Since Schwarzschild solution describes exterior not only of black holes, but of any spherically symmetric non-rotating objects, then any such object should emit Hawking radiation, no? Then how exactly is that working? Let's set up a thought experiment. Say, we construct a spherically symmetric non-rotating object from ordinary atoms (say, a sphere of pure silicon). We know exactly how many atoms is there. We cool it to zero K (IOW: it has no thermal energy to create any particles) and position it in an empty space, devoid of any matter and radiation. Now we observe it. When we detect a quantum of "Hawking-radiated" emission, where did the object get energy to create it? Is there one less Si atom in the object?