On Effective Spacetime Dimension in the Hořava-Lifshitz Gravity

Abstract

In this manuscript we explicitly compute the effective dimension of spacetime in some backgrounds of Hořava-Lifshitz (H-L) gravity. For all the cases considered, the results are compatible with a dimensional reduction of the spacetime to $d+1=2$, at high energies (ultraviolet limit), which is confirmed by other quantum gravity approaches, as well as to $d+1=4$, at low energies (infrared limit). This is obtained by computing the free energy of massless scalar and gauge fields. We find that the only effect of the background is to change the proportionality constant between the internal energy and temperature. Firstly, we consider both the non-perturbative and perturbative models involving the matter action, without gravitational sources but with manifest time and space symmetry breaking, in order to calculate modifications in the Stephan-Boltzmann law. When gravity is taken into account, we assume a scenario in which there is a spherical source with mass $M$ and radius $R$ in thermal equilibrium with radiation, and consider the static and spherically symmetric solution of the H-L theory found by Kehagias-Sfetsos (K-S), in the weak and strong field approximations. As byproducts, for the weak field regime, we used the current uncertainty of the solar radiance measurements to establish a constraint on the $\omega$ free parameter of the K-S solution. We also calculate the corrections, due to gravity, to the recently predicted attractive force that black bodies exert on nearby neutral atoms and molecules.

arXiv commentreferences added

References in corpus (26)

• Quantum Gravity at a Lifshitz Point
• Thermodynamics of Spacetime: The Einstein Equation of State
• On the Origin of Gravity and the Laws of Newton
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• The black hole and FRW geometries of non-relativistic gravity
• Solutions to Horava Gravity
• Horava-Lifshitz Cosmology: A Review
• The Black Hole and Cosmological Solutions in IR modified Horava Gravity
• On Horava-Lifshitz "Black Holes"
• Solar system tests of Hořava-Lifshitz gravity
• The Cosmological Constant and Horava-Lifshitz Gravity
• High energy modifications of blackbody radiation and dimensional reduction
• Phenomenological constraints on the Kehagias-Sfetsos solution in the Horava-Lifshitz gravity from solar system orbital motions
• Horava-Lifshitz modifications of the Casimir effect
• Gödel-type universes and chronology protection in Horava-Lifshitz gravity
• Stability of the de Sitter spacetime in Horava-Lifshitz theory
• Black-body radiation in extra dimensions
• Attractive Optical Forces from Blackbody Radiation
• Horava-Lifshitz Gravity Effects on Casimir Energy in Weak Field Approximation and Infrared Regime
• Multiverse in the Third Quantized Horava-Lifshits Theory of Gravity
• Relic gravitational wave spectrum, the trans-Planckian physics and Hořava-Lifshitz gravity
• Some remarks on Relativistic Diffusion and the Spectral Dimension Criterion
• Note on nonsingular cyclic universes in the deformed Horava-Lifshitz gravity
• Weak and strong field approximations and circular orbits of Kehagias-Sfetsos space-time
• Spectral dimension of Horava-Snyder spacetime and the $Ad{S}_2\times S^2$ momentum space

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• Dependence of the Black-body Force on Spacetime Geometry and Topology
• Sign Switching Dark Energy from a Running Barrow Entropy