An exotic star is a hypothetical compact star composed of something other than electrons, protons, neutrons, and muons; and balanced against gravitational collapse by degeneracy pressure or other quantum properties. These include quark stars (composed of quarks) and perhaps strange stars (based upon strange quark matter, a condensate of up, down and strange quarks), as well as speculative preon stars (composed of preons, a hypothetical particle and "building block" of quarks, if quarks prove to be decomposable into component sub-particles). Of the various types of exotic star proposed, the kind we have best understanding of, and evidence for, is the quark star.
Exotic stars are largely theoretical, because it is difficult to test in detail how such forms of matter may behave, and (prior to the fledgling technology of gravitational-wave astronomy) we also lack satisfactory means of detection of cosmic objects that do not radiate electromagnetically or through known particles, or ways to verify and distinguish novel cosmic objects from other known objects. For preon stars (and similar) we also lack knowledge about whether quarks are indeed composed of some kind of sub-particle, and therefore whether preons physically exist.
However candidates for such objects are occasionally identified as such, based on indirect evidence gained from properties we can observe, when the object exhibits properties suggesting such a nature.
Quark stars and strange stars
A quark star is a hypothesized object that results from the decomposition of neutrons into their constituent up and down quarks under gravitational pressure. It is expected to be smaller and denser than a neutron star, and may survive in this new state indefinitely if no extra mass is added. Effectively, it is a very large nucleon. Quark stars that contain strange matter are called strange stars.
Based on observations released by the Chandra X-Ray Observatory on April 10, 2002, two objects, designated RX J1856.5-3754 and 3C58, were suggested as quark star candidates. The former appeared much smaller and the latter much colder than expected for neutron stars, suggesting that they were composed of material denser than neutronium. However, these observations were met with skepticism by researchers who said the results were not conclusive.[who?]. After further analysis, RX J1856.5-3754 was later excluded from the list of quark star candidates.
An electroweak star is a theoretical type of exotic star, whereby the gravitational collapse of the star is prevented by radiation pressure resulting from electroweak burning, that is, the energy released by conversion of quarks to leptons through the electroweak force. This process occurs in a volume at the star's core approximately the size of an apple, containing about two Earth masses.
The stage of life of a star that produces an electroweak star is theorized to occur after a supernova collapse. Electroweak stars are denser than quark stars, and may form when quark degeneracy pressure is no longer able to withstand gravitational attraction, but may still be withstood by electroweak burning radiation pressure. This phase of a star's life may last upwards of 10 million years.
A preon star is a proposed type of compact star made of preons, a group of hypothetical subatomic particles. Preon stars would be expected to have huge densities, exceeding 1023 kg/m3. They may have greater densities than quark stars and neutron stars although they are smaller and, therefore, less massive than white dwarfs and neutron stars. Preon stars could originate from supernova explosions or the big bang. Such objects could be detected in principle through gravitational lensing of gamma rays. Preon stars are a potential candidate for dark matter. However, current observations from particle accelerators speak against the existence of preons, or at least do not prioritize their investigation, since the only particle detector presently able to explore very high energies (the Large Hadron Collider) is not designed specifically for this, and its research program is directed towards other areas such as the Higgs boson, quark-gluon plasma and evidence related to physics beyond the Standard Model.
In general relativity, if the star collapses to a size smaller than its Schwarzschild radius, an event horizon will exist at that radius and the star will become a black hole. Thus, the size of a preon star may vary from around 1 metre with an absolute mass of 100 earths to the size of a pea with a mass roughly equal to the Moon.
A boson star is a hypothetical astronomical object that is formed out of particles called bosons (conventional stars are formed out of fermions). For this type of star to exist, there must be a stable type of boson with self-repulsive interaction; one possible candidate particle is the still-hypothetical "axion" (which is also a candidate for the not-yet detected "non-baryonic Dark Matter" particles that appear to compose roughly 25% of the matter in the Universe).
Boson stars may have been formed through gravitational collapse during the primordial stages of the big bang. At least in theory, a supermassive boson star could exist at the core of a galaxy, which might explain many of the observed properties of active galactic cores.
Boson stars have also been proposed as a candidate dark matter object, and it has been hypothesized that the "Dark Matter Halos" surrounding most galaxies might be viewed as enormous "Boson Stars." 
The compact boson stars and boson shells are often studied involving fields like the massive (or mass-less) complex scalar fields, the U(1) gauge field and gravity with conical potential. The presence of a positive or negative cosmological constant in the theory facilitates a study of these objects in the de Sitter or Anti-de Sitter spaces.    
A Planck star is a hypothetical astronomical object that is created when the energy density of a collapsing star reaches the Planck energy density. Under these conditions, assuming gravity and spacetime are quantized, there arises a repulsive 'force' derived from Heisenbergs Uncertainty Principle. Namely, if gravity and spacetime are quantized, the accumulation of mass-energy inside the Planck Star cannot collapse beyond this limit because it violates the Uncertainty Principal for spacetime itself.
The key feature of this theoretical object is that this repulsion arises from the energy density, not the Planck length, and starts taking effect far earlier than might be expected. This repulsive 'force' is strong enough to stop the collapse of the star well before a singularity is formed, and indeed, well before the Planck scale for distance. Since a Planck Star is calculated to be considerably larger than the Planck scale for distance, this means there is adequate room for all the information captured in the black hole to be encoded upon the star, thus avoiding information loss.
While it would be expected that such a repulsion would act very quickly to reverse the collapse of a star, it turns out that the relativistic effects of the very extreme gravity such an object generates slows down time for the Planck Star to a similarly extreme degree. Seen from outside, the rebound from a Planck Star of stellar mass takes longer than the timescale of the universe to date, such that stellar mass black holes seem to be stable to an external observer. Even more elegantly, the emission of Hawking radiation can be calculated to correspond handily to the timescale of the gravity effects on time, such that the event horizon that 'forms' a black hole naturally evaporates as the rebound proceeds.
In 2014 Carlo Rovelli and Francesca Vidotto proposed that there is a Planck star inside a black hole. This theory, if correct, would resolve the black hole firewall and black hole information paradox. This idea is based on loop quantum gravity.
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