Electromagnetic quasitopological gravities
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Springer
Received: July 21, 2020 Accepted: September 16, 2020 Published: October 20, 2020
Electromagnetic quasitopological gravities
a
Instituut voor Theoretische Fysica, KU Leuven. Celestijnenlaan 200D, B-3001 Leuven, Belgium b Instituto de F´ısica Te´ orica UAM/CSIC, C/ Nicol´ as Cabrera, 13-15, C.U. Cantoblanco, 28049 Madrid, Spain
E-mail: [email protected], [email protected] Abstract: We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function f (r) = −gtt = 1/grr . These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for f (r). Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed. Keywords: Black Holes, Classical Theories of Gravity ArXiv ePrint: 2007.04331
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)125
JHEP10(2020)125
´ Pablo A. Canoa and Angel Murciab
Contents 1 Introduction
1
2 Some generalities on L(Rµνρσ , Fαβ ) theories 2.1 Equations of motion 2.2 Duality transformations 2.3 Mass, charges and thermodynamics
5 5 6 7 9 9 11
4 Electromagnetic Quasitopological gravities 4.1 Spherically symmetric solutions with magnetic charge 4.2 Explicit non-singular solutions in quadratic-curvature theories 4.3 Black hole thermodynamics 4.4 Extremal black holes
14 16 18 21 24
5 Electromagnetic Generalized Quasitopological gravities 5.1 Black holes 5.2 Black hole thermodynamics 5.3 Extremal and near-extremal black holes
27 29 31 33
6 Conclusions
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A Dualizing theories of quadratic order in F
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B Equations of motion from the reduced action
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C All Electromagnetic (Generalized) Quasitopological Gravities of the form RF 2 and R2 F 2 42 2 C.1 RF theories 42 2 2 C.2 R F theories 43
1
Introduction
Higher-deriv
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