Can mass be shunted off into hyperspace, but the matter remains?

My question is this: can excess mass be bled off into hyperspace (the large and compact extra dimensions, not the Star Wars-esque swirling vortex), yet the matter remains in our universe?

Is mass too fundamentally tied to matter for this to happen, or is it possible to condense a galaxy into a "small" area, but shunt off mass so it doesn't collapse into a black hole?

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Can mass be shunted off into hyperspace, but the matter remains?

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