Trying to come up with a way to have a galactic unified time/date system, I turned my eye on the sidereal rotation period of, for example, the Sun, or, on the desired larger scale, Sagittarius A*.
Do black holes rotate? In other words, is there a "Sagittarius A*-Day" I can use? If so, how fast, or slow, is that rotation?
The Pioneer plaques use pulsars as a universal (or at least galactic) reference (image source)
Pulsars are rotating neutron stars that emit radio waves in a "lighthouse" fashion. These have proven to be extraordinarilly stable. For example, the pulsar J0437−4715 har been shown to have precision of $1.7×10^{−17} s$.
By having a catalogue of known pulsars, their period, their location in the galaxy, and — most important — their phase, you have a galactic clock in these, that will provide a reference time for any star system in the galaxy, no matter their location, or distance to any other object in the galaxy. Via pulsars, midnight Valentines Day 2024, 00:00:00 UTC, can be determined to the exact same second no matter if you are in the Perseus or Centaurus arm of the galaxy.
"Space, is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is." (source)
Bonus, with the pulsar catalogue, you also have a GPS: Galactic Positioning System.
This is the reasoning behind the spikey symbol on the Pioneer placqes, by showing the relative direction of the earth, to known pulsars — the dashes and bars denoting their relative rotational period to each other — we have on these paques essentially left our home address, in case aliens should ever find the Pioneer probes and wonder where they came from.
Hence...
Yes, it is possible to create a galactic clock. And this has already been suggested.
But — no — this would not be done via any black hole, but via pulsars.
Yes, supermassive black holes can spin, but your proposal for using their rotation as a timekeeping system isn't ideal.
First, the rotation period is likely quite small. The angular speed of a spinning black hole is $$\Omega=\frac{c^3}{G}\frac{a}{2M^2 + 2M\sqrt{M^2 - a^2}}$$ where $a$ is the spin parameter, $M$ is the mass, and $c$ and $G$ are the speed of light and the gravitational constant. As discussed in other answers, the parameter $a$ falls in the range $0\leq a\leq1$; the larger the value of $a$, the smaller it is spinning. For actual calculations, we write $a$ in the same units as the mass of the black hole -- so if you see $a=0.1$, that means $a=0.1M$.
According to the latest results from the Event Horizon Telescope, the mass of the black hole at the center of the Milky Way, Sgr A*, is close to $M\approx4\times10^6M_{\odot}$. $a$ is less well constrained by those results, but in line with other studies, let's estimate $a\sim0.5$. That gives us an angular speed of $\Omega=0.0068$ radians/second. This translates to a rotation period of $T=2\pi/\Omega\approx15.4$ minutes! Now, it's possible that the black hole is spinning slower, at $a\sim0.1$. Even then, we get $\approx82.3$ minutes -- still quite short.
Fast-spinning supermassive black holes aren't abnormal, either! Studies indicate that many spin at $a\geq0.8$ (Reynolds 2021). There seem to be a few that would have periods on the order of days to a week, but those are usually just the most massive ones, hundreds to thousands of times more massive than Sgr A*.
The second problem is one of actually using the black hole as a clock. The rotation of Earth is a nice timekeeping system because it's usually easy for me to tell the difference between, say, 4 AM and 5 PM, or even between 12 PM and 2 PM. But how could you tell where in a black hole's rotation it is at any given moment? It's one thing to be able to determine how fast a black hole is spinning, but calculating when in its "day" it is by observation seems much harder.
The question is not whether a BH can spin, but rather how you would prevent it from spinning. BHs, like everything else in the universe, must preserve angular momentum. And thus, everything that it captures contributes such momentum given how improbable it is for an object to fall directly into the hole. This is why basically every massive object in the universe spins: they are all created by the accretion of smaller objects on somewhat tangential trajectories that contribute angular momentum when captured.
Once you leave the region of a single solar system, the notion of a broadly shared clock or calendar becomes less and less tenable. It may not even make sense for planets in the same solar system to do so. The reason, of course, is the slow speed of light on interstellar distances. Does it really matter what is happening 10,000 ly away? You won't know for another 10,000 years.
And if it does matter, that suggests you have FTL travel. And if you have FTL, then you can simply make distributed clocks with local nodes much like NTP: every planet maintains its own standard clock/calendar, but sends FTL messages to every other cooperating node to sync them. How often you need to send these messages depends on how closely the clocks need to be synced, and how consistent/reliable FTL is in your universe.
For ships that might temporarily be outside the network, they can use a temporal version of dead reckoning by syncing their shipboard clock at port, and adjusting for all gravitational fields they fly through to predict the time at various destinations. Then when they arrive in port, they can sync their clocks again.
Yes, black holes can spin. Everyone here is confirming that. In fact, a black hole can be entirely described by only three properties, and spin is one of them.
But let me kill your joy, because science ruins everything.
Trying to come up with a way to have a galactic unified time/date system
Date and time systems work on Earth because given the small difference in velocities between any two humans, we have an illusion of simultaneity. But at large scales, that does not exist.
Considering three people: one orbiting Sagittarius A*, one on Earth and one on the rim of the galaxy. They do have light-cone interactions, and they can count the rotations of Sagitarius A* (or the movemenrs of its orbiting stars). But here is the kicker: they do not agree on the sequences of events that are not causally connected.
