Memory Burden Effect in Black Holes

• Memory Burden Effect is a quantum backreaction mechanism in high-entropy systems, notably black holes, where information storage impedes decay processes like Hawking evaporation.
• It extends the lifetime of primordial black holes and modifies astrophysical signatures, influencing dark matter models and gravitational-wave phenomena.
• The effect originates from interactions between a master mode and nearly gapless memory modes, a mechanism with universal implications in quantum systems beyond black holes.

The memory burden effect is a quantum backreaction phenomenon arising in systems with enhanced information-storage capacity, most notably black holes. It manifests as a suppression of decay channels—such as Hawking evaporation—due to the stabilization provided by the information (i.e., entropy) internally stored in a highly degenerate set of “memory modes.” The effect predicts drastic deviations from semiclassical self-similar evolution, influences the life cycle of primordial black holes (PBHs), and has direct implications for astroparticle searches and gravitational-wave phenomenology (Chianese et al., 10 Oct 2024, Alexandre et al., 21 Feb 2024, Dvali et al., 2020, Dondarini et al., 16 Jun 2025).

1. Definition and Microscopic Origin

In the semiclassical picture, a black hole evaporates by emitting Hawking quanta at temperature

$T_{\rm H}(M)=\frac{1}{8\pi G M}$

and loses mass at rate

$$\dot{M}_{\rm Hawking}(M) = -\frac{\mathcal{G}g_{\rm SM}}{30720\pi G^2 M^2}$$

with $\mathcal{G}\sim 3.8$ (grey-body factor), $g_{\rm SM}\simeq 102.6$ (relativistic degrees of freedom).

The memory burden effect arises when the entropy $S(M) = 4\pi G M^2$ —which quantifies the degeneracy of microstates or “memory modes” supported by the system—acts to impede further decay. These memory modes, nearly gapless at the critical occupation of the “master” mode (analogous to soft gravitons in the black hole’s quantum $N$-portrait), experience an increase in energy gap as the black hole radiates. Any attempt to deplete the master mode triggers an energy penalty for these modes, thus creating an effective energetic barrier and suppressing further emission (Dvali et al., 2020, Dvali et al., 21 May 2024, Dvali, 2018).

2. Theoretical Modeling and Evaporation Dynamics

The standard dynamical model entails a two-phase evolution:

• (a) An initial semiclassical Hawking evaporation regime, lasting until the black-hole mass drops to a fraction $q$ of its initial mass.
• (b) A memory-burdened phase, where quantum backreaction dominates and the mass-loss rate is universally suppressed by the black-hole entropy raised to a power $k$: $$\dot M_{\rm MB}(M) = \frac{\dot M_{\rm Hawking}(M)}{[S(M)]^k}$$ Typically $k$ is a positive model-dependent parameter, undetermined by current microphysics (Chianese et al., 10 Oct 2024). The transition from semiclassical to memory-burdened phase can be either sharp ($\delta \ll 1$) or gradual, with cosmological implications sensitive to the nature of this crossover (Montefalcone et al., 26 Mar 2025, Dondarini et al., 16 Jun 2025).

The overall effect is to extend the lifetime of a PBH drastically: $\tau_{\rm MB} \propto M^{3+2k}$ so that even PBHs with initial mass $M\ll 10^{15}\,$g can survive to the present epoch (Alexandre et al., 21 Feb 2024). In the limit $k=0$ one recovers the standard Hawking result; for $k>0$, the effect induces a significant slow-down.

3. Quantum Information Storage and Prototype Hamiltonians

At the microscopic level, the quantum system is modeled by a master mode (e.g., soft graviton condensate) strongly coupled to a large number $K\sim S$ of memory modes: $$H = \epsilon_0 \hat n_0 + \epsilon_K \left(1 - \frac{\hat n_0}{N_c}\right)^p \sum_{k=1}^K \hat n_k$$ where $p$ is the critical exponent controlling the gap reopening as the system departs from the optimal memory-storing configuration (Dvali et al., 27 Mar 2025, Dvali, 2018). When the system is maximally loaded, the transfer of information outside (i.e., via Hawking emission) is drastically slowed; alternatively, the information can only be “rewritten” into secondary memory sectors on timescales that scale as inverse powers of the system entropy $S$: $\Gamma_{\rm rw} \lesssim \Gamma_0 / S^2$ where $\Gamma_0$ is the typical decay rate in the absence of burden (Dvali et al., 2020).

This universal mechanism appears in other “saturons” (objects with maximal microstate entropy) such as solitons and critical scalar field configurations (Dvali et al., 21 May 2024).

4. Phenomenological Implications for PBHs and Cosmology

4.1. Dark Matter and Relic Abundance

Due to memory burden, the late-time abundance of small PBHs ($10^5\text{--}10^9$ g or $10^5\text{--}10^{10}$ g, depending on parameter choices) can be substantial, opening a previously excluded dark-matter mass window. For $k\sim 1$ or $p\sim 2$, and a sharp memory-burden onset prior to BBN, both BBN and CMB distortion bounds are evaded, allowing all $\Omega_{\rm DM}$ to be composed of such PBHs (Alexandre et al., 21 Feb 2024, Takeshita et al., 25 Jun 2025, Dondarini et al., 16 Jun 2025).

