Not true. There is an overriding ethics here: the room is the owner’s, which means that nobody is allowed to use it without their permission. The OP’s aunt has been granted permission to use it as part of her lease, but that has nothing to do with the OP unless they or their contract say so.
Take Sugar and Spice’s advice, and just ask them.
I think it is an ambiguous situation.
First of all, I believe that you would be a guest of your aunt. In a guest situation for using perks of any other accommodations of places, the host need not be with the guest, so it is a bit dumb to say the aunt should be with you.
OTOH, do we know what the lease says about guests?
I am torn, so I don’t have a suggestion, but I don’t think it is as clear cut as everybody says.
Best wishes,
hh
Just to clarify, I’m a guy. Not that it has anything to do with the question at hand. 
The Aunt should simply inquire if her guests are permitted to use the gym facilities, when they are visiting. I’d put money on the answer being ‘yes’. Any other tenant who asks will also be told, ‘guests are permitted’, one assumes, should it become an issue.
This is kind of a “if you have to ask” situation. Yes, it is unethical, and you knew that before you ever posted the question.
But, go to the complex office and ask - they may very well allow you to use it in place of your aunt or for a nominal fee.
It depends on the complex. My apartment complex has a pool. I’m allowed to use it for free, of course, and they give one guest pool pass per resident per season. Any extra guests beyond that first one have to pay $5/person.
I would only use it if I was spending the night at my aunt’s house. Don’t ask me why that makes a difference, but it does.
An unmanned, communal use treadmill? The chances that it is adjusted, waxed, and in usable condition is pretty low in my experience.
I would ask Aunt to make request to management on your behalf. Maybe she can explain that she doesn’t use the equipment, and that you’ll not be bringing anyone else along, that it will be just you using the workout room. If they’re nice and she presents this well, permission will likely be granted.
Otherwise I have to agree with others in this thread who say uncool.
The room and equipment are maintained at these facilities (most apartment complexes around here have them.) By unmanned, I mean that off-hours, entrance is gained by use of a combination keypad. It’s attached to the complex’s office, which is staffed during business hours.
I don’t know. My son had a similar situation–his complex had a gym and indoor pool, and there was a sign saying it was for residents and their guests. Our younger son went over there a lot and used the facilities (although always with supervision, as he was young enough that he would have required supervision even if he lived there).
I’m with people who think you could be considered a guest of your aunt. It would be most helpful if you actually visited her on some of the occasions when you used the facility.
I say if you are worried about it, go sit outside in the Parking lot when you would normally want to use the gym. Watch to see if anyone uses it during the time you would be in there. If no one uses it then you are inconveniencing no one, and who is going to complain about that ?
I was actually planning on doing that this week. I’m definitely more concerned about preventing someone else from (rightfully) using the equipment than that the wear and tear I’d put on it.
Which can raise further problems with the OP’s aunt if she has a “no roommates” clause in her lease.
His using it raises that percentage from 1% to 1.1%. One additional person using the machines isn’t going to noticeably affect the upkeep budget.
While I’d put it on the unethical side of the equation, I’m with elbows in that it’s more or less harmless. To me, ethical questions matter because of who may be harmed by the choice.
I’ll give you that since I’m not the type of person to use the “Well if everyone…” argument, but as an accounting type person, it still bugs me. Let me ask you this; What happens if the OP accidentally does some expensive damage to one of the machines or is hurt by a poorly maintained machine? Let’s also assume, for the sake of the argument, that he’s not alone when it happens, so “hit and run” isn’t an option. More then likely the apartment will fix any machine a resident breaks, assuming they weren’t being reckless. Also, I would assume the apartment carries insurance to cover injuries that residents may incur as well as they probably make residents sign some sort of waiver to protect them. But what happens when it’s a non-resident?
Well, again, it would simply come back to whether the facilities are for residents…“and their guests”, wouldn’t it? I’ve never been in residence where this wasn’t the case, so I’m assuming, whatever liability insurance they carry, covers both.
In every place I’ve been which had any kind of sports facilities, they were “for residents and their guests”, and the rules listed whether the host had to be with the guest or not, and if not, what process to follow so the workers would know that person was authorized. I suggest looking at the lease and speaking with the location’s management, but in principle I see nothing wrong with the invitation.
I reckon you should use the room. If you’re like me you’ll give up exercising after a couple of times anyway! 
If you find you have stronger will-power and are still going after a couple of months then get gym membership.
Fair point; however, it really was an aside that the chances of him getting in trouble for it are slim to none, so the reason not to do it isn’t because of risk of getting in trouble, but simply because it’s unethical. Obviously, if she has such a clause in her lease, then it wouldn’t work, but we really don’t have that information available.
Others have responded to this point, but I want to add some of my own thoughts on it. Let’s ignore the whole lease part and just look at it like a gym membership, which it basically is (so we can ignore any weird language in the lease. Gym memberships work based on assumptions about how much a typical member will use the gym. Generally, a majority of people will use the gym little or none at all, and this makes up for the people who use it regularly or even excessively. Technically, everyone has the option to use the gym as much as they want for as long as they want, and it would present a problem if, for some reason, everyone wanted to use it at the same time, but it’s just not going to happen. Not terribly unlike how banks run on the assumption that not everyone is going to want to pull all their money out all at the same time.
If we were to run with the assumption that whenever a particular member isn’t using it, they’re still paying for upkeep, then why not just let a member share his membership with anyone he wants since, theoretically, he could be at the gym 12 hours a day for the same price, so why not share it with other people since he’s essentially paying for that much usage. But if everyone did that, the place would be packed and the equipment would wear out quickly and everyone’s fees would go up to such a point where it would probably be roughly equivalent to if all those people that were being shared with had just gotten their own memberships.
So this whole situation is very much like any number of other “death by a thousand paper cuts” type situations, like littering. A single cigarette butt or candy wrapper or whatever doesn’t amount to anything, but it’s wrong precisely because if everyone does it it creates a very serious problem.
So to relate that all back to the rental agreement, even if we imagine that guests are allowed to use it, or that some apparentments have multiple people using it, that’s all built into those agreements. Guests won’t be around indefinitely, and apartments with multiple residents also have other complexities in the agreements, like probably paying more rent, if for not other reason, because they need more space. Regardless, the agreement is between her and the apartment complex; you might be able to finagle a justification for it out of the contract, but it’s still nothing more than a justification.