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arXiv · 1110.1636

Static electromagnetic fields and charged black holes in general covariant theory of Horava-Lifshitz gravity

Ahmad Borzou·Kai Lin·Anzhong Wang
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Abstract

In this paper, we study electromeganetic static spacetimes in the nonrelativisitc general covariant theory of the Horava-Lifshitz (HL) gravity, proposed recently by Horava and Melby-Thompson, and present all the electric static solutions, which represent the generalization of the Reissner-Nordstrom solution found in Einstein's general relativity (GR). The global/local structures of spacetimes in the HL theory in general are different from those given in GR, because the dispersion relations of test particles now contain high-order momentum terms, so the speeds of these particles are unbounded in the ultraviolet (UV). As a result, the conception of light-cones defined in GR becomes invalid and test particles do not follow geodesics. To study black holes in the HL theory, we adopt the geometrical optical approximations, and define a horizon as a (two-closed) surface that is free of spacetime singularities and on which massless test particles are infinitely redshifted. With such a definition, we show that some of our solutions give rise to (charged) black holes, although the radii of their horizons in general depend on the energies of the test particles.

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Ahmad Borzou, Kai Lin, Anzhong Wang. 2012-01-23. Static electromagnetic fields and charged black holes in general covariant theory of Horava-Lifshitz gravity. https://doi.org/10.1088/1475-7516%2F2012%2F02%2F025

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