Memory-Burden Scenario: PBH Evaporation & Dark Matter

• Memory-Burden Scenario is defined as a phenomenon where systems with high memory capacity incur an energetic backreaction that suppresses further decay.
• Microscopic models using assisted gaplessness demonstrate how enhanced memory storage triggers a two-stage evolution in black holes, transitioning from a semiclassical to a burdened phase.
• Applied to primordial black holes, the scenario suggests model-dependent dark matter windows and underscores the impact of transition dynamics on observational signatures.

Searching arXiv for papers on memory burden and primordial black holes to ground the article in the latest literature. In high-energy theory and cosmology, the memory-burden scenario denotes the claim that systems with enhanced memory-storage capacity are subjected to a backreaction in which the information they carry suppresses further decay. In the prototype microscopic literature, “the ones with heavier loaded memories survive longer than those that store emptier patterns,” and the mechanism was proposed as universal for systems with enhanced memory-storage capacity, such as black holes (Dvali, 2018). Applied to black holes, the scenario replaces strictly self-similar Hawking evaporation by a two-stage evolution in which a semiclassical phase is followed by a burdened phase with strongly reduced emission, and this possibility has been invoked to reopen low-mass primordial-black-hole (PBH) dark-matter windows (Dvali et al., 2020, Alexandre et al., 2024). More recent work, however, emphasizes that the phenomenology depends critically on how the transition is modeled, especially whether the onset of burden is taken to be instantaneous or continuous (Montefalcone et al., 26 Mar 2025).

1. Microscopic origin: assisted gaplessness and the burden of stored information

The original memory-burden construction is a solvable bosonic model in which a macroscopically occupied “master mode” lowers the gaps of many “memory modes,” producing a family of holographic states with an area-law microstate count (Dvali, 2018). In that setting, the effective Hamiltonian can be written in the assisted-gaplessness form

$$\hat H=\epsilon_0 \hat n_0 + \epsilon_K \left(1-\frac{\hat n_0}{N_c}\right)^p \sum_{k=1}^K \hat n_k,$$

so that the effective memory-mode gap is

$$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$

At the critical point $n_0=N_c$, the memory modes become gapless, many occupation-number patterns become degenerate, and the system acquires exponentially large memory space and entropy (Dvali et al., 27 Mar 2025).

In this framework, the burden is the energetic cost of preserving a memory pattern after the system is pushed away from criticality. A convenient parametrization is

$$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$

which grows as the master occupation decreases and thereby backreacts against further depletion (Zhang et al., 3 Jun 2026). In the prototype black-hole-inspired literature, the same effect is described as a universal property of high-capacity information storage: efficient storage requires nearly gapless modes, but once the background maintaining their gaplessness changes, the same stored pattern becomes expensive and resists the evolution (Dvali et al., 2020).

This mechanism admits a second process, “rewriting,” in which information is off-loaded from one enhanced-memory state into another. The prototype analyses show that rewriting can overcome burden in principle, but the rate of rewriting is suppressed, so the later evolution becomes extremely slow compared to the initial stage (Dvali et al., 2020). This suggests that memory burden does not necessarily imply absolute stability; rather, it generically implies a drastic slowdown whose detailed endpoint is model dependent.

2. Black-hole implementation and evaporation laws

In the PBH literature, the starting point is the usual Schwarzschild-Hawking system. The Hawking temperature is

$T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$

with $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$, and the semiclassical evaporation rate is

$$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$

where $\mathcal G\simeq 3.8$ and $g_{\star,H}$ counts the weighted radiated degrees of freedom lighter than $T_{\rm BH}$ (Montefalcone et al., 26 Mar 2025). The corresponding lifetime scales as $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$0, so black holes lighter than about $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$1 evaporate within the age of the Universe in the standard picture (Montefalcone et al., 26 Mar 2025).

The entropy entering memory-burden phenomenology is the dimensionless Bekenstein-Hawking entropy

$$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$2

A widely used phenomenological prescription assumes that the black hole remains semiclassical until its mass falls to $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$3, and then enters a burdened phase: $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$4 Here $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$5 is the onset fraction and $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$6 is the entropy-power suppression exponent (Montefalcone et al., 26 Mar 2025).

Several papers instead motivate an early-onset regime. In one such mapping, the black-hole dictionary

$$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$7

gives

$$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$8

so that for $$\mathcal E_K = \left(1-\frac{n_0}{N_c}\right)^p \epsilon_K.$$9,

$n_0=N_c$0

This is the “early onset” case, whereas large $n_0=N_c$1 can push the onset to an $n_0=N_c$2 mass loss (Dvali et al., 27 Mar 2025).

The main formal distinction in recent work is between abrupt and continuous crossover. A representative smooth interpolation is

$n_0=N_c$3

where $n_0=N_c$4 sets the transition width (Montefalcone et al., 26 Mar 2025). Another study uses the same $n_0=N_c$5 profile but contrasts multiplicative and additive combinations,

$n_0=N_c$6

versus the multiplicative prescription above, and shows that this choice materially changes the inferred cosmological bounds (Zhang et al., 3 Jun 2026).

