Quantum Phase Transitions and the Breakdown of Classical General Relativity

TL;DR

This work recasts a black hole horizon as a continuous quantum phase transition of space-time, analogous to a Bose liquid's liquid-vapor critical point, with a diverging coherence length $\xi = \hbar /(M v_s)$ that invalidates classical general relativity near the horizon while preserving a global notion of time. It develops a bosonic-fluid–inspired model that yields a Bogoliubov-type dispersion and a critical surface at which $v_s \to 0$, and it derives quantum-critical dissipation, horizon reflectivity, inelastic scattering, and a finite horizon heat capacity as testable signatures. The interior metric is proposed to be de Sitter-like, stabilized by a small cosmological constant that matches boundary conditions, while the horizon acts as a quantum ground state distributing entropy across many degrees of freedom and potentially resolving the information paradox. The theory makes falsifiable astronomical predictions—distinct reflectivity features and red-shifted scattering patterns—that can distinguish it from classical GR and certain holographic scenarios, offering concrete avenues for empirical validation or refutation.

Abstract

It is proposed that the event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapor critical point of a bose fluid. The equations of classical general relativity remain valid arbitrarily close to the horizon yet fail there through the divergence of a characteristic coherence length. The integrity of global time, required for conventional quantum mechanics to be defined, is maintained. The metric inside the event horizon is different from that predicted by classical general relativity and may be de Sitter space. The deviations from classical behavior lead to distinct spectroscopic and bolometric signatures that can, in principle, be observed at large distances from the black hole.

Figures (9)

• Figure 1: Prototype time dilation factor $\gamma(r)$ in the vicinity of a black hole event horizon.
• Figure 2: Phenomenological equation of state defined by Eq. (\ref{['eos']}) for various values of the parameter $c$ near the critical value. The dotted lines indicate the Maxwell loops.
• Figure 3: Illustration of thought experiment in which pressure increases toward the bottom of a tank of quantum fluid. Sound emitted from a transducer on the side of the tank is refracted downward toward the critical surface where the sound speed collapses to zero. The wave fronts shown are for a solution of Eq. (\ref{['wave']}) with the pressure and sound speed profiles given by Eq. (\ref{['profile']}) and plotted on the right. The quantum pathologies in this case are exactly the same as those at a Schwarzschild black hole.
• Figure 4: Lowest-order scattering processes in the critical region. The process on the left causes mass renormalization and decay at zero temperature. The one on the right causes critical opalescence.
• Figure 5: Top: Reflectivity as a function of $\omega \tau_0$ predicted by Eq. (31) for the case of $Q/Q_0 = 10^{-5}$, with $Q_0 = (2M / \hbar \tau_0)^{1/2}$. The interface thickness is assumed to be of order $1/Q_0$ to make the resonances visible. The dotted line is the $Q \rightarrow 0$ limit described by Eq. (\ref{['normal']}). Bottom: Dispersion relation of interface bound states plotted both linearly (left) and semi-logarithmically (right).