Speed of Gravitational Waves from Strongly Lensed Gravitational Waves and Electromagnetic Signals

Abstract

We propose a new model-independent measurement strategy for the propagation speed of gravitational waves (GWs) based on strongly lensed GWs and their electromagnetic (EM) counterparts. This can be done in a twofold way: by comparing arrival times of GWs and EM counterparts and by comparing the time delays between images seen in GWs and EM counterparts. The lensed GW-EM event is perhaps the best way to identify an EM counterpart. Conceptually this method does not rely on any specific theory of massive gravitons or modified gravity. Its differential setting (i.e. measuring the difference between time delays in GW and EM domains)makes it robust against lens modeling details (photons and GWs travel in the same lensing potential) and against internal time delays between GW and EM emission acts. It requires, however, that the theory of gravity is metric and predicts gravitational lensing similar as General Relativity. We expect that such test will become possible in the era of third-generation gravitational-wave detectors, when about 10 lensed GW events would be observed each year. The power of this method is mainly limited by timing accuracy of the EM counterpart, which for kilonova is around 10 4 sec. This uncertainty can be suppressed by a factor of ∼ 10 10 , if strongly lensed transients of much shorter-duration associated with the GW event can be identified. Candidates for such short transients include short gamma-ray burst and fast radio bursts. PACS numbers: 95.30.Sf, 95.85.Sz

The perturbative approach for the weak deflection angle

“…The GL were then used to study properties of the lens [16], coevolution of supermassive black holes (BHs) and galaxies [17], cosmological parameters such as large scale structure (for a review see [18]), properties of the supernova [19], dark matter substructure [20,21], and to discriminate alternative gravitational theories. More recently, with the discovery of gravitational wave (GW) [22][23][24][25], observation of its GL effects has also been proposed and put to use [26,27].…”

What if LIGO’s gravitational wave detections are strongly lensed by massive galaxy clusters?

“…The GW detections have stimulated a flurry of articles on strong lensing of GWs, discussing the effect of lens magnification on the detectability of GWs (Dai et al 2017), forecast event rates including the effects of strong lensing by galaxies (Ng et al 2017), relative arrival times of GW and electromagnetic (EM) signals (Takahashi 2017), prospects for measuring the speed of GWs (Collett & Bacon 2017;Fan et al 2017), and the impact of strong lensing on cosmography (Baker & Trodden 2017;Liao et al 2017). In this article, we investigate the probability that one or more of the GW sources detected to date was strongly lensed by a massive galaxy cluster.…”

Time delay of timelike particles in gravitational lensing of the Schwarzschild spacetime

“…To avoid this problem, Refs. [25][26][27] proposed to use the difference between time delays of GW images and time delay of GRB images in GL to accurately determine the GW velocity. However, the time delay used in these works (Eq.…”

“…However, in the computation of the time delay of timelike particles, the formulas for null ones are usually used [23][24][25][26][27], i.e., the timelike nature of the massive particle/wave was not fully accounted. Although the neutrinos from supernova and GWs from mergers are usually relativistic, the time delay itself indeed is the difference between the total travel times, which are large quantities too.…”