4 time within a small time window. Therefore it is possible that, if “dark matter emulators” describe gravity then we might be looking at the wrong place. This possibility was suggested before and the possible time lag was calculated for certain events [32]. But it is crucial for GW observers (especially the people who are involved with externally triggered search) to know how big this effect is for a par- ticulat object and the amount of error. In this work we provide an estimate of this possible time lag for any ob- ject located at Milky Way and current uncertainties are discussed in the next section. of the recent mass estimates for both M31 and Milky- Way galaxy are shown in Table II. The results of virial mass estimates are quite different from one another. This might be misleading since the virial radius which is con- sidered in these works are sometimes different from one another. But even taking that into consideration, the er- ror bars of these estimates are too big, varying from 13% to 140% ,that we can not give a precise estimate of the time lag for objects that are far from us. To summarize, our prediction of this time lag has cer- tain uncertainties, where the biggest one is the input coming from the numerical simulations of dark matter density profiles of the galaxies. For an event which will occur at a very distant location, more than 100kpc, we can only conclude that the time lag will be big. Therefore the predictivity of this test is much better for an event which is closer to us ( ∼ 10 kpc ). The errors of the most recent mass estimates are at the order of 20% and nu- merical simulation community is hopeful that these mass estimates will get much better in recent future for our galaxy [56]. There are three kinds of uncertainties in the time lag calculation. First one is the position of the assumed source. The uncertainity in the angular position of the GRB’s and other sources are determined by a relatively good accuracy. In a previous work For GRB-070201 the error was shown to be of the order of 2% [32]. The second kind of uncertainty is the choice of the dark matter den- sity profile and this choice had an effect which wass less than 1% [32]. The third kind of uncertainty is the data input(parameters) coming from different groups who are working on numerical simulations of dark matter density profiles. And this choice has the biggest effect on the calculation. In order to calculate the time lag in Eq.(2) we need to use these parameters coming from numerical simula- tions. They enter into the calculation through the mass function. In this work, to get the mass function, we used NFW dark matter density profile for modified gravity models to mimic dark matter. One can see from Table I. that using a data set of a different group changed the time lag from 383 days to 634 days for the Andromeda galaxy. And this difference is expected; since the virial mass estimation of M31 is almost twice of one another. Therefore the biggest uncertainty comes from the de- termination of the mass of the galaxies. Looking at Table I. the results for our galaxy are not very different, unlike M31. But still one naturally ould start wondering about the case of mass estimate for our galaxy as well. Some We also have to point that Bekenstein takes the ap- proach as velocity of GWs is smaller than photons [19]. But this would lead to an immediate invalidation of TeVeS from the boundary of Moore and Nelson[57] via gravitational cherenkov-radiation. Therefore we do not agree with Bekenstein’s point of view and force the “dark matter emulators” to agree with the observed rotation curve and weak lensing results. By a numerical analysis we made a rough estimation of the time lag for any source in our galaxy as far as 400 kpc, and demonstrated it in Figure 1. The time lag de- pends almost linearly on the distance of the source from us, and is approximately 10 − 6 times the total time of flight. Estimation of the time lag depends on the data input(mass function of Milky-Way) which is provided by numerical simulations. Therefore the accuracy of this, highly depends on the error bars coming from these sim- ulations. The current state of affairs of the numerical simulations of Milky-Way galaxy puts some constraints on our prediction. Therefore, at this stage we can con- clude that the best objects, for this proposed test, are the ones that are close to us( ∼ 10 kpc). A peculiar property of dark matter emulators is that gravitational waves couple to a different metric than the ordinary matter. This results in a time lag between the arrival times of these particles coming from the same source, which would be a powerful check of these models with a single detection of a gravitational wave. A si- multaneous detection of gravitational wave and a photon would rule out entire class of modified gravity models. But if a time lag is observed which is at the order magni- tude of the one mentioned in this work, that would mean general relativity is wrong and there is no dark matter. VI. CONCLUSIONS V. UNCERTAINTIES IN THE CALCULATION TABLE II: Different mass estimates of the Milky Way and the Andromeda with the corresponding error bars. M31 M tot (10 $^{12}$M ⊙ ) Milky Way M tot (10 $^{12}$M ⊙ ) Corteau [46] 1 . 33 +0 . 18 − 0 . 18 Xue [51] 1 . 0 +0 . 3 − 0 . 2 Evans [47] 1 . 23 +1 . 8 − 0 . 6 Smith [52] 1 . 42 +1 . 14 − 0 . 54 Fardal [48] 0 . 74 +0 . 12 − 0 . 12 Wilkinson [53] 1 . 9 +3 . 6 − 1 . 7 Seigar [49] 0 . 73 +0 . 02 − 0 . 02 Sakamoto [54] 1 . 8 +0 . 4 − 0 . 7 Ibata [50] 0 . 75 +0 . 25 − 0 . 13 Battaglia [55] 1 . 5 +0 . 2 − 0 . 2