One problem I have with this usage of Exotic Matter, is having it be a place holder in math for mythical things like worm holes.
Okay, well, here's the thing. Physicists don't actually use it that way.
In the case of wormholes, it goes like this: Einsteinian General Relativity allows for wormholes to exist. However, if we subject the result to perturbations (small changes - like say a star goes by in the vicinity, changing the local space by a small amount) we find that the wormhole should collapse. Wormholes are found to be not stable to even very small perturbations, like "a butterfly flapping its wings in the China Sea" is big enough to make the thing collapse.
So, some folks tried to figure out what would be necessary to keep a wormhole open. The answer seems to be that you need to create a region of negative energy density around the thing - the exact shape can vary somewhat, as I recall. Now, we know how to make
very small regions with
very small amounts of negative energy density. But this would be of a different order entirely. As a practical matter, we posit that we'd need some material we currently don't have to manage it - not only dont we have this material, but we've no observatiosn that suggest it exists. Thus, it is "exotic".
The argument that you need exotic matter to keep a wormhole open is typically an argument *against* stable wormholes existing.
There are a couple of things that we expect do actually exist, that we have next to no chance of getting our hands on, that are also lumped in with "exotic matter". Neutronium - the stuff that neutron stars are made of, very likely exists (we have observed objects that have all the properties we'd expect a neutron star to have), but getting it? How? The stuff is down in a friggin' neutron star!
There's also "degenerate matter", which you find in the cores of large stars, or in their white dwarf remnants, in which the main source of pressure is not the temperature of particles that bang against each other, but the quantum mechanical Pauli Exclusion Principle, is also considered exotic, but is not really possible to get.