Black holes are objects in space that have such a strong gravitational pull that nothing, not even light, can escape their grasp once it passes a point called the event horizon. While it is true that we cannot directly measure the mass of the region inside the event horizon of a black hole, there are several indirect ways in which we can infer its mass.
Effects on surrounding matter: As matter falls towards a black hole, it can form an accretion disk, which is a rotating disk of material spiraling into the black hole. The gravitational pull of the black hole affects the motion and behavior of this surrounding matter. By studying the properties and behavior of the matter in the vicinity of the black hole, such as its orbital speeds or the radiation it emits, scientists can infer the mass of the black hole.
Gravitational effects on nearby objects: The presence of a black hole can have observable gravitational effects on nearby objects, such as stars or gas clouds. By studying the motion of these objects and the gravitational forces they experience, astronomers can estimate the mass of the black hole.
Gravitational waves: Black holes can emit gravitational waves, which are ripples in the fabric of spacetime caused by the acceleration of massive objects. By detecting and analyzing these gravitational waves using specialized detectors like LIGO (Laser Interferometer Gravitational-Wave Observatory), scientists can estimate the mass of the black holes involved in such events.
It is important to note that the mass we attribute to a black hole refers to the mass of the region contained within its event horizon. While we cannot directly measure this mass, we can infer it through the effects of the black hole's gravity on its surroundings. These indirect measurements have provided substantial evidence for the existence of black holes and have allowed us to study their properties and behavior.