Ruiz Cembranos, José AlbertoCruz Dombriz, Álvaro de laJarillo Díaz, Javier2023-06-182023-06-182015-021475-751610.1088/1475-7516/2015/02/042https://hdl.handle.net/20.500.14352/24014© 2015 IOP Publishing. We would like to thank Pablo Jimeno Romero for his useful advice, and to Luis J. Garay and José Beltrán Jiménez for helpful discussions. J.A.R.C. and A.d.l.C.D. acknowledge financial support from MINECO (Spain) projects FPA2011-27853-C02-01, FIS2011-23000 and Consolider-Ingenio MULTIDARK CSD2009-00064. J.J. acknowledges financial support the Spanish Ministerio de Educación, Cultura y Deporte for support through grant FPU-13/02934. J.A.R.C. thanks the support of the Becas Complutense del Amo program. A.d.l.C.D. thanks Kavli Institute for Theoretical Physics China (KITPC) for their hospitality and the ACGC University of Cape Town, for support during the early stages of preparation of this manuscript. A.d.l.C.D. is also indebted to the Centre de Cosmologie Physique des Particules et Phénoménologie CP3, Université catholique de Louvain, Louvain-la-Neuve, Belgium for its assistance with the final steps prior to the release of this manuscript. J.J. is grateful to the Theoretical Physics and the Atomic, Molecular and Nuclear Physics Departments, Complutense University of Madrid for technical facilities.We study electric and magnetic monopoles in static, spherically symmetric and constant curvature geometries in the context of the inverse electrodynamics model. We prove that this U(1) invariant Lagrangian density is able to support the standard metric of a Reissner-Nordstrom Black Hole, but with more complex thermodynamical properties than in the standard case. By employing the Euclidean Action approach we perform a complete analysis of its phase space depending on the sign and singularities of the heat capacity and the Helmholtz free energy.engjournal articlehttp://dx.doi.org/10.1088/1475-7516/2015/02/042http://iopscience.iop.org/open access53Born-infeld actionNonlinear electrodynamicsGeneral-relativityParticle creationEinstein's theoryQuantum gravityThermodynamicsFieldIntegralsFísica (Física)22 Física