The behavior of particles, including the Higgs boson, inside a black hole is currently a topic of speculation and active research. Our understanding of black holes is based on general relativity, which describes their properties as regions of extremely curved spacetime from which nothing, including light, can escape. However, general relativity does not fully incorporate quantum mechanics, which is necessary to describe the behavior of particles at the smallest scales.
Inside a black hole, the extreme conditions of immense gravity and density would likely have a significant impact on the behavior of particles, including the Higgs boson. However, without a complete theory of quantum gravity, we cannot make definitive statements about what exactly happens to particles, such as the Higgs boson, within a black hole.
Regarding the Higgs boson's role in granting mass to particles, it is important to note that the Higgs field permeates all of space and interacts with particles throughout the universe, regardless of their location or the density of space-time. The Higgs field is thought to give mass to elementary particles by interacting with them and endowing them with mass. The Higgs boson is the particle associated with fluctuations in the Higgs field.
As for the frequency at which the Higgs boson grants mass, it is not directly related to the expansion or replication of space-time. The expansion of the universe, as described by the theory of cosmic inflation or the ongoing expansion observed today, is driven by other factors, such as dark energy. The Higgs boson's role in mass generation is a separate aspect of particle physics and is not directly linked to the expansion of space-time.
It is important to note that our current understanding of the Higgs boson and its interactions is based on the Standard Model of particle physics, which is a highly successful theory but has certain limitations. Exploring the behavior of particles, including the Higgs boson, in extreme conditions, such as inside black holes or during the early moments of the universe, requires a deeper understanding of the interplay between quantum mechanics and gravity, which is an active area of research in theoretical physics.