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It’s worth stepping back and considering where our understanding of black holes, and where all of our predictions about their behavior, comes from.Ultimately our understanding of black holes, as well as all of our predictions for their bizarre behavior, stems from the math we use to describe them. It also turns out that no experiment can tell the difference between floating motionless in deep space and accelerating under the pull of gravity (when you fall you’re weightless). Sarcasm aside, what was genuinely impressive was the effort it took to turn those singsong statements into useful math.This equation is based on two principles: “matter and energy make gravity…somehow” and “when you don’t feel a push or pull in any direction, then you’re moving in a straight line”. The path of a freely falling object (even an orbiting object) is a straight line through a non-flat spacetime.The extremely short answer to this question is: the math says nothing can escape, and that the gravity doesn’t “escape” so much as it “persists”. Einstein’s whole thing was considering the results of experiments at face value. Einstein’s stunning insight (paraphrased) was “dudes! What if there’s no difference between falling and floating? After a decade of work, and buckets of differential geometry (needed to deal with messed up coordinate systems like the surface of Earth, or worse, curved spacetime) the “Einstein Field Equations” were eventually derived, and presumably named after Einstein’s inspiration: the infamous Professor Field.When test after test always showed the speed of light was exactly the same, regardless of how the experiment was moving, Einstein said “hey, what if the speed of light is always the same regardless of how you’re moving? The left side of this horrible mess describes the shape of spacetime and relates it to the right side, which describes the amount of matter and energy (doesn’t particularly matter which) present.
“Resolving power” is a measure of the smallest angle that the telescope can reliably detect.The short answer is that gravity isn’t “emitted” by matter.Instead, it’s a property of the spacetime near matter and energy.It’s not used/taught/believed merely because it’s pretty, but because it works.Importantly, the curvature described isn’t merely dependent on the presence of “stuff”, but on the curvature of the spacetime nearby.