Swift Memory Burden in Merging Black Holes: how information load affects black hole's classical dynamics (2509.22540v1)

Abstract: In this paper we argue that the information load carried by a black hole affects its classical perturbations. We refer to this phenomenon as the ``swift memory burden effect" and show that it is universal for objects of high efficiency of information storage. The effect is expected to have observable manifestations, for example, in mergers of astrophysical black holes in Einstein gravity. The black holes with different information loads, although degenerate in the ground state, respond very differently to perturbations. The strength of the imprint is controlled by the memory burden parameter which measures the fraction of the black hole's memory space occupied by the information load. This represents a new macroscopic quantum characteristics of a black hole. We develop a calculable theoretical framework and derive some master formulas which we then test on explicit models of black holes as well as on solitons of high capacity of information storage. We show that the effect must be significant for the spectroscopy of both astrophysical and primordial black holes and can be potentially probed in gravitational wave experiments. We also provide a proposal for the test of the memory burden phenomenon in a table-top laboratory setting with cold bosons.

• The paper introduces the swift memory burden effect, demonstrating how quantum information load modulates the classical dynamics of merging black holes.
• It employs an effective Hamiltonian framework to connect master and memory modes, with the memory burden parameter μ quantifying the information load in the system.
• The analysis predicts observable gravitational wave signal modifications, including amplitude suppression and spectral shifts, and outlines laboratory analog proposals.

Swift Memory Burden in Merging Black Holes: Information Load and Classical Dynamics

Introduction and Motivation

This paper introduces and formalizes the "swift memory burden effect," a phenomenon whereby the quantum information load stored in a black hole directly influences its classical dynamical response to perturbations, particularly during mergers. The effect is argued to be universal for systems with high information storage efficiency, such as black holes and saturated solitons, and is expected to have observable consequences in gravitational wave signals. The central claim is that, although black holes of equal mass are degenerate in their ground state regardless of information load, their response to perturbations is strongly modulated by the fraction of their memory space occupied by information, quantified by a "memory burden parameter" $\mu$.

Theoretical Framework: Assisted Gaplessness and Memory Modes

The paper builds on the concept of "assisted gaplessness," wherein a system creates an environment such that certain degrees of freedom (memory modes) become gapless, allowing for energetically efficient information storage. The memory modes are typically labeled by angular momentum and species indices, and their excitation patterns span a high-dimensional memory space. The system's ability to store information efficiently is controlled by master modes, whose macroscopic occupation numbers tune the gap of the memory modes.

The effective Hamiltonian for such systems is constructed to capture the interplay between master and memory modes, with the energy cost of memory patterns vanishing at critical occupation numbers of the master mode. The universality of this mechanism is established by mapping it onto both black holes and QFT solitons, with explicit bounds on microstate entropy derived from unitarity, area law, and occupation number considerations.

Memory Burden Effect: Gradual vs. Swift Regimes

The memory burden effect manifests as a back-reaction that resists departures from the critical state of assisted gaplessness. Two regimes are distinguished:

• Gradual Memory Burden: Activated during slow quantum decay processes (e.g., Hawking evaporation), leading to a progressive increase in the energy gap of memory modes and a slowdown of decay rates.
• Swift Memory Burden: Triggered by rapid, classical perturbations (e.g., mergers), resulting in an immediate and significant modification of the system's classical dynamics.

The strength of the effect is controlled by the memory burden parameter $\mu$, defined as the ratio of energy invested in the master mode to the vacuum energy cost of the memory pattern. For $\mu \ll 1$, the system exhibits strong resistance to perturbations, and the classical evolution is substantially altered.

Application to Black Hole Mergers

The paper applies the framework to astrophysical and primordial black holes, identifying the memory modes as gapless angular momentum modes deposited by gravitons and other species. The diversity of these modes is shown to scale with the area of the horizon, independent of the number of species due to the species scale cutoff.

During a merger, the information load carried by each black hole is "activated," and the classical dynamics of the merger is modulated by the respective $\mu$ parameters. The analysis demonstrates that the amplitude and spectrum of gravitational wave emission are sensitive to the memory burden, with strong suppression and spectral shifts for black holes with significant information loads. The effect is argued to be observable in gravitational wave experiments, with the potential to probe the hidden quantum hair of black holes.

Extension to Saturated Solitons

The universality of the swift memory burden effect is illustrated using saturated solitons, specifically 't Hooft-Polyakov monopoles endowed with maximal microstate entropy via localized fermionic or Goldstone zero modes. The merger of such solitons exhibits analogous memory burden dynamics, with the energy cost of misaligned or excited memory patterns leading to macroscopic modifications of the classical evolution and radiation spectra.

Laboratory Proposals

The paper outlines experimental proposals for observing the memory burden effect in table-top systems, such as attractive cold bosons on a ring. By tuning the system to the critical state of assisted gaplessness and encoding information in nearly-gapless Bogoliubov modes, the resistance to quantum depletion and classical perturbations can be measured, providing a direct analog of the black hole memory burden phenomenon.

Implications and Outlook

The swift memory burden effect introduces a new macroscopic quantum characteristic for black holes, supplementing mass, charge, and angular momentum with the memory burden parameter $\mu$. This challenges the classical no-hair paradigm by demonstrating that quantum information load, while dormant in the ground state, becomes dynamically relevant upon perturbation. The effect is predicted to be significant for astrophysical black holes formed from high-diversity sources, as well as for primordial black holes, and is expected to leave imprints in gravitational wave signals.

The theoretical implications extend to the universality of information retention and the energetic bounds on information storage in QFT, while the practical implications suggest new avenues for probing black hole microstructure and quantum hair via gravitational wave spectroscopy. The laboratory proposals further open the possibility of testing these ideas in controlled quantum systems.

Conclusion

The paper provides a comprehensive and calculable framework for understanding how the quantum information load of black holes and other saturated systems influences their classical dynamics under perturbation. The introduction of the swift memory burden effect offers a novel perspective on black hole mergers, with concrete predictions for gravitational wave observables and potential laboratory analogs. The work establishes a bridge between quantum information theory, black hole physics, and experimental many-body systems, with significant implications for both theoretical and observational studies of quantum gravity.