The concept of mass in the context of black holes is based on the effects that black holes have on their surroundings and how they interact with matter and energy outside their event horizons. While it is true that we cannot directly measure the mass of the matter and energy trapped inside the event horizon of a black hole, we can infer their existence and properties based on their gravitational effects.
Black holes are formed from the collapse of massive stars, and during this collapse, the mass of the star becomes concentrated into an extremely compact region. The event horizon is the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. It is this boundary that defines the size of the black hole as we observe it from the outside.
The mass of a black hole is determined by observing its gravitational effects on nearby objects. For example, we can measure the orbital motion of stars around a black hole or the bending of light passing near a black hole. By analyzing these observations, scientists can calculate the mass of the black hole.
Additionally, the concept of mass is a fundamental property of matter and energy in general relativity, which is the theory that describes gravity and the behavior of black holes. Mass affects the curvature of spacetime, and it is this curvature that determines the gravitational effects of black holes. So, even though we cannot directly measure the mass inside the event horizon, we can still attribute mass to a black hole based on its gravitational influence on its surroundings.
It's important to note that while the matter and energy within the event horizon cannot be measured directly, our understanding of black holes is based on the theoretical framework of general relativity, observations of their effects on surrounding matter and energy, and various mathematical models that describe their properties.