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Gutiérrez-Piñeres A.C. López-Monsalvo, C.S. 2020-03-26T16:32:54Z 2020-03-26T16:32:54Z 2013 Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics; Vol. 718, Núm. 4-5; pp. 1493-1499 03702693 https://hdl.handle.net/20.500.12585/9079 10.1016/j.physletb.2012.12.014 Universidad Tecnológica de Bolívar Repositorio UTB 25225467000 56013682900 We present an exact, axially symmetric, static, vacuum solution for f(R)-gravity in Weyl's canonical coordinates. We obtain a general explicit expression for the dependence of df(R)/dR upon the r and z coordinates and then the corresponding explicit form of f(R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f(R)≠R, this solution corresponds to a naked singularity. © 2012 Elsevier B.V. Consejo Nacional de Ciencia y Tecnología: 290679_UNAM Recurso electrónico application/pdf eng http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/restrictedAccess Atribución-NoComercial 4.0 Internacional https://www.scopus.com/inward/record.uri?eid=2-s2.0-84872489993&doi=10.1016%2fj.physletb.2012.12.014&partnerID=40&md5=d90838981eaf88ea4c99ddc4fc58eb30 A static axisymmetric exact solution of f(R)-gravity Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Exact solution F(R)-gravity Static axisymmetric A.C.G.P. was partially supported by a TWAS-CONACYT Postdoctoral Fellowship Programme. C.S.L.M. acknowledges support from CONACYT grant 290679_UNAM . Sotiriou, T., Faraoni, V., (2010) Reviews of Modern Physics, 82 (1), p. 451 Nojiri, S., Odintsov, S., (2011) Physics Reports, 505 (2), p. 59 Multamäki, T., Vilja, I., (2006) Physical Review D, 74 (6), p. 064022 Azadi, A., Momeni, D., Nouri-Zonoz, M., (2008) Physics Letters B, 670 (3), p. 210 Capozziello, S., De Laurentis, M., Stabile, A., (2010) Classical and Quantum Gravity, 27 (16), p. 165008 Cembranos, J., de la Cruz-Dombriz, A., Romero, P., Kerr-Newman black holes in f(r) theories, , arxiv:1109.4519 Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., Herlt, E., (2003) Exact Solutions of Einstein's Field Equations, , Cambridge University Press Carmeli, M., (1977) Group Theory and General Relativity: Representations of the Lorentz Group and Their Applications to the Gravitational Field, , Imperial College Press http://purl.org/coar/access_right/c_16ec http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/version/c_970fb48d4fbd8a85 Publicationmetadata.only