Asymptotic Freedom and Vacuum Polarization Determine the Astrophysical End State of Relativistic Gravitational Collapse: Quark--Gluon Plasma Star Instead of Black Hole

TL;DR

This work argues that the final state of relativistic gravitational collapse can be a self-bound, ultra-magnetized QGP star, stabilized by the combined effects of NLED vacuum polarization and QCD asymptotic freedom, rather than a black hole. By deriving a nonlinear Tolman–Oppenheimer–Volkoff equation (N-TOV) that couples an NLED effective metric to a QCD-inspired equation of state, the authors obtain a broad mass–radius relation with $0 \lesssim M^{\rm QGP}_{\rm Star} \lesssim 7\,M_\odot$ and $0 \lesssim R^{\rm QGP}_{\rm Star} \lesssim 24$ km, under surface fields $B^{\rm QGP}_{\rm Star} \sim 10^{14}$–$10^{16}$ G (and potentially higher in the core). The model predicts a GECKO state with a surface redshift $z_{\rm Grav} \gtrsim 10^8$ and observational signatures via gravitational waves or lensing (e.g., gravitational rainbows) that differ from true BH horizons. The framework hinges on the Born–Infeld NLED treatment of extreme EM fields and the QCD asymptotic freedom pressure that prevents singular collapse, offering a concrete alternative to BHs and guiding future multi-messenger searches for such QGP stars.

Abstract

A general relativistic model of an astrophysical hypermassive extremely magnetized ultra-compact self-bound quark--gluon plasma object that is supported against its ultimate gravitational implosion by the simultaneous action of the vacuum polarization driven by nonlinear electrodynamics (NLED: light-by-light scattering) and the quantum chromodynamics (QCD) asymptotic freedom, is presented. These QCD stars can be the final figures of the equilibrium of collapsing stellar cores. Post-supernova fallback material pushes the nascent remnant beyond its stability to collapse into a hybrid hypermassive neutron star (HHMNS). Hypercritical accretion can unbind the whole HHMNS's baryons to spontaneously break away color confinement, powering a first-order hadron-to-quark phase transition to a sea of ever-freer quarks and gluons. This core is hydro-stabilized by the steady, endlessly compression-admitting asymptotic freedom state, possibly via gluon-mediated enduring exchange of color charge among bound states. The nonlinear TOV equation indicates the occurrence of hypermassive QGP/QCD stars with a wide mass spectrum ($0\lesssim$ M$^{\rm{QGP}}_{\rm{Star}}\lesssim$\,7\,M$_\odot$ and beyond), for star radii ($0\lesssim R^{\rm{QGP}}_{\rm{Star}}\lesssim 24$\,km and beyond) with B-fields ($10^{14} \leq$ B$^{\rm{QGP}}_{\rm{Star}} \leq 10^{16}$\,G and beyond). Such QCD stars can emulate what the true black holes are supposed to gravitationally do in most astrophysical settings. This color quark star could be found through a search for its eternal ``yo-yo'' state gravitational-wave emission, or via lensing phenomena like gravitational rainbows, as in this scenario it is expected that the light deflection angle, directly influenced by the larger effective mass/radius and magnetic field of the deflecting object, increases as the incidence angle decreases for impact parameter lower values.

Figures (4)

• Figure 1: Plot of the attractive (green curve) vs. repulsive (red curve) potentials $V(r)$ as a function of distance $r$, for the QCD interaction. (Plot taken from "Unveiling the strong interaction among hadrons at the LHC" ALICE(2020)).
• Figure 2: This plot highlights the location of proto-neutron stars, the deconfinement transition, the QGP state as per heavy-ion collisions, and the Lattice QCD limit. (Plot taken from "Introduction to Heavy-Ion Physics|ATLAS Open Data". ATLAS-open-data) The Z$_3$-symmetry breaking label was introduced by the authors.
• Figure 3: A sample of the mass vs. radius relations calculated for the QGP Star model according to the physical framework here presented. For this, the MIT Bag Model EoS with specific values for the central density $\rho_c$ and the B$_{bag}$ constant was used. The relations are obtained by satisfying the conditions that define the actual stellar radius ($\rho(r)|_{r=R^{QGP}_{Star}}, p(r)|_{r=R^{QGP}_{Star}} = 0$!) as a function of the magnetic field strength $B$ at the QGP star surface, and for a field strength maximum value $b$ in the Born-Infeld theory of nonlinear electrodynamics (NLED). This graph exhibits a fundamental trend indicating that there appears not to exist any mass/radius upper bound to the general relativistic hypermassive (up to $7\,M_\odot$ in this plot) QGP star figure of equilibrium. This also means that the quark-gluon plasma can built astrophysical objects with masses spread over a wide spectrum so as to include the central supermassive compact bodies observed in most galaxies. A wide range of models exhibiting the relentless trend pictured in this graph will be discussed in forthcoming papers wherein the parameter space involving the EoS, the field strength at both QGP star core and surface, as well as the NLED Born-Infeld theory maximum field strength $b$ (including the upper threshold derived from the ATLAS/LHC experiment, as quoted above) are explored. [This plot is taken from the paper in preparation by H.J. Mosquera Cuesta, R. Francisco dos Santos and L.G. de Almeida: General relativistic figures of equilibrium of anisotropic hypermagnetized quark-gluon plasma stars as the ultimate astrophysical state of gravitational collapse supported by NLED-driven vacuum polarization. In that paper, a wide number of graphs describing key relations (e.g., density vs. radius, pressure vs. radius, compacticity (Buchdahl limit), etc.) among the QGP star astrophysical properties are given, along with an extended analysis of the physical implications of the results obtained within this scenario.
• Figure 4: Effective surface gravitational redshift $z_{_{\rm Grav}}$ for B-fields up to $10^{20}$ G. This graph clearly indicates the trend of an increase in $z_{_{\rm Grav}}$ for the extremely large B-fields, as the subject of this analysis. Its trend is exponentially increasing but it never reaches an infinite value, as is the case for true BHs. (Plot taken from the paper IJMPA(2006)).