Abstract
In this work we focus on a toy model: (3+1)-dimensional Hořava–Lifshitz gravity coupling with an anisotropic electromagnetic (EM) field which is generated through a Kaluza-Klein reduction of a (4+1)-dimensional Hořava–Lifshitz gravity. This model exhibits a remarkable feature that it has the same velocity for both gravitational and electromagnetic waves. This feature makes it possible to restrict the parameters of the theory from GRB 170817A. In this work we use this feature to discuss possible constraints on the parameter beta in the theory, by analyzing the possible Lorentz invariance violation effect of the GRB 170817A. This is achieved by analyzing potential time delay of gamma-ray photons in this event. It turns out that it places a stringent constraint on this parameter. In the most ideal case, it gives |1-sqrt{beta }|<(10^{-19}-10^{-18}).
Highlights
More recent progress on these theoretical efforts, namely, the Horava–Lifshitz (HL) gravity [9], has taken this necessity one step further
We focus on the last scenario, which is a HL gravity in (4 + 1) dimensions
Since we are interested in the propagation of gravity and electromagnetic modes, and the scalar modes do not influence the propagation of these two modes [47,48], in what follows we only focus on the gravity mode and electromagnetic mode
Summary
More recent progress on these theoretical efforts, namely, the Horava–Lifshitz (HL) gravity [9], has taken this necessity one step further. On the way of searching for possible LV we have a new method: the GW170817, which the first GW event from a binary neutron star merger as detected by LIGO and Virgo Collaboration [21] It was accompanied by a gamma-ray burst (GRB 170817A) with a time delay t = (1.74±0.05)s as observed by Fermi-GBM [22]. J. C (2020) 80:1062 event provides a strong constraint on the propagation speed of GWs by analyzing the observed time delay between GW and GRB signals. C (2020) 80:1062 event provides a strong constraint on the propagation speed of GWs by analyzing the observed time delay between GW and GRB signals This in turn imposes a strong constraint on modified gravity theories such as [23–28] (see [29] for a review).
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