Quantum fields on self-similar spacetimes

TL;DR

The paper analyzes quantum effects for massless scalar fields on self-similar spacetimes using Hadamard renormalization, showing that the renormalized stress tensor in self-similar states exhibits a universal scaling with a quantum Lyapunov exponent $\omega_q = 2$ and a leading geometric term $V_{\mu\nu}$. In continuous self-similarity, $\langle T_{\mu\nu} \rangle$ scales as $e^{2u}$ with a linear-in-$u$ correction, and the exponent emerges from matching the semiclassical Einstein equations, independent of the quantum state at leading order. The authors construct explicit self-similar Hadamard states in three settings (Minkowski patch, Hayward spacetime, and critical Roberts spacetime), compute the relevant $V_{\mu\nu}$ contributions, and demonstrate that the leading growth is geometric while renormalization ambiguities contribute via two tensors. These results provide a robust, geometry-driven prediction for quantum backreaction in self-similar collapse and connect to broader universality results for quantum fields on curved backgrounds.

Abstract

We study (scalar, not necessarily conformal) quantum fields on self-similar spacetimes. It is shown that in states respecting the self-similarity the expectation value of the stress tensor gives rise to a quantum Lyapunov exponent $ω_q = 2$, with a leading coefficient which is state-independent and geometric. Three examples for states respecting self-similarity are presented.