  P-stars are compact relativistic stars made of deconfined up and down quarks
in a chromomagnetic condensate proposed by us long time ago. P-stars do not
admit a critical mass thereby they are able to overcome the gravitational
collapse to black holes. In this work we discuss in greater details our
theoretical proposal for P-stars. We point out that our theory for compact
relativistic stars stems from our own understanding of the confining quantum
vacuum supported by estensive non-perturbative numerical simulations of Quantum
ChromoDynamics on the lattice. We compare our proposal with the constraints
arising from the recent observations of massive pulsars, the gravitational
event GW170817 and the precise determination of the PSR J0030+0451 mass and
radius from NICER data. We argue that core-collapsed supernovae could give rise
to a P-star instead of a neutron star. In this case we show that the birth of a
P-star could solve the supernova explosion problem leading to successful
supernova explosions with total energies up to $10^{53}$ erg. We critically
compare P-stars with the gravitational wave event GW170817 and the subsequent
electromagnetic follow-up, the short Gamma Ray Burst GRB170817A and the
kilonova AT2017gfo. We also present an explorative study on gravitational wave
emission from coalescing binary P-stars with masses $M_1 \simeq M_2 \simeq 30
\; M_{\odot}$. We attempt a qualitative comparison with the gravitational wave
event GW150914. We find that the gravitational wave strain amplitude from
massive P-star binaries could mimic the ringdown gravitational wave emission by
coalescing black hole binaries. We point out that a clear signature for massive
P-stars would be the detection of wobble frequencies in the gravitational wave
strain amplitude in the post-merger phase of two coalescing massive compact
objects with unequal masses.