4.2. Astrophysical Signatures

Surviving PBHs emit ultra-high-energy neutrinos due to their elevated Hawking temperatures in the burdened regime ($T_H \sim 10^4$–$10^{6}$ GeV for $M\sim 10^6$–$10^9$ g), leading to fluxes accessible to IceCube, GRAND, and similar observatories (Chianese et al., 10 Oct 2024, Dvali et al., 27 Mar 2025).

The effect strongly modifies cosmic-ray, $\gamma$-ray, and neutrino backgrounds. Direct searches and multimessenger probes (including gravitational-wave detectors) thus set complementary constraints on the parameter space $(M, k)$ (Kohri et al., 10 Sep 2024, Dondarini et al., 16 Jun 2025).

4.3. Gravitational Waves

The memory burden effect alters the stochastic gravitational-wave background (SGWB) produced by PBH formation and evaporation, including both “induced” (second-order curvature) and merger-driven high-frequency components. The SGWB spectrum features characteristic doubly peaked shapes: the effect can mimic or be disentangled from nonstandard reheating scenarios via careful disentangling of the low- and high-frequency peaks (Bhaumik et al., 6 Sep 2024, Kohri et al., 10 Sep 2024).

5. Constraints and Critical Exponent Phenomenology

The onset and severity of the memory burden effect depend on the critical exponent parameter $p$ (or, equivalently, the suppression power $k$). Observational bounds on PBH contributions to cosmological relic abundance, high-energy astrophysical fluxes, and CMB distortions can be mapped to constraints on $p$.

For $p \simeq 2$ and $k \simeq 2$, the burdened phase typically begins early (after a small fraction $q \simeq S^{-1/2} \ll 1$ is radiated), evading standard bounds and allowing a wide PBH mass window for dark-matter (Dondarini et al., 16 Jun 2025). For larger $p$ or gradual (non-instantaneous) transitions, CMB and BBN constraints become severe, closing most windows below $M \sim 10^{16}$ g unless the transition is extremely sharp (Montefalcone et al., 26 Mar 2025).

Table: Summary of transition scenarios and dark-matter possibility

Transition Type	Allowed PBH Mass Range as DM	Observational Consequence
Instantaneous ($\delta\to 0$)	$10^{5}$–$10^{9\,/\,10}$ g	DM viable, evades BBN/CMB; high-energy $\nu$ signal
Gradual ($\delta \gg 0$)	Excluded below $10^{16}$ g	CMB/BBN strong constraints, DM not possible

For the “swift memory burden” that modifies classical perturbation responses (quasinormal modes of post-merger BHs), observational constraints from GW ringdown spectroscopy can translate to bounds on $p$. Data (e.g., GW250114) currently require $\log_{10}p \gtrsim 2$, with future detectors probing even higher (Yuan et al., 22 Oct 2025).

6. Universality and Analogues in Other Quantum Systems

The memory burden effect is not exclusive to black holes. It arises universally in systems exhibiting “assisted gaplessness” with highly degenerate microstate spaces: solitons in quantum field theory (saturons), Q-balls, and even certain critical neural networks display analogous stabilization-by-memory mechanisms (Dvali et al., 21 May 2024, Dvali, 2018).

The effect imposes a macroscopic quantum hair—controlled by a memory burden parameter—distinct from mass, charge, or angular momentum. This parameter governs the system’s response to decay or classical perturbations and can, in principle, be probed experimentally both in astrophysical contexts and in cold-atom laboratory simulations (Dvali, 26 Sep 2025).

7. Open Questions and Future Directions

The microphysical derivation of the suppression factor $S^{-k}$ remains an open problem in quantum gravity. Key issues include the computation of the “memory-mode” contribution to the black-hole path integral, the treatment of the transition between Hawking and burdened phases, and the effect of additional quantum corrections (e.g., higher curvature terms, non-thermal spectra) (Chianese et al., 10 Oct 2024).

Several experimental avenues are being developed:

• High-energy neutrino telescopes and multimessenger facilities to restrict the burdened PBH DM window.
• CMB observations, particularly for slow or partial transitions.
• Gravitational-wave observatories, both for induced spectra and for ringdown spectroscopy that can probe the “swift” memory burden component (Yuan et al., 22 Oct 2025).

The effect implies a model-independent spread in PBH remnant masses, even for initially monochromatic PBH populations, with observable consequences for gravitational waves and microlensing (Dvali et al., 21 May 2024).

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The memory burden effect thus represents a universal quantum-stabilization mechanism with profound implications for black-hole physics, primordial black hole dark matter, and the phenomenology of cosmic relics. Its rigorous elucidation and observational constraints remain at the frontier of both theoretical and experimental research.