity tensor. The existence of the Einstein frame representation for RBG theories was devised in [28,29], and it has been explicitly proven and used for applications for different matter sectors: perfect and anisotropic fluids, scalar fields and non-linear electrodynamics [30][31][32][33][34]. The deviation from the Riemannian condition ∇ μ g αβ = 0 in the RBG frame is intimately related to a departure of the space-time metric from its Minkowskian form whenever matter fields are present even if the effects of curvature (i.e.…”

Multicenter solutions in Eddington-inspired Born–Infeld gravity

“…δq μν . This procedure establishes a correspondence or mapping between RBGs coupled to L m and GR coupled toL m , as established in [27][28][29][30]. Note that, in general, both L m and L m will contain fields of the same kind (that is, scalar fields map into scalar fields, electromagnetic into electromagnetic, and so on), though the functional dependence will be different, yielding in general non-canonical Lagrangians in one (or both) sides.…”

“…From this frame one can take (when known) the corresponding GR solution, and find the counterpart in the RBG frame via purely algebraic transformations. This is known as the mapping method, whose reliability was originally proven for anisotropic fluids [27], and has allowed to obtain new solutions for electromagnetic [28] and scalar fields [29,30].…”