Viktor Toth

You can easily find out yourself. First use a black hole temperature calculator like

https://www.omnicalculator.com/physics/black-hole-temperature

or

https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator

to find the Hawking temperature T_BH of your black hole. Then use the fact that CMB temperature T_CMB is inversely proportional to the cosmological scale factor a(t), where t is time:

https://physics.stackexchange.com/questions/76241/cmbr-temperature-over-time

Set a(t_now) = 1 for convenience; then

T_CMB(t) = T_CMB(t_now) / a(t)

and you want to find the time t when T_BH = T_CMB(t).

That depends on how the scale factor will change over time:

https://en.wikipedia.org/wiki/Scale_factor_(cosmology)

We don't know that, but if we assume for simplicity that dark energy will keep dominating, a(t) will grow exponentially, i.e.

a(t) = a(t) / a(t_now) ~ exp(H_0 * (t - t_now))

where H_0 is Hubble's constant. So

T_CMB(t) = T_CMB(t_now) / a(t) ~ T_CMB(t_now) / exp(H_0 * (t - t_now))

Numbers:

T_CMB(t_now) ~ 2.7 K

H_0 ~ 71 km/s/Mpc ~ 2.3e-18 s^-1

t_now ~ 14 Gyr ~ 3.2e16 s

so, with t expressed in seconds,

T_CMB(t) ~ 2.7 / exp(2.3e-18 * (t - 3.2e16)) K

Setting this equal to T_BH and solving for t, I get

t = 3.2e16 + ln(2.7 / T_BH) / 2.3e-18 s

So let's say you have a solar mass black hole. Then

T_BH ~ 6.16871e-8 K

and so

t ~ 7.7e18 s ~ 2.4e11 years

i.e. 240 billion years (17 times the current age of the universe).

That's actually not a humongous…

The stiff-to-soft-to-stiff phase transition in the neutron star is probably microscopic black holes popping into existence and evaporating via Hawking radiation where convection creates zones dense enough to collapse for a moment:

https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator

If we switch the units to kg, we see that a mass of 278000 kg (139 metric tons) has a lifetime of about 1 second. That's a rounding error for something with a mass of the sun, or 2x10^30 kg.

I wonder if there's a black hole oscillating in and out of existence at the center of neutron stars, creating a resonance that might be detectable.

Also as a thought experiment, we could imagine dropping 1 more atom into a neutron star on the brink of total collapse. The star would start running down the "drain" of the black hole, red shifting away from us beneath its event horizon. We'd see it grow redder and redder, dimmer and dimmer as it recedes from us, while staying the same size due to the holographic effect of black holes. If we jumped in after it, the red shift would stay the same because we could never reach the star, but we'd experience severe tidal forces until we're ripped into spaghetti. Our clock would stay synced with an observer on the outside as we fall along the geodesic without outside forces acting upon us. Space just gets added between particles, which creates the red shift. I believe that passing the singularity means coming out the other side in a white hole…

> A black hole bright enough to see its hawking radiation has to be tiny and would be quite short lived with an origin of unknown mechanism.

Depends on what distance you want to see it from.

A black hole that glows as hot as an incandescent filament would have as much mass as a 250km cube of rock and it would last for 10^35 years. It would have a radius of 60nm and emit less than a microwatt.

> a black hole small enough to emit xrays

To reach the low end of xrays, 100 electron volts, we'd need a black hole 100 times smaller. It would still have 10^29 years of lifetime, and would be emitting 2 milliwatts of xrays.

To reach the high end of xrays, 100k electron volts, we'd need a black hole 100k times smaller. It would still have 10^20 years of lifetime, and would be emitting 2 kilowatts of xrays.

To go the other way around, if I calculate a black hole that has "only" 10 billion years of lifetime left, weighing a dainty 190 million tons, it would be emitting 10 gigawatts of gamma rays. At 10 gigawatts of output, it would shrink by 1 ton every 285 years. The speed of light squared is an enormous number.

https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator

It would be neat to also get stats about the black hole depending on where you are in relation to it (obviously this breaks physics as a micro black hole would immediately fall into the earth). Everything is based on the hawking radiation calculator: https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator

Example: Set mass of black hole to 1e12 metric tons, or about 100,000 great pyramids.

This has a schwarzschild radius of 1485 femtometers (1 femtometer is around size of a proton).

Nominal luminosity is 356 watts. You could power your computer! Lifetime is 1e12 gigayears.

An interesting thing comes with gravity. Gravity at the schwarzschild radius for this mass is 3e28 m/s^2, but this is at a smaller-than-an-atom radius.

If you put your hand within a foot of it, gravity would be 700,000 m/s^2.

You would need to be at a distance of 270ft to experience gravity from it that compares to earth (9.8 m/s^2).

Here's a Hawking radiation calculator that you can use to get an idea of some of the numbers involved: https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator

Using this calculator, we find that a black hole with the mass of 433 Eros, 6.687E15 kg, would be quite hot, some 18 million kelvin, but emitting just 8 watts of power, and be 0.009 nanometres in radius. Pretty hard to find.

Let's try something smaller. 162173 Ryugu, the rock that Hayabusa2 landed on, is only 4.5E11 kg. This gives you a much brighter hole: 1758 megawatts at 2.72657E11 kelvin.

Interestingly, this may make it harder to detect! Its blackbody emission peak is at 9,211 KeV, and the Chandra X-Ray observatory only goes up to 10 KeV. (Focusing very-high-energy photons is not easy) You'd have to detect it from the fraction of total power it emits lower down in the spectrum.

For a language with a C-like syntax that compiles into minimal x86 executables check out W [1]. It was designed for use in a small, single-executable self-hosting compiler targeting the HP 95LX family of early MS-DOS "calculators"/PDAs [2] and hence has no equivalent of libc; instead it expects you to code your own basic routines in assembly. I once wrote a bootable toy application in it that ran on regular x86 desktops (a command-line interpreter and calculator) and found the experience quite pleasant.

Here's a "Hello, World" in W:

write := 0x8B55, 0x8BEC, 0x085E, 0x4E8B, 0x8B04, 0x0656, 0x00B8,
0xCD40, 0x7321, 0x3102, 0x8BC0, 0x5DE5, 0x90C3

_() :=
{
write(1, "Hello, World!\r\n", 15)
}

[1] http://www.vttoth.com/CMS/index.php/projects/49

[2] https://en.wikipedia.org/wiki/HP_200LX