Article

# Gödel solution in modified gravity

Departamento de Física, Universidade Federal da Paraíba Caixa Postal 5008, 58051-970, João Pessoa, Paraíba, Brazil *; Instituto de Física, Universidade Federal de Alagoas CEP, 57072-970, Maceió, Alagoas, Brazil

Physical review D: Particles and fields 07/2009; 79(12). DOI: 10.1103/PHYSREVD.79.124039 - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider a theory which involves an extension of general relativity known as Chern–Simons modified gravity (CSMG). In this theory the standard Einstein–Hilbert action is extended with a gravitational Pontryagin density that is obtained from a divergence of a Chern–Simons topological current. The extended theory has the standard Schwarzchild metric as solution, however, only a perturbed Kerr metric holds solution. From the exact Kerr metric we construct dual metrics to search for rotating black hole solutions. The conditions on the Killing tensors associated with dual metrics entail nontrivial solutions to CSMG.International Journal of Modern Physics D 01/2012; 19(08n10). · 1.03 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We show that Chern-Simons (CS) modified gravity with a prescribed CS scalar field admits rotating black hole/string/> solutions with cylindrical topology of the horizon, and we present two intriguing physical examples of such configurations. First, we show that the Banados-Teitelboim-Zanelli stationary black string, which is obtained by adding a spacelike flat dimension to the Banados-Teitelboim-Zanelli black hole metric of three-dimensional gravity, solves the field equations of CS modified gravity with a specific source term irrespective of the choice of CS scalar field. Next, we consider the Lemos solution for a rotating, straight black string in general relativity and show that, for the CS scalar field being a function of the radial coordinate alone, this solution persists in CS modified gravity. We also present a new nontrivial (non-general relativity) Goedel-type solution to the vacuum field equations of CS modified gravity.Physical review D: Particles and fields 07/2010; 82(2):024043-024043. - [Show abstract] [Hide abstract]

**ABSTRACT:**We prove the consistency of the Gödel metric with the Horava-Lifshitz gravity whose action involves terms with z=1, z=2, and z=3. We show that, for different relations between the parameters of the theory, this consistency is achieved for different classes of matter; in particular, for the small cosmological constant, it is achieved only for the exotic matter---that is, ghosts or phantom matter.Physical review D: Particles and fields 01/2011; 84.

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