Stephen Hawking's theory of black hole evaporation, known as Hawking radiation, suggests that black holes can gradually lose mass and energy over time and eventually evaporate. According to this theory, pairs of virtual particles can spontaneously appear near the event horizon of a black hole. Occasionally, one particle falls into the black hole while the other escapes into space, resulting in a net loss of mass for the black hole.
However, it's important to note that the process of black hole evaporation is extremely slow for astrophysical black holes. The evaporation time for a black hole is inversely proportional to its mass. For supermassive black holes, which reside at the centers of galaxies, the evaporation timescale is far longer than the current age of the universe. Therefore, the evaporation process is negligible for supermassive black holes within the timescale we observe.
In the case of elliptical galaxies, which are generally considered to be older galaxies, they indeed contain supermassive black holes at their centers. These black holes have accumulated mass over billions of years through various mechanisms such as mergers with other galaxies, accretion of surrounding matter, and the growth of galactic bulges. While Hawking radiation predicts that black holes can slowly lose mass, the rate of evaporation for supermassive black holes is minuscule compared to the rate of mass accretion or growth via other mechanisms. Consequently, supermassive black holes in elliptical galaxies are expected to persist for an extremely long time, far beyond the current age of the universe.
It's worth noting that Hawking radiation has not been directly observed, as it is incredibly weak for astrophysical black holes. However, the concept of Hawking radiation is an important theoretical prediction within the framework of quantum field theory in curved spacetime, and it has had significant implications for our understanding of black hole thermodynamics and the nature of information loss in black hole evaporation.