For example: say we somehow sync clocks at the three places mentioned above. Then, 100,000 years later (from each point's own perspective) a riot happens on the rim, Valve releases Half-Life 3 on Earth and the emperor is assassinated close to Sagittarius A*. A person in the rim of the galaxy will see these things happening in a specific order (and hence on three specific dates). A person on Earth will see it in a different order and on different dates, and so again for those around the emperor in the core of the galaxy.
This renders a universal timekeeping system useless, as anything and everything only makes sense in its own frame. You can't tell someone in Andromeda that an event X happened on an absolute galactic date and time Y.
For more on this, see Relativity of Simultaneity
Rotating black holes are possible.
Quoting from the answers to this Astronomy.SE post:
A rotating black hole is known as a Kerr Black Hole (named after Roy Kerr who found the numerical solution to GR equations for rotating black holes). In the case of a rotating black hole, there are two important parameters used to describe the black hole. The first is of course the mass of the black hole $M$. The second is the spin $a$. Really $a$ isn't the spin itself $-$ it's defined by $a=J/M$ (see footnote) where $J$ is the angular momentum of the black hole $-$ but it's a good proxy for spin so often you'll see scientists get lazy and just call it the spin of the black hole. The mathematics will tell you that Kerr black holes have the limitation that
$$0 \le a/M \le 1$$
[...]
Footnote: In GR, to make the math easier, often scientists adopt special units known as [geometrized units][8]. These are units chosen in just such a way that the gravitational constant, $G$, and the speed of light, $c$, are equal to one. There's infinitely many units which allow this. Essentially this means no GR equations have $G$ or $c$ in them, but they're implicitly there, they're just equal to one and so not shown.
and
The limiting angular momentum of a black hole is (in suitable units) the square of its mass, while the Schwarzschild radius grows as the mass. So consider a large (near) maximally spinning black holes of mass $M$ which will have Schwarzchild radius $2M$.
The maximum orbital angular momentum you can add to it by firing a particle of mass $m$ just inside the event horizon and velocity almost $c$ (which is 1 in these units) is therefore $2Mm$. If that particle is a smaller maximally spinning black hole of mass $m$ and angular momentum $m^2$ then the total angular momentum of the coalesced holes is $M^2+2Mm+m^2$ which is exactly $(M+m)^2$, so the new black hole is still just maximally spinning.
There is also a specific question about the rotation rate of Sagittarius A*:
Using normalised units where 0 is no spin and 1 is the maximum possible spin, Fragione and Loeb give an upper limit of 0.1 for the spin of Sagittarius A*.
That corresponds to a spin speed at the event horizon of 0.1c, which sounds rather fast. However, it's common for SMBHs (supermassive black holes) to have spins greater than 0.5.
As you mentioned in the comments you are not limited to using the galaxy spin as time reference so I propose a different solution.
In your world numerous wonderful breakthroughs in technology happened. Allowing for colonization of the galaxy and most likely FTL-travel.
A much minor breakthrough was that some scientists were able to determine the age of the universe much more precise than back in 2024.
Back then the age was narrowed down to a few hunderd million years (already quite precise) but with modern technology the age of the universe was determined to nanosecond level precision. With newer technology and techniques any moderatly equipped astrolaboratory can redo the experiment and calculation.
This led to the introduction of "NSBB" (also more commonly known as Epoch 3.0) as new time reference in intergalactic computing and communication.
Nanoseconds since Big Bang.
Soon this was reduced to just BB, replacing AD and BC in the process.
Due to the relativly easy process of calculation every colony, space station or bigger space ship can calibrate a new clock easily. All you need is a medium sized telescope, a handfull of caesium-133, an average computer and a few other simple measurement tools. And ofcourse a clear sky.
This is actually a really good idea!
The great thing about supermassive black holes like A* is that they’re basically impossible to stop - imagine trying to stop our Sun from rotating, and then magnifying the required effort by several orders of magnitude. As it turns out, rotating black holes are very real and of interest for study because they deform spacetime in a very special way. Specifically, they “pull” spacetime in the direction that they’re rotating - this is known as the Lense-Thirring effect and has been measured with extremely high precision by such spacecraft as Gravity Probe B.
What I think you’re asking is whether or not the rotation of a black hole can be accurately quantified if it exists at all. The answer is that, yes, it can be quantified, and it can be specifically measured by observing how spacetime is deformed by the black hole. Rotating black holes cause eccentric orbits around them to precess, so by observing Sagittarius A*’s orbiting stars, we can determine that it’s rotational velocity is around 60% of the maximum value, so how long is a “Sagittarius A* day”?
The maximum value is the greatest value of angular momentum $J$ such that
$$\frac{c^2J^2}{GM^2}\le GM^2,$$
where $J$ is the rotational parameter, $c$ is the speed of light (exactly $299,792,458$), and G is Newton’s gravitational constant (about equal to $6.6743\cdot10^{-11}$). In other words,
$$c^2J^2\le G^2M^4,$$ $$Jc\le GM^2,$$ $$J=\omega m\le \frac{GM^2}{c},$$ $$\omega=\frac{GM}{c}.$$
Plugging in the numbers and taking 60% of that maximum value, this gives a rough estimate of Sagittarius A*’s angular speed (radians per second) of about $1.14\cdot 10^{18}$. Cooooool.
This gives a period of about $1.4\cdot 10^{-19}$ seconds. A* will not be a “day counter”, but more of an extremely precise computer clock that can synchronize two systems across great distance.
You do have the technology to accurately count to a trillion trillion in about a second … right?
