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Out there in the Universe, size definitely matters. An evolved red giant star, our Sun, and a white dwarf can all have the same mass, but the size difference between these three classes of objects is tremendous. While there might be some quantum effects that play a role for objects that are very small — in their energy, position, lifetime, etc. — there are some properties that remain the same regardless of any uncertainties. Objects that are stable, both microscopically and macroscopically, are described by measurable properties such as mass, volume, electric charge, and spin/angular momentum.
But “size” is a bit of a tricky one, particularly if your object is extremely small. The most extreme objects in terms of density are black holes, but for them, size isn’t necessarily a well-defined property. After all, if all the mass and energy that goes into making a black hole inevitably collapses to a central singularity, then what does the concept of “size” even mean? As it turns out, there’s actually more than one definition for a black hole’s size, and they all have their uses. From the outside in, let’s take a look at what a black hole’s size can tell us.
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Instead of an empty, blank, three-dimensional grid, putting a mass down causes what would have been ‘straight’ lines to instead become curved by a specific amount. The curvature of space beyond a certain distance, outside of a large mass, remains unchanged even as you vary the volume the interior mass occupies. (Credit: Christopher Vitale of Networkologies and the Pratt Institute)
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James' World 2 
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