Is there any known way of shrinking mass?
dm/dt < 0?
This happens all the time. In a naive sense, this occurs for a rocket/payload system that is accelerating through space because the rocket must expell exhaust in order to do so. A more interesting example is the mechanism that utilizes E=mc2 in a more straightforward way, such as fusion of hydrogen into helium. The consideration has the added bonus that it allows even black holes to eventually "evaporate."
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