Four dimensional string solutions in Hořava-Lifshitz gravity

Abstract

We investigate string-like solutions in four dimensions based on Hořava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black strings are solutions in Hořava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the "conformal" lapse function is not constrained in Hořava-Lifshitz gravity. It turns out that if $\lambda \ne 1$, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., $\lambda =1$), there exists an additional solution of which the conformal lapse function is determined. Interestingly, this solution admits a uniform BTZ black string along the string direction, which is distinguished from the warped BTZ black string in Einstein gravity. Therefore, it is a good candidate for the test of the theory.

15 pages, references added, minor corrections made

References in corpus (35)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• A healthy extension of Horava gravity
• Horava-Lifshitz Cosmology
• The black hole and FRW geometries of non-relativistic gravity
• Strong coupling in Horava gravity
• Solutions to Horava Gravity
• Chiral Primordial Gravitational Waves from a Lifshitz Point
• Phenomenologically viable Lorentz-violating quantum gravity
• Cosmology of the Lifshitz universe
• Thermodynamics of Black Holes in Horava-Lifshitz Gravity
• Dark matter as integration constant in Horava-Lifshitz gravity
• The Black Hole and Cosmological Solutions in IR modified Horava Gravity
• Lifshitz Black Hole in Three Dimensions
• Cosmological perturbations in Horava-Lifshitz theory without detailed balance
• A dynamical inconsistency of Horava gravity
• Perturbative instabilities in Horava gravity
• Thermodynamics of black holes in the deformed Hořava-Lifshitz gravity
• On the z=4 Horava-Lifshitz Gravity
• Horava-Lifshitz Dark Energy
• Thermodynamics and classification of cosmological models in the Horava-Lifshitz theory of gravity
• On the Renormalizability of Horava-Lifshitz-type Gravities
• Thermodynamics of Hořava-Lifshitz black holes
• Primordial Perturbation in Horava-Lifshitz Cosmology
• Extremal rotating solutions in Horava Gravity
• Detailed balance in Horava-Lifshitz gravity
• Caustic avoidance in Horava-Lifshitz gravity
• Correlation Functions in Non-Relativistic Holography
• Dyonic solution of Horava-Lifshitz Gravity
• On IR solutions in Horava gravity theories
• A Test of Horava Gravity: The Dark Energy
• Entropy of black holes in the deformed Hořava-Lifshitz gravity
• Branes at Quantum Criticality
• Surplus Solid Angle as an Imprint of Horava-Lifshitz Gravity

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• The generalized second law of thermodynamics in Horava-Lifshitz cosmology
• New agegraphic dark energy in Horava-Lifshitz cosmology
• Slowly rotating black holes in the Horava-Lifshitz gravity
• Particle Probe of Horava-Lifshitz Gravity
• The Rotating Black Hole in Renormalizable Quantum Gravity: The Three-Dimensional Hořava Gravity Case
• Black Holes in Hořava Gravity with Higher Derivative Magnetic Terms
• Complete Classification of Four-Dimensional Black Hole and Membrane Solutions in IR-modified Hořava Gravity
• Extended Hořava Gravity with Physical Ground-State Wavefunction
• Black Strings in Hořava-Lifshitz Gravity
• Solutions in IR modified Horava-Lifshitz Gravity
• Constraints on Flows in Horava-Lifshitz Gravity by Classical Solutions
• Domain Wall solutions to Horava gravity