About 0.4 s after the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a transient gravitational-wave (GW) signal GW150914, the Fermi Gamma-ray Burst Monitor (GBM) also found a weak electromagnetic transient (GBM transient 150914). Time and location coincidences favor a possible association between GW150904 and GBM transient 150914. Under this possible association, we adopt Fermi's electromagnetic (EM) localization and derive constraints on possible violations of the Weak Equivalence Principle (WEP) from the observations of two events. Our calculations are based on four comparisons: (1) The first is the comparison of the initial GWs detected at the two LIGO sites. From the different polarizations of these initial GWs, we obtain a limit on any difference in the parametrized post-Newtonian (PPN) parameter ∆γ 10 −10 . (2) The second is a comparison of GWs and possible EM waves. Using a traditional super-Eddington accretion model for GBM transient 150914, we again obtain an upper limit ∆γ 10 −10 . Compared with previous results for photons and neutrinos, our limits are five orders of magnitude stronger than those from PeV neutrinos in blazar flares, and seven orders stronger than those from MeV neutrinos in SN1987A. (3) The third is a comparison of GWs with different frequencies in the range [35 Hz, 250 Hz]. (4) The fourth is a comparison of EM waves with different energies in the range [1 keV, 10 MeV]. These last two comparisons lead to an even stronger limit, ∆γ 10 −8 . Our results highlight the potential of multi-messenger signals exploiting different emission channels to strengthen existing tests of the WEP.

The successful detection of the binary neutron star merger GW 170817 and its electromagnetic counterparts has provided an opportunity to explore the joint effect of the host galaxy and the Milky Way (MW) on the weak equivalence principle (WEP) test. In this paper, using the Navarro–Frenk–White profile and the Hernquist profile, we present an analytic model to calculate the galactic potential, in which the possible locations of the source from the observed angle offset and the second supernova kick are accounted for. We show that the upper limit of Δγ is 10−9 for the comparison between GW 170817 and a gamma-ray burst (GRB 170817A), and it is 10−4 for the comparison between GW 170817 and a bright optical transient (SSS 17a, now with the IAU identification of AT 2017gfo). These limits are more stringent by one to two orders of magnitude than those determined solely using the measured MW potential in the literature. We demonstrate that the WEP test is strengthened by the contribution from the host galaxy to the Shapiro time delay. Meanwhile, we also find that large natal kicks produce a maximum deviation of about 20% from the results with a typical kick velocity of 400 to ∼500 km s−1. Finally, we analyze the impact from the halo mass of NGC 4993 with a typical 0.2 dex uncertainty and find that the upper limit of Δγ, with a maximum mass , is nearly two times more stringent than that of the minimum mass .

In various gravity theories, Friedmann equations can be cast to a form of the first law of thermodynamics in a Friedmann–Robertson–Walker (FRW) cosmological setup. However, this result failed in recent infrared (IR) modified Hořava–Lifshitz (HL) gravity. The difficulty stems from the fact that HL gravity is Lorentz-violating. Motivated by this problem, we use the Misner–Sharp mass to investigate the thermodynamics near the apparent horizon in HL cosmology. We find that the Friedmann equations can be derived from the first law of thermodynamics. The Misner–Sharp mass used here inherits the specific properties of HL gravity since it is directly from the gravitational action of HL theory. We also prove that the first law of thermodynamics with logarithmic entropy still holds at the apparent horizon in FRW. The results suggest that the general prescription of deriving the field equation from thermodynamics still works in the HL cosmology.

In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant Λ and a 4D de Sitter (dS) space. In this paper we present that, if the extra dimension is timelike oppositely, the negative Λ will be emerged and the induced 4D space will be an asymptotic Anti-de Sitter (AdS). Under the minimum assumption, we solve the Kaluza-Klein equation RAB = 0 in a canonical system and obtain the AdS solution in a general case. The result shows that an AdS space is induced naturally from a Kaluza-Klein manifold on a hypersurface (brane). The Lagrangian of test particle indicates the equation of motion can be geodesics if the 4D metric is independent of extra dimension. The causality is well respected because it is appropriately defined by a null higher dimensional interval.In this 5D relativity, the holographic principle can be used safely because the brane is asymptotic Euclidean AdS in the bulk. We also explore some possible holographic duality implications about the field/operator correspondence and the two-points correlation functions.