Can tiny Mario Galaxy like planets exist?

Four students from the Department of Physics and Astronomy at the University of Leicester have tried to examine the physics behind the small planets in Nintendo's masterpiece, Super Mario Galaxy.

It turns out that it isn't impossible to have such small worlds with Earth-like gravity. But there are some complications though, according to the report It's a-me Density. The paper asks:

"If a planet with the density of a white dwarf, a 50m radius, and Earth-like gravity were to be constructed what would happen?"

Unfortunately, it seems Mario wouldn't fare to well on such a strange planet and it "would likely explode due to the severe imbalance of gravitational pressure to degeneracy and coulomb pressures."

Also, Mario would have to be really (REALLY) fast to be able to finish his adventures on each planet:

"The outcome of this discrepancy is that if constructed, the planet would survive for only a very brief moment before violently destroying itself and any short plumbers who happen to be running about on its surface."

So there you have it. Mario games have turned out to be unrealistic. Who'd have thought it!?