title: 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 two ways: by comparing arrival times of GWs and their EM counterparts and by comparing the time delays between images seen in GWs and their 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 to general relativity. We expect that such a 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 the timing accuracy of the EM counterpart, which for kilonovae is around 10^{4}  s. 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 γ-ray bursts and fast radio bursts.
authors.affiliation: School of Physics and Technology, Wuhan University, Wuhan 430072, China.|Departments of Physics and Mechanical & Electrical Engineering, Hubei University of Education, Wuhan 430205, China.
authors.forename: Xi-Long
authors.initials: XL
authors.lastname: Fan
authors.affiliation: School of Science, Wuhan University of Technology, Wuhan 430070, China.
authors.forename: Kai
authors.initials: K
authors.lastname: Liao
authors.affiliation: Department of Astrophysics and Cosmology, Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland.|Department of Astronomy, Beijing Normal University, Beijing 100875, China.
authors.forename: Marek
authors.initials: M
authors.lastname: Biesiada
authors.affiliation: Department of Astrophysics and Cosmology, Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland.
authors.forename: Aleksandra
authors.initials: A
authors.lastname: Piórkowska-Kurpas
authors.affiliation: School of Physics and Technology, Wuhan University, Wuhan 430072, China.|Department of Astronomy, Beijing Normal University, Beijing 100875, China.
authors.forename: Zong-Hong
authors.initials: ZH
authors.lastname: Zhu