  If due attention is given in formulating the basic equations for the
Gamma-Ray Burst (GRB) phenomenon and in performing the corresponding
quantitative analysis, GRBs open a main avenue of inquiring on totally new
physical and astrophysical regimes. This program is one of the greatest
computational efforts in physics and astrophysics and cannot be actuated using
shortcuts. A systematic approach has been highlighted in three paradigms: the
relative space-time transformation (RSTT) paradigm, the interpretation of the
burst structure (IBS) paradigm, the GRB-supernova time sequence (GSTS)
paradigm. In fundamental physics new regimes are explored: (1) the process of
energy extraction from black holes; (2) the quantum and general relativistic
effects of matter-antimatter creation near the black hole horizon; (3) the
physics of ultrarelativisitc shock waves with Lorentz gamma factor $\gamma >
100$. In astronomy and astrophysics also new regimes are explored: (i) the
occurrence of gravitational collapse to a black hole from a critical mass core
of mass $M\agt 10M_\odot$, which clearly differs from the values of the
critical mass encountered in the study of stars ``catalyzed at the endpoint of
thermonuclear evolution" (white dwarfs and neutron stars); (ii) the extremely
high efficiency of the spherical collapse to a black hole, where almost 99.99%
of the core mass collapses leaving negligible remnant; (iii) the necessity of
developing a fine tuning in the final phases of thermonuclear evolution of the
stars, both for the star collapsing to the black hole and the surrounding ones,
in order to explain the possible occurrence of the "induced gravitational
collapse". A new class of space missions to acquire information on such extreme
new regimes are urgently needed.
