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Geodesically complete BTZ-type solutions of 2  +  1 Born-Infeld gravity

D. Bazeia, L. Losano, G. J. Olmo, D. Rubiera-Garcia

Abstract
We study Born–Infeld gravity coupled to a static, non-rotating electric field in 2  +  1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom.

Keywords
Born–Infeld gravity, BTZ, wormholes, nonsingular solutions, geodesic completeness

Classical and Quantum Gravity
Volume 34, Number 4, Page 21
2017 January

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa Fundação para a Ciência e a Tecnologia
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