Einstein-scalar–Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows
R. A. KonoplyaInstitute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-746 01 Opava, Czech RepublicThomas D. PappasDivision of Theoretical Physics, Department of Physics, University of Ioannina, Ioannina GR-45110, GreeceA. ZhidenkoCentro de Matemática, Computação e Cognição (CMCC), Universidade Federal do ABC (UFABC), Rua Abolição, CEP: 09210-180, Santo André, SP, Brazil
2020en
ABI
Abstract
Recently, numerical solutions to the field equations of Einstein-scalar--Gauss-Bonnet (EsGB) gravity that correspond to black holes with nontrivial scalar hair have been reported. Here, we employ the method of the continued-faction expansion in terms of a compact coordinate in order to obtain an analytical approximation for the aforementioned solutions. For a wide variety of coupling functionals to the Gauss-Bonnet term we were able to obtain analytical expressions for the metric functions and the scalar field. In addition we estimated the accuracy of these approximations by calculating the black-hole shadows for such black holes. Excellent agreement between the numerical solutions and analytical approximations has been found.
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