Stephen Hawking's theory of black hole evaporation, known as Hawking radiation, suggests that black holes can slowly lose mass over time and eventually evaporate. This process occurs through a quantum mechanical phenomenon near the event horizon of the black hole, where pairs of particles and antiparticles are constantly being created and annihilated.
According to Hawking's theory, occasionally one of these particle pairs can be separated, with one particle falling into the black hole while the other escapes into space. This process leads to a net loss of mass and energy for the black hole, causing it to gradually lose mass and potentially evaporate entirely over an immensely long timescale.
However, it is important to note that the rate of black hole evaporation is incredibly slow for astrophysical black holes, such as supermassive black holes found at the centers of galaxies. The timescale for a black hole to evaporate through Hawking radiation is astronomically long, on the order of 10^67 years for a black hole with the mass of the Sun.
Therefore, despite the potential for black hole evaporation, the timescale for it to occur is significantly longer than the age of the universe. Thus, the supermassive black holes found at the centers of galaxies, including elliptical galaxies, have not had sufficient time to evaporate completely, even if they have been present for a long time.
In summary, while Hawking radiation provides a theoretical mechanism for black holes to lose mass and eventually evaporate, the timescale for this process is so long that it is not observable within the age of the universe. Therefore, the presence of black holes, including those at the centers of elliptical galaxies, is consistent with our current understanding of astrophysics and black hole evolution.