not only are your sources promoting a lie...each of the sources you mention has a history of promoting anti biblical lies...
eran elhaik believes that adam and eve did not exist...and that the twelve tribes of israel never existed...he is also an orthodox darwinian evolutionist...
shlomo sand believes that there was never a nation of israel at all...and that the kingdom of david was a myth...and that the exile of the jews from judea under the romans never actually happened...in fact he claims that the exile was a falsehood invented by christians in order to get jews to convert to christianity...
arthur koestler was a paranormalist and promoter of psychic phenomena such as ESP and telepathy and telekinesis and levitation...he was also a lamarckian evolutionist...
elhaik's entire study is actually based on a historical and geographical error... if you read his paper you would know that since we don't actually have any khazar DNA samples he had to substitute samples from 'proxies'...that is other ethnic groups that he believed were related to the khazars... however the proxies he chose were the armenians and georgians...presumably because like the khazars they lived in the caucusus region... the problem with elhaik's choice of proxies is that the armenians and georgians had -already- been living in that region since ancient times...and the khazars in fact -migrated- to caucusus region much -later- from central asia... so actually these two populations are -not- valid proxies for the khazars...basically -none- of the populations elhaik studied actually have anything to do with the khazars!
furthermore the georgians and especially the armenians had connections with the middle east in ancient times...so not only are they not related to the khazars...they were involved in the ancient middle east... consequently by showing a genetic similarity between ashkenazi jews and the armenians and georgians...elhaik actually -reinforced- the conclusion that the jews have a middle eastern origin!
of course this was all lost in him...and on you...because neither bothered to do their historical or geographical homework before coming to their preconceived conclusion...
Again, with no documentation whatsoever, you call research not agreeing with your opinion a lie. Neither do you even try to reconcile your idea of an Israel which rejected Jesus with the Christian Israelites so clearly described in Hebrews, James, 1 Peter and others. You still believe, apparently, that "...the twelve tribes...scattered abroad" (James 1:1) are described in James as an anti-Christ people, those you exalt as "Israel." You are confused at best. Your basis for identifying Israelites (a denial that Jesus is Messaih), is that used by the apostle John to identify "anti-Christs." Read the context of the word anti-Christ (1 John 2:18, 22, 4:3; 2 John v. 7). It identifies the counterfeit synagogue of Satan type Jews you worship.