Abstract
Hořava gravity has been proposed as a renormalizable, higher-derivative gravity without ghost problems, by considering different scaling dimensions for space and time. In the non-relativistic higher-derivative generalization of Einstein gravity, the meaning and physical properties of black hole and membrane space-times are quite different from the conventional ones. Here, we study the singularity and horizon structures of such geometries in IR-modified Hořava gravity, where the so-called “detailed balance” condition is softly broken in IR. We classify all the viable static solutions without naked singularities and study its close connection to non-singular cosmology solutions. We find that, in addition to the usual point-like singularity at r = 0, there exists a “surface-like” curvature singularity at finite r = r S whichisthecuttingedgeofthereal-valuedspace-time. Thedegreeofdivergenceof such singularities is milder than those of general relativity, and the Hawking temperature of the horizons diverges when they coincide with the singularities. As a byproduct we find that, in addition to the usual “asymptotic limit”, a consistent flow of coupling constants, that we called “GR flow limit”, is needed in order to recover general relativity in the IR.
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Argüelles, C., Grandi, N. & Park, MI. Complete classification of four-dimensional black hole and membrane solutions in IR-modified Hořava gravity. J. High Energ. Phys. 2015, 100 (2015). https://doi.org/10.1007/JHEP10(2015)100
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DOI: https://doi.org/10.1007/JHEP10(2015)100