Spotted the republican
If you ask /dev/random "What is 2+2?", that question makes no sense as /dev/random does not listen to you and just spits out random binary output.
Go and disagree with /dev/random.
While dumping matter into a black hole destroys the matter, it doesn’t destroy the mass. It just confines all of the mass in one place. Powering your Birch World is just a matter of using the Penrose process to extract energy from the black hole for the next few million trillion trillion trillion trillion trillion trillion trillion years (about 3×10¹⁰⁴ years give or take a few). The stars will only last for about a million trillion years (10²⁰ years plus or minus a bit), so this plan extends your your lifetime by a factor of a trillion trillion trillion trillion trillion trillion years.
Maximal extension perhaps, but not quite forever. Forever takes a lot more work.
I liked the DS9 episode where the mutants realized that the universe was collapsing into the Big Crunch, so they demanded “antigravity generators, lots of them!” Their cosmology was wrong, but only because the show had the misfortune to be written in the past. Their enthusiasm was great :)
Living forever is such a strange desire, considering that complex life has existed on earth for just a fraction of the time it has existed, and humanity even less than that. I recommend watching the Kurtzgesagt video called All of History in one hour (https://www.youtube.com/watch?v=S7TUe5w6RHo&t=3670s). It displays all of earths history in one hour, and humanity is merely a few seconds of it.
Earth is ~4.5 billion years old, that's 4500000000 years, and in 1300000000 years it will be uninhabitable by humans, and in another 4.5 billion years (roughly 3.2 billion years after becoming uninhabitable) it will be engulfed by the sun.
Assuming humanity manages interstellar space flight you could possibly escape earth and live somewhere else until that also dies, but in case it is not practical or possible, you get to enjoy 3.2 billion years of literally choking and being burned alive on earth.
Assuming you did escape earth (or you're immortal so escaping doesn't matter) In 1000000000000 years the last star will be born, and in 100000000000000 years the last star will die out.
You now have an extremely long time to enjoy suffocating in hard vacuum with your body being boiled by the low pressure, and all in complete darkness until the heat death of the universe occurs in roughly 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 years
Please read this article first before damning yourself to an unimaginable hell.