Singularities as Solitons? Quantum Vacuum Architecture of Black Holes

TL;DR

The paper addresses black hole singularities by proposing horizonless, soliton-like compact objects formed in ghost-free $f(R)=R+αR^2$ gravity. It introduces the Lamarina boundary, a surface of maximal redshift that replaces the event horizon and is supported by quantum vacuum dispersion, hosting a sub-threshold oscillaton core $R(t,r)=\mathcal{R}(r)\cos(Ω t)$ with dispersion length $L_{\rm QV}=\sqrt{6α}$; near the wall the metric behaves as $y(x)=y_0+\tfrac{1}{2}\kappa_{\rm loc}^2 x^2$, allowing a controlled adiabatic evolution. The analysis shows that null geodesics near the Lamarina produce Hawking-like radiation with a Planckian spectrum characterized by $T_{\rm eff}=\frac{\hbar}{2\pi k_B}\,\kappa_{\rm peel}$ and redshifted to infinity as $T_{\infty}=\sqrt{A_{\min}}\,T_{\rm eff}$, while a Dyson-type ceiling caps the radiated power at $P_{\infty}^{\max}\approx \eta\frac{c^5}{G}$ and EFT matching imposes a global envelope $R_{L,\min}^{(\mathrm{env})}=\frac{2 L_{\rm QV}}{\chi^2}$, yielding a mass scale $M_{\star}=\frac{c^2}{2G}\frac{L_{\rm QV}}{\chi^2}$. Together, these results present a concrete mechanism by which quantum vacuum dispersion shapes horizonless black-hole architectures and imposes universal radiative bounds, while leaving open questions of nonlinear stability and full saturation of the envelope.

Abstract

We propose that black holes are \emph{soliton-esque} objects, where gravitational collapse is balanced by quantum vacuum dispersion, modeled via \(R+αR^{2}\) gravity. Classical singularities are replaced by oscillating, finite-radius cores, thereby evading static no-go theorems. The event horizon is replaced by the \textit{Lamarina}, a surface of maximum redshift whose surface geometry yields Hawking-like radiation with corrections. The Raychaudhuri equations impose a Dyson-type ceiling on the maximum radiated power \((P_{\infty} \lesssim c^{5}/G)\), while effective field theory matching dictates a universal minimum Lamarina radius set by the dispersion scale.

Figures (1)

• Figure 1: Schematic representation of the proposed quantum vacuum soliton structure. Illustrating the Lamarina replacing the classical horizon and the localized curvature profile.