Is it true that the Day of Judgement will come on a Friday, 10th Muharram?

my question is with regards to the day of judgement. from what i have read in the sahih(accurate) hadith it is stated that the day of judgement will come on friday(10th moharram).My question is if it is friday in saudi arabia then it will be another day in USA and so on....so basically it is never friday all over the world at one time...please answer, this has been troubling me for sometime.

Praise be to Allaah. 

Everyone who gives a specific time or date for the onset of the Day of Judgement is a fabricator and a liar. The onset of the Day of Resurrection is the “Hour” of which Allaah says (interpretation of the meaning):

 “They ask you about the Hour (Day of Resurrection): ‘When will be its appointed time?’ Say: ‘The knowledge thereof is with my Lord (Alone). None can reveal its time but He’” [al-A’raaf 7:187]

 But when the Day of Resurrection comes, at the time which is known to Allaah, which will be a Friday, then the system of this universe, with its night and day, sun and moon and stars, will be changed. We do not know whether the America which exists today will exist then or not, for Allaah is Able to destroy whichever of these nations He wills before the Day of Resurrection, for Allaah is Able to do all things.