Question: **Side note: This is for an actual nation roleplay, and there is QUITE a bit of leeway there, but I highly recommend you base your answer on science. It's fine if you don't, but please try.**

The Fortnite Zero Point is this big ball that has *unimaginable* energy.
In a way, I thought of an idea like that. Let's just call it "the point" for now.  

Basically, it is this big sphere of compressed energy, and it somehow generates its own energy. In a way, it's a recharging megabattery.

The thing is, *would this even be possible?* Or would there be absolutely NO WAY that could exist?

Current rules:

* Cannot exponentially gain energy (energy put into it makes it generate faster, but there has to be a way to stop it from exponentially gaining more energy)
* Should not grow in size (Do you want it to eat the entire earth?)
* If possible, it shouldn't emit any radiation (But if needed, its OK)
* Needs occasional bursts of mass or energy to keep it "charged" (will slowly run out of energy if not fed)
* Nuclear reactors and variants (fusion reactors, etc) are banned. I do not know why, it was an admin decision.

Answer: 
It's a very, very, very small [white hole](https://en.wikipedia.org/wiki/White_hole).

That is, there's a black hole out there with the usual gravity field: nothing that falls in can escape, including light. Tidal forces will tear apart anything that tries. Consequently as the remnants fall through space and time until they exit the white hole, only energy remains.

It's the bursts of mass or energy to keep it "charged" that would need some handwaving. Perhaps they are needed to stabilize the space-time continuum and keep it in place, or in place relative to the people using it. (That white holes are purely theoretical gives you a lot of hand-waving room where someone can say that no one predicted this in advance.)
**Nuclear reactor with extra steps**

I am one of those people who do not know what that "Fortnite Zero point" is, but what you have described here kinda fills the bill of a nuclear reactor.

By your rules:

* Cannot exponentially gain energy (energy put into it makes it generate faster, but there has to be a way to stop it from exponentially gaining more energy) - **Check**.

The energy will depend on the neutron flux inside the reactor. Too much flux will cause a chain reaction that can spiral [out of control](https://en.wikipedia.org/wiki/Chernobyl_disaster), too little will cause the reactor to shut down (in simplified terms). This can be regulated by introducing additional material, like boron to adjust the neutron flux to the level you need it at.

* Should not grow in size (Do you want it to eat the entire earth?) - **Check**

Nuclear reactors do not, in fact, grow.

* If possible, it shouldn't emit any radiation (But if needed, its OK) - **Check**

There is obviously radiation, but you can (and probably should) shield the reactor.

* Needs occasional bursts of mass or energy to keep it "charged" (will slowly run out of energy if not fed) - **Check**

Radioactive material will eventually decay and you will need to replace it with a new portion.

As for "Unimaginable" power, that is a pretty broad definition. Nuclear materials can be used to generate A LOT of power so it depends what you consider unimaginable.

There are also various propositions for different reactor designs. If you want a big glowy ball of light to represent your energy sphere, perhaps a gas-core reactor with electrostatically or magnetically confined fission material will fit your bill. And if you want even more power, go for fusion reactor. In any case the rest is just a case of capturing the energy and using it (most likely) to generate electricity, which is exactly what nuclear reactors do.