Nonlinear σ -models in the Eddington-inspired Born-Infeld gravity

J R Nascimento,A R Soares,A Yu Petrov,Gonzalo J Olmo,P J Porfírio

doi:10.1103/physrevd.101.064043

J R Nascimento, A R Soares + Show 3 more

Open Access

https://doi.org/10.1103/physrevd.101.064043

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Abstract

In this paper we consider two different nonlinear $\sigma$-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though with important physical consequences. In particular, wormhole structures always arise, though this does not guarantee by itself the geodesic completeness of those space-times. In one of the models, quadratic in the canonical kinetic term, we identify a subset of solutions which are regular everywhere and are geodesically complete. We discuss characteristic features of these solutions and their dependence on the relationship between mass and global charge.

Highlights

It is well established that topological defects could arise in the primordial universe due to phase transitions occurring during rapid expansion and cooling periods [1,2]
In this work we have considered two different nonlinear σ-models minimally coupled to EiBI gravity as a way to explore new gravitational phenomena related with a global monopole symmetry breaking [SOð3Þ → Uð1Þ]
The second model describes a theory with quadratic kinetic term and leads to an effective configuration closely related to an electric field coupled to a global monopole

Summary

INTRODUCTION

It is well established that topological defects could arise in the primordial universe due to phase transitions occurring during rapid expansion and cooling periods [1,2]. The EiBI theory provides, already at the classical level, interesting solutions like regular black holes, wormholes, nonsingular cosmologies, and many other results without requiring exotic matter sources (for a review on EiBI and its applications see [10]). It differs from GR in the presence of matter In this sense, in the innermost regions of compact objects, where the energy density reaches its highest values, new effects arise that can avoid geodesic incompleteness in some cases [11,12,13,14]. In [23], Lambaga and Ramadhan investigated black holes with GM topological charge in EiBI, in the metricaffine formalism They explored only the external region of the solution, favoring a positive value for the theory’s parameter ε which, in this case, leads to a singular solution. In the Appendix, we give a general description of the topologically charged Ellis wormhole

BORN-INFIELD GRAVITY

STATIC SPHERICALLY SYMMETRIC SOLUTIONS FOR ANISOTROPIC FLUIDS

NONLINEAR σ-MODEL

Power law case

CONCLUSION