Most likely, no

There are approximately 10,000 asteroids over 10 km in radius in the main asteroid belt (Masiero et al., 2011; Figure 5).

There are 636,499 identified objects in the asteroid belt as of May 2015 (Jones et al., 2015).

We have almost certainly detected every asteroid in the main belt (and the inner solar system, too) that is larger than 10 km in diameter.

If you want this to be true, for fiction reasons, I'm sure you can make something up, but that would be the topic of a separate question.

I agree with the No answers regarding detection, but like some other recent answers by me I wonder if recognition may be missing. That is,

• the asteroid has a catalog number in astronomical databases,


• there is a rough size estimate,


• rotation speed may or may not be known with any precision,


• but no human analyst ever looked at the data in any detail.

Data mining is an extremely powerful tool, but as of today it mostly finds what people train it to find, intentionally or unintentionally.

Almost certainly no. Aside from Kingledion's answer regarding discovery with existing and older technology, by the time there's a significant human population in space puttering around, it wouldn't be unreasonable to assume that anything signficant in size (say over 100 meters) within the orbit of Jupiter would be cataloged.

Second issue, the spinning. Due to rotational effects, a cylinder (which your asteroid is, roughly speaking) is unstable rotating along its long axis and will eventually start tumbling around its short axis (see this question here explaining why). That means the asteroid will be tumbling end-over-end, which means changes in the area exposed to light and any observer, thus the rotation will be trivially visible even if the surface has a uniform albedo and is otherwise featureless.

Unfortunately, your asteroid will be known about long before anyone ever gets there.

EDIT

Taking into account some of the clarifications, here's some other problems:

1. If it's just been found by a mining crew, that immediately raises a concern about why it wasn't already catalogued, because it clearly should have been.




2. If it's being stabilized by the inhabitants to prevent tumbling so it only rotates around the long axis, that's going to raise flags all by itself because of not rotating around its short axis as a natural object would. That would instantly be a screaming indication something is wrong.

Yes, if you hide it inside another asteroid

This may sound like cheating, however I have some reason behind this madness. There are many problems with hollowed out asteroids as space stations. If you are thinking long term, you want a thick shell, to avoid damage by the occasional impacts of smaller asteroids. You also want the inside to be even, even if the outside isn't. All this makes the shell needlessly heavy, requiring a lot of energy and reaction mass to get it to rotate. There is also the structural problem, since you do not know how the shell will react to the stresses of centrifugal forces. Also whenever some maintenance guy working on the outside drops his wrench, it will be catapulted off to who knows where...

You could of course use up the whole asteroid to simply build a well armored rotating space station, however this would kind of defeat the purpose. Instead an advanced space-faring civilization might combine both approaches:

1. Hollow out an asteroid. Leave a thick enough shell to withstand whatever impact you think might occur and only leave a small opening at one end. (maybe put an angle in there to avoid freak asteroid-strikes.)


2. Build a lightweight cylindrical space station inside the asteroid and affix it at the ends with some alien, frictionless, superconducting magnetic bearings.


3. Spin up just the inner space station, leaving the shell motionless.

This leaves you with artificial gravity inside, a solid shell and even some protected zero-gravity parking spaces for you spaceships inside the cavern (Think of the insurance bill). It also solves the wrench dropping problem.

(I remember having already read about an idea like this somewhere else, however I do not remember a source)

Implications of Detection

Detection has been fairly well-covered in other answers, so I feel like I should address the "what-if" in the case that your asteroid is catalogued and characterized.

Roughly speaking your asteroid would need to be spinning at ~0.02224 rad/s (0.00354 rev/s, 0.21252 rev/m, 12.751 rev/h, 306.03 rev/d, etc...) to generate the equivalent of Mars surface gravity against the inner walls - if it has relatively thin walls.

I am not a materials scientist, but it does seem that the size you propose is small enough to not become a sphere under its own gravity. Whether a rocky body could naturally stay cohesive under this spin rate is out of my wheelhouse but my guess is it would.

This paper does a nice job of comparing size to rotation rate (just look at the plots to get all the info you need). Unfortunately, it seems that for an object over 100m there is a max observed spin rate of ~10 rev/d. If astronomers found a cylindrical asteroid 15km by 30km spinning at 306 rev/d you can bet they'd be taking a REAL close look.

**EDIT: I originally used 15km as the radius, now the calculated values reflect a diameter of 15km.

While I generally agree with everyone else's conclusion of no, I'd like to add a maybe, a rather tenuous yes.

Sure, we have detected to date 636,499 objects tumbling about in space, but how long has that taken us? The first asteroid was detected in 1801, and we didn't really start detecting asteroids "en-masse" until somewhere around the mid 1990's to early 2000's. That leaves 200 years of wiggle room for something to hide, which brings me to my next point that space is big. You have to be looking in the right place at the right time to really find something. Given your beings have already colonised the nearby surrounding heavens, the level of technology would be more advanced than we have today and as such detection methods would likely be greater. However what this may not mean is that vast amounts of time and man-power have gone into looking at the area that you're interested in.

Maybe it's not located around or near another populated area and doesn't get much interest from researchers. Maybe it's on the other side of something larger, that just refuses to get out of the way in any timely fashion. Maybe it's near a militarized zone, and looking in that direction too closely with a powerful telescope will bring about the unwanted attention of men in black coats driving black cars. Maybe it's just a new area for researchers, and the task of identifying all these tumbling dark objects is large and daunting, therefore slow work.

This all depends on the level of technology you have portrayed your beings to have. If they scanning the skies and detecting in-coming enemies from another far off planet for example, the above is probably moot.

[EDIT]

Based on your recent edit, I feel there's a higher chance that something would simply not be seen, in any decent time-frame anyway. The time between detecting, identifying, cataloging, explaining, and then releasing of information can be hilariously long. Especially if there is something anomalous about the object, something that can't be explained with science of the day, something that might be noticed but remain solely with one or two scientists who are trying to solve the mystery before releasing the information to the world.