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

my question is with regards to the day of judgement. from what i have
read in the sahih(accurate) hadith itis 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. Theonset of the Day of
Resurrection is the "Hour" of which Allaah says (interpretation of the
meaning):
"They ask you about theHour (Day of Resurrection): 'When willbe 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 knownto
Allaah, which will be aFriday, 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.