This is correct. Relativity destroys all notions of simultaneity between 2 distant objects. We only have causally and non-causally related events. In this case,

This is correct. Relativity destroys all notions of simultaneity between 2 distant objects. We only have causally and non-causally related events. In this case, the black hole at age 35 can only causally affect us in the year 2015. To put it simply, there exists a frame of reference in which the year 2010 on earth occurs before the 35th birthday of the black hole. So to say that the black hole is 50,000,030 years old in the year 2010 on earth is misleading. It is only true for one very particular frame of reference i.e. the earth.