The concept of an event in relativity as a point in spacetime with arbitrarily high precision size breaks down when considering the uncertainty principle, which stipulates that there is a minimum size or accuracy for measurements made in the universe, and you cannot have arbitrary precision in measurements. This has practical effect for example, next to a black hole. Everywhere in spacetime, there are virtual (A.K.A. unmeasurable) particle-antiparticle pairs which spontaneously appear and then disappear, due to the uncertainty principle. Directly next to a black hole's event horizon, one of the elements of a virtual particle-antiparticle pair (either the particle or the antiparticle) gets sucked into the black hole, leaving the other to be emitted out into spacetime; this is the source of Hawking radiation.