3. Claimed PBH dark-matter windows

A central application of the memory-burden scenario is the claim that very light PBHs can survive until today and constitute all or part of the dark matter. Different papers, however, obtain different windows because they adopt different onset criteria, entropy suppressions, dimensional settings, or regular-black-hole backgrounds.

Reference and setup	Stated viable range	Key condition
“New Mass Window for Primordial Black Holes as Dark Matter from Memory Burden Effect” (Alexandre et al., 2024)	$n_0=N_c$7	Minimal slowdown $n_0=N_c$8
“Induced Gravitational Waves probing Primordial Black Hole Dark Matter with Memory Burden” (Kohri et al., 2024)	$n_0=N_c$9	Approximate range shown for $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$0
“Does Memory Burden Open a New Mass Window for Primordial Black Holes as Dark Matter?” (Montefalcone et al., 26 Mar 2025)	$$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$1	Step-like suppression with practically instantaneous transition
“Memory burden effect of regular primordial black holes” (Du et al., 19 May 2026)	around $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$2–$$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$3 g	Regular PBHs with benchmark $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$4
“Micron-sized Extra Dimensions and Primordial Black Holes: Charges, Rotating, and Memory Burdened” (Leontaris et al., 30 Apr 2026)	sub-gram mass PBHs	6D setup with entropy-power suppression

These windows are not interchangeable. In one class of models, the surviving PBHs are effectively frozen after losing an order-one fraction of their mass (Kohri et al., 2024). In another, the burden turns on almost immediately, requiring only a tiny fractional loss such as $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$5 (Dvali et al., 27 Mar 2025). In yet another, the low-mass reopening is strengthened by regular-black-hole thermodynamics or by extra-dimensional entropy scalings (Du et al., 19 May 2026, Leontaris et al., 30 Apr 2026).

A plausible implication is that “the memory-burden scenario” is better understood as a family of stabilization prescriptions than as a single phenomenological model. The quantitative dark-matter window is therefore inseparable from the choice of onset rule, interpolation rule, and background black-hole model.

4. Continuous crossover, BBN, recombination, and the closure of the light-PBH window

The sharpest recent criticism is that the previously advertised low-mass window survives only if the transition from the semiclassical phase to the memory-burdened phase is practically instantaneous (Montefalcone et al., 26 Mar 2025). In the step-function picture, once the mass crosses $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$6, Hawking radiation is not literally zero, but is suppressed by the huge factor $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$7, so for practical cosmological purposes it is nearly halted. This allows PBHs with $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$8 to reach the burdened phase before Big Bang nucleosynthesis (BBN) and thus avoid the usual BBN and late-Universe energy-injection limits (Montefalcone et al., 26 Mar 2025).

The same paper shows that the conclusion changes once the transition is made continuous. In that case the PBH spends an extended time in an intermediate regime where the evaporation rate is still substantial compared to the fully burdened rate, and the resulting Hawking emission persists during BBN and recombination. The cosmological argument is standard: during BBN, electromagnetic and hadronic injection changes the proton-neutron ratio, increases helium, and causes photodissociation and hadrodissociation; during recombination and the pre-reionization era, continued emission ionizes and heats the gas and alters the CMB anisotropies and spectral properties (Montefalcone et al., 26 Mar 2025). The headline result is that, for a gradual or continuous transition, the authors “rule out the possibility that black holes lighter than $$\mu=\sum_k n_k\, \frac{\partial \mathcal E_k}{\partial n_0},$$9 could make up all or most of the dark matter” (Montefalcone et al., 26 Mar 2025).

That conclusion is not claimed to be completely model independent. The same analysis emphasizes a major caveat: it assumes the burdened phase begins only after an order-one mass loss, $T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$0–$T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$1. If the onset occurs almost immediately after formation, the constraints weaken. In the supplement, a new window can reappear only if

$T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$2

so that almost no semiclassical evaporation occurs before stabilization (Montefalcone et al., 26 Mar 2025). The effect of the entropy-power parameter $T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$3 is reported to be weak compared with the effect of $T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$4 and $T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$5 (Montefalcone et al., 26 Mar 2025).

A subsequent BBN-specific study sharpened the interpolation issue by comparing additive and multiplicative crossover rules with the same smooth $T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$6 profile (Zhang et al., 3 Jun 2026). Its main conclusion is that “the additive crossover always gives weaker bounds than the multiplicative one, while both are tighter than the instantaneous transition.” In the range

$T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$7

the additive case can permit

$T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$8

where the multiplicative case gives

$T_{\rm BH}=\frac{M_{\rm Pl}^2}{8\pi M},$9

This does not restore the old instantaneous window; rather, it shows that even among continuous prescriptions, the inferred BBN exclusion can move by up to about an order of magnitude in the allowed initial fraction (Zhang et al., 3 Jun 2026).

