Yes, the total mass of a black hole increases as more matter falls into it. When matter, such as gas, dust, or even stars, comes close enough to a black hole, it can be captured by its strong gravitational pull and fall into the black hole. This process is called accretion.
As matter falls into a black hole, it adds to its mass and increases its overall gravitational pull. The mass of a black hole is a measure of the total amount of matter it contains, including both the original mass it had at its formation and any additional mass acquired through accretion.
In simple terms, the more matter a black hole accretes, the more massive it becomes. As the black hole's mass increases, its gravitational influence on surrounding objects also grows stronger.
It's important to note that while the mass of a black hole increases, the size of its event horizon—the boundary beyond which nothing can escape—also expands accordingly. The event horizon is determined by the mass of the black hole, so as the mass increases, the event horizon's radius increases as well.
This process of matter falling into a black hole and increasing its mass is a fundamental aspect of black hole growth and is central to our understanding of their formation and evolution.