Why does gravity have negative energy?

The zero-energy universe hypothesis states that the total amount of energy in the universe is exactly zero. The amount of positive energy in the form of matter is exactly canceled out by the negative energy in the form of gravity.

Can someone explain why gravity have negative energy? If energy= mass*c^2 what would happen if we convert all the matter to energy? Wouldn’t this theory fail since gravity is caused by mass and energy is massless?

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