5. Other observational realizations and probes

Beyond BBN and the CMB, the memory-burden scenario generates a wide phenomenology because it modifies both PBH survival and the time profile of energy release. One proposal treats the same primordial perturbations that formed memory-burdened PBHs as a source of scalar-induced gravitational waves, yielding a peak amplitude

$M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$0

with the claim that PBH dark matter with initial mass above about $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$1 can be tested by future observations such as Cosmic Explorer (Kohri et al., 2024). The same work also discusses an ultra-high-frequency merger background with

$M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$2

although it notes that there are currently no known realistic detection methods (Kohri et al., 2024).

High-energy neutrinos provide a second class of probes. One PBH-focused study assumes a burdened two-stage history with $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$3 and an entropy suppression $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$4, and uses IceCube data to constrain the $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$5 space (Chianese et al., 2024). In that framework, for $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$6 and $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$7, viable PBH dark matter requires

$M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$8

and near the evaporation threshold neutrino observations improve bounds on $M_{\rm Pl}\approx 2.2\times 10^{-5}\,\mathrm g$9 by up to two orders of magnitude (Chianese et al., 2024). A different phenomenological deformation of the Hawking spectrum introduces an energy-dependent suppression

$$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$0

which suppresses the high-energy tail while leaving the infrared behavior unchanged; in that model, IceCube-derived bounds at $$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$1 are weakened by a factor $$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$2 for IceCube 2020 and $$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$3 for HESE 2022 when going from $$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$4 to $$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$5 (Chaudhuri, 8 Apr 2026). These two neutrino analyses do not use the same suppression law, but both show that observable flux limits remain competitive in memory-burdened PBH scenarios.

The scenario also modifies the local plasma response to PBH evaporation. A transfer-function treatment of thermal hot spots derives

$$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$6

so that a suppressed mass-loss rate lowers the hot-spot temperature and enlarges the core (Levy et al., 21 Nov 2025). In the “vanilla” rigid MB picture, hot spots form only if roughly

$$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$7

whereas a self-similar suppression can allow

$$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$8

(Levy et al., 21 Nov 2025).

A further proposal constrains memory-burdened PBHs through observables tied to an earlier unsuppressed semiclassical phase. In one scenario, semiclassically emitted gravitons later convert to photons in filament magnetic fields; in another, PBH mergers produce fresh semiclassical black holes whose evaporation clock is effectively reset (Tseng et al., 3 Nov 2025). Under the adopted benchmarks, graviton-photon conversion excludes

$$\left.\frac{dM}{dt}\right|_{\rm SC} = -\frac{\mathcal G\, g_{\star,H}(T_{\rm BH})\, M_{\rm Pl}^4}{30720\pi\, M^2},$$9

with $\mathcal G\simeq 3.8$0 and $\mathcal G\simeq 3.8$1, while the merger scenario restricts PBH dark matter lighter than

$\mathcal G\simeq 3.8$2

(Tseng et al., 3 Nov 2025).

6. Swift memory burden, merger spectroscopy, and present assessment

The evaporation-based scenario has a merger-era analogue. In the “swift memory burden effect,” the information load carried by a black hole affects its classical perturbations, so two holes with the same classical $\mathcal G\simeq 3.8$3 but different microscopic information loads need not ring down identically after merger (Dvali, 26 Sep 2025). In the effective description, the strength of the imprint is controlled by a memory-burden parameter

$\mathcal G\simeq 3.8$4

and the paper argues that the relevant perturbative dynamics at frequencies $\mathcal G\simeq 3.8$5 can be shifted, suppressed, and driven toward the infrared when $\mathcal G\simeq 3.8$6 (Dvali, 26 Sep 2025). This is not presented as a modification of Einstein’s equations, but as a quantum characteristic dormant in the stationary state and activated by perturbation.

A later phenomenological ringdown analysis confronts this swift-burden picture with GW250114-like spectroscopy (Yuan et al., 22 Oct 2025). In its minimal model, the SMB-induced ringdown shift is encoded through a gap-reopening parameter $\mathcal G\simeq 3.8$7, and a Bayesian analysis of the $\mathcal G\simeq 3.8$8 and $\mathcal G\simeq 3.8$9 modes yields the lower bound

$g_{\star,H}$0

while a Fisher forecast for a GW250114-like event in Cosmic Explorer gives

$g_{\star,H}$1

The interpretation offered there is that current data already disfavour rapid gap reopening (Yuan et al., 22 Oct 2025). This does not establish the swift memory burden effect; it constrains one minimal phenomenological realization of it.

Taken together, the literature now presents the memory-burden scenario as a technically rich but strongly model-dependent framework. The original microscopic picture and its black-hole extrapolation motivate the possibility that information storage can suppress decay (Dvali, 2018, Dvali et al., 2020). PBH applications show that such suppression can, under specific assumptions, reopen low-mass dark-matter windows (Alexandre et al., 2024, Kohri et al., 2024). The most important recent qualification is that the result is not generic: once the transition from semiclassical evaporation to the burdened regime is made continuous in a realistic way, prolonged Hawking emission through BBN and recombination can close the claimed low-mass window unless the burden turns on essentially immediately after formation (Montefalcone et al., 26 Mar 2025). This suggests that the decisive questions are no longer whether memory burden can be parameterized, but how the onset, interpolation, and microscopic gap structure are fixed in a full theory.