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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

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.

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

Classical and Quantum Gravity
Volume 34, Number 4
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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