# Finding out the mass of a black hole for it to last ten thousand years

In my story, one of the characters essentially possesses something akin to true invulnerability and is essentially immortal due to [redacted]. In this part of the story, a group of terrorists with stolen sci-fi grade technology use it to open a tear in space-time right next to said character, a tear which creates a portal between his current location and a point in space at 10 meters away from an artifical (man-made) black hole's event horizon. This causes the character to be sent into space and sucked into the black hole.

The main scenario is: said character, due to [plot-armor] his composition, manages to not end up reduced to another chunk of compressed matter, and thus he is left trapped inside the black hole until it completely evaporates.

The problem: I'm having trouble stipulating the size and mass of the black hole, since I'm not very knowledgeable and I'm yet to comprehend how to use the black hole calculators I've found. I want this black hole to last a reasonably long time for human standards, but no more than 10000 years. Is there any easy(ier) to understand black hole calculators that I could use to have a better idea of its mass and size? In the scenario in question the black hole would be positioned in a place where, ideally, it wouldn't gain any additional mass other than what it had the moment the tear was open.

(this isn't the last time I plan to use black holes in this story, so I'm in need of a simpler calculator until I can understand more about them. )

According to this calculator, you want a black hole with a mass of 1.55 million metric tons and measuring 0.0000000046 nanometers across (~40 times wider than an atom). Any gas around it may reach a temperature over dozens of trillions of kelvin. At the distance characters and portals will be from the black hole, that means enough luminosity to probably cause a lot of destruction. As per the comments in this answer:

The black hole will emit 150 TW of blackbody radiation at 80 tera-Kelvin. You won't be as much sucked in as literally torn apart by gamma radiation. The black hole will "only" emit 16 grams of photons per second (yup, you read that right), but they'll be moving at the speed of light. For comparison, the Hoover dam produces measly 2GW, and it's much bigger than a 20-meter sphere.

150 TW means that, in a little over four hours, the black hole emits as much energy as all nukes ever detonated in history (until 2020), combined. That will not bode well for whatever is on the other side of the portal.

Even if you only keep it open for a second, that's still like two Fat Man bombs. Of course the portal won't get all of that energy through it since the black hole would spread energy in all directions. But it would be just like opening a portal next to a big modern nuke detonation.

Generally speaking, black holes that have a considerable enough size for you to to be able to "see their disc" from afar could outlast practically everything else in the universe. A 2 km (~1.25 miles) wide black hole would have a lifetime of 8.13 $$\times$$ 1065 years. Read it without scientific notation to let that sink in: 813,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years. That's almost the expected development time for Half-Life 3. Yet it would have only about a third of a solar mass. Its energy output would also be orders of magnitude greater than the nanometer black hole calculated above.

• That joke hurts me... Sep 29, 2020 at 12:27
• I don't think your estimate for Half Life 3 includes the time that will be needed to fix all the bugs in the initially released version. :-) Sep 29, 2020 at 13:28
• @Alexander just Hawking radiation. The black hole will emit 150 TW of blackbody radiation at 80 tera-Kelvin. You won't be as much sucked in as literally torn apart by gamma radiationt. The black hole will "only" emit 16 grams of photons per second (yup, you read that right), but they'll be moving at the speed of light. For comparison, the Hoover dam produces measly 2GW, and it's much bigger than a 20-meter sphere. Sep 29, 2020 at 17:08
• @Renan No objection again. We just need to be clear what we mean by "outshine the sun". 1. Outshine the Sun luminosity as seen by Earth observer (easy); 2. Outshine the Sun by surface brightness (very easy, given the tiny size of black hole); 3. Outshine the Sun at a certain distance (still easy); 4. Outshine the Sun by total luminosity (or radiant flux, very hard). I assume you mean #3, correct? Sep 29, 2020 at 17:23
• Interestingly enough, a black hole with exactly 1 sun luminosity in Hawking radiation would have a mass of 0.964 metric tons (964 kg) ... and a lifetime of about 75 ns. Sep 29, 2020 at 21:13