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research_article
We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential. We also generalize the construction to involve a generic non-minimally coupled p-form field strength. We then focus on one low-lying example in four dimensions and construct the exact magnetically charged black holes. We also construct exact electrically charged z=2 Lifshitz black holes. We obtain approximate dyonic black holes for the small coupling constant or small charges. We find that the thermodynamics based on the Wald formalism disagrees with that derived from the Euclidean action procedure, suggesting this may be a general situation in higher-derivative gravities with non-minimally coupled form fields. As an application in the AdS/CFT correspondence, we study the entropy/viscosity ratio for the AdS or Lifshitz planar black holes, and find that the exact ratio can be obtained without having to know the details of the solutions, even for this higher-derivative theory.
2016-04-01
en
Higher-derivative gravity with non-minimally coupled Maxwell field
articles
2019-04-11T13:11
http://link.springer.com/10.1140%2Fepjc%2Fs10052-016-4007-y
2016-04
178
true
H.
Lü
4
1434-6052
1434-6044
The European Physical Journal C
76
Mathematical Sciences
10.1140/epjc/s10052-016-4007-y
doi
7cfeb2fed1926b4c62e019cda769b863979f58d9f26a2cfc6811599d3cd0759f
readcube_id
pub.1026237683
dimensions_id
Pure Mathematics
Feng
Xing-Hui
Springer Nature - SN SciGraph project
Beijing Normal University
Department of Physics, Center for Advanced Quantum Studies, Beijing Normal University, 100875, Beijing, China