Anisotropic coupling of gravity and electromagnetism in Hořava-Lifshitz theory

Abstract

We analyze the electromagnetic-gravity interaction in a pure Hořava-Lifshitz framework. To do so we formulate the Hořava-Lifshitz gravity in 4 + 1 dimensions and perform a Kaluza-Klein reduction to 3 + 1 dimensions. We use this reduction as a mathematical procedure to obtain the 3 + 1 coupled theory, which at the end is considered as a fundamental, self-consistent, theory. The critical value of the dimensionless coupling constant in the kinetic term of the action is λ = 1/4. It is the kinetic conformal point for the non-relativistic electromagnetic-gravity interaction. In distinction, the corresponding kinetic conformal value for pure Hořava-Lifshitz gravity in 3 + 1 dimensions is λ = 1/3. We analyze the geometrical structure of the critical and noncritical cases, they correspond to different theories. The physical degrees of freedom propagated by the noncritical theory are the transverse traceless graviton, the transverse gauge vector and two scalar fields. In the critical theory one of the scalars is absent, only the dilaton scalar field is present. The gravity and vector excitations propagate with the same speed, which at low energy can be taken to be the speed of light. The field equations for the gauge vector in the non-relativistic theory have exactly the same form as the relativistic electromagnetic field equations arising from the Kaluza-Klein reduction of General Relativity, and are equal to them for a particular value of one of the coupling constants. The potential in the Hamiltonian is a polynomial of finite degree in the gauge vector and its covariant derivatives. * Electronic address:

Pure electromagnetic-gravitational interaction in Hořava–Lifshitz theory at the kinetic conformal point

“…Hořava-Lifshitz geometry is then guaranteed. In [4] we followed this approach for a Hořava-Lifshitz gravity in 4 + 1 dimensions at a non-critical value of the kinetic coupling constant.…”

“…We consider the Hořava-Lifshitz gravity in 4 + 1 dimensions at its critical value of the kinetic coupling, the kinetic conformal point, and perform a Kaluza-Klein reduction to The point of view we consider in this work, as we did in [4], is to interpret the 4+1 theory and Kaluza-Klein reduction only as a geometrical mechanism to obtain the anisotropic theory in 3 + 1 dimensions, which it is expected to be renormalizable in the framework of perturbative quantum field theory. The point of view of considering the Hořava-Lifshitz gravity theory as an effective theory of a more fundamental theory at higher dimensions is also a interesting one, but is not the one we follow here.…”

Constraints on Hořava–Lifshitz gravity from GRB 170817A

“…As to HL gravity, this refers to the issue: what is the general form of matter Lagrangians consistent with the Diff F (M) symmetry of HL gravity? There are some scenarios to construct the general form of matter Lagrangians consistent with the reduced symmetry group of HL gravity, such as symmetry consistency [43][44][45], spectral action approach [46] and dimension reduction approach [47,48]. In this work, we focus on the last scenario, which is a HL gravity in (4 + 1) dimensions.…”

“…In this work, we focus on the last scenario, which is a HL gravity in (4 + 1) dimensions. The electromagneticgravitational coupling in the usual (3 + 1)-dimensional HL gravity is achieved by considering the (4+1)-dimensional HL gravity and then performing a Kaluza-Klein (KK) reduction to 3 + 1 dimensions [47,48]. The propagation speed of the GWs and the GRBs in this model can be obtained by considering the propagation of the gravitational tensor mode and the electromagnetic vector mode, respectively.…”

Extended phase-space analysis of the Hořava–Lifshitz cosmology

“…In [65] it was proposed a possible solution to the flatness problem, in which it is assumed that the initial condition of the Universe is set by a small instanton respecting the same scaling. In [66] it is analyzed the electromagnetic-gravity interaction in a pure HL framework formulated in 4+1 dimensions and it is performed a Kaluza-Klein reduction to 3+1 dimensions. In [67] it was studied a noncommutative version of the Friedmann-Robertson-Walker (FRW) cosmological models within the gravitational HL theory.…”