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# Gödel solution in modified gravity

• ##### A. F. Santos
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

ABSTRACT We consider the modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the gravitational Chern-Simons term and show that the Gödel metric solves the modified equations of motion, thus proving that the closed timelike curves whose presence is characteristic for the Gödel solution are not forbidden in the case of the Chern-Simons modified gravity as well.

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ABSTRACT: We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that the G\"{o}del metric solves the modified Einstein equations under a corresponding modification of the matter, while, for the small Lorentz-breaking corrections, the matter turns out to be usual (neither ghost nor phantom one). From the other side, if the matter is suggested to be the same as in the usual general relativity, the G\"{o}del metric must be modified by additive terms proportional to the Lorentz-breaking parameter to achieve its consistency with new equations of motion. Moreover, despite such a modification turns out to be nontrivial and cannot be completely removed via change of variables, nevertheless, the closed timelike curves (CTCs) can exist for a new metric.
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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.
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