---
title: 'Memory-Burden Scenario: PBH Evaporation & Dark Matter'
url: https://www.emergentmind.com/topics/memory-burden-scenario
type: topic
---

# Memory-Burden Scenario: PBH Evaporation & Dark Matter

Searching arXiv for recent 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 [1810.02336]. 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 [2006.00011], [2402.14069]. 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 [2503.21005].

## 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 [1810.02336]. 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 [2503.21740].

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 [2606.04707]. 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 [2006.00011].

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 [2006.00011]. 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 \(T_{\rm BH}\) [2503.21005]. The corresponding lifetime scales as \(M_i^3\), so black holes lighter than about \(5\times 10^{14}\,\mathrm g\) evaporate within the age of the Universe in the standard picture [2503.21005].

The entropy entering memory-burden phenomenology is the dimensionless Bekenstein-Hawking entropy
\[
\tilde S \equiv \frac{S}{k_B} = \frac{\pi r_g^2}{\hbar G} \approx 2.6\times 10^{30} \left(\frac{M}{10^{10}\,\mathrm{g}}\right)^2.
\]
A widely used phenomenological prescription assumes that the black hole remains semiclassical until its mass falls to \(qM_i\), and then enters a burdened phase:
\[
\frac{dM}{dt}= \begin{dcases} \left.\frac{dM}{dt}\right|_{\rm SC}, & M\ge qM_i,\\[1mm] \left.\frac{dM}{dt}\right|_{\rm MB}, & M<qM_i, \end{dcases}
\qquad
\left.\frac{dM}{dt}\right|_{\rm MB} = \frac{1}{\tilde S(qM_i)^k}\, \left.\frac{dM}{dt}\right|_{\rm SC}\right|_{M=qM_i}.
\]
Here \(q\) is the onset fraction and \(k\) is the entropy-power suppression exponent [2503.21005].

Several papers instead motivate an early-onset regime. In one such mapping, the black-hole dictionary
\[
\epsilon_0 = r_g^{-1},\qquad N_c = K = S,\qquad N_m = \frac{S}{2},\qquad \epsilon_k = \sqrt{S}\, r_g^{-1}
\]
gives
\[
q \simeq \left(p^2 S\right)^{-1/(2(p-1))},
\]
so that for \(p=2\),
\[
q = \frac{1}{\sqrt S}.
\]
This is the “early onset” case, whereas large \(p\) can push the onset to an \(\mathcal O(1)\) mass loss [2503.21740].

The main formal distinction in recent work is between abrupt and continuous crossover. A representative smooth interpolation is
\[
\frac{dM}{dt} = \left(\left.\frac{dM}{dt}\right|_{\rm SC}\right)^h \left(\left.\frac{dM}{dt}\right|_{\rm MB}\right)^{1-h},
\qquad
h(M)=\frac12\left(1+\tanh\left[\frac{M-qM_i}{\delta\,(qM_i/2)}\right]\right),
\]
where \(\delta\) sets the transition width [2503.21005]. Another study uses the same \(\tanh\) profile but contrasts multiplicative and additive combinations,
\[
\frac{dM}{dt} = h(M)\left.\frac{dM}{dt}\right|_{\mathrm{SC}} + [1-h(M)]\left.\frac{dM}{dt}\right|_{\mathrm{MB}},
\]
versus the multiplicative prescription above, and shows that this choice materially changes the inferred cosmological bounds [2606.04707].

## 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” [2402.14069] | \(10^6\,\mathrm{g}\lesssim M^{(1)} \lesssim 10^{14}\,\mathrm{g}\) | Minimal slowdown \(n=1\) |
| “Induced Gravitational Waves probing Primordial Black Hole Dark Matter with Memory Burden” [2409.06365] | \(10^5\,\mathrm g \lesssim M_{\rm PBH,ini} \lesssim 10^{10}\,\mathrm g\) | Approximate range shown for \(n_{\rm MB}=2\) |
| “Does Memory Burden Open a New Mass Window for Primordial Black Holes as Dark Matter?” [2503.21005] | \(10^{4}\,\mathrm g < M_i < 10^{10}\,\mathrm g\) | Step-like suppression with practically instantaneous transition |
| “Memory burden effect of regular primordial black holes” [2605.19463] | around \(10^6\)–\(10^8\) g | Regular PBHs with benchmark \(k=1\) |
| “Micron-sized Extra Dimensions and Primordial Black Holes: Charges, Rotating, and Memory Burdened” [2605.00252] | 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 [2409.06365]. In another, the burden turns on almost immediately, requiring only a tiny fractional loss such as \(q=1/\sqrt S\) [2503.21740]. In yet another, the low-mass reopening is strengthened by regular-black-hole thermodynamics or by extra-dimensional entropy scalings [2605.19463], [2605.00252].

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 [2503.21005]. In the step-function picture, once the mass crosses \(qM_i\), Hawking radiation is not literally zero, but is suppressed by the huge factor \(\tilde S^k\), so for practical cosmological purposes it is nearly halted. This allows PBHs with \(10^{4}\,\mathrm g < M_i < 10^{10}\,\mathrm g\) to reach the burdened phase before Big Bang nucleosynthesis (BBN) and thus avoid the usual BBN and late-Universe energy-injection limits [2503.21005].

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 [2503.21005]. The headline result is that, for a gradual or continuous transition, the authors “rule out the possibility that black holes lighter than \(\sim 4\times 10^{16}\,\mathrm g\) could make up all or most of the dark matter” [2503.21005].

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, \(q\sim 0.1\)–\(0.9\). If the onset occurs almost immediately after formation, the constraints weaken. In the supplement, a new window can reappear only if
\[
1-q \lesssim 10^{-10},
\]
so that almost no semiclassical evaporation occurs before stabilization [2503.21005]. The effect of the entropy-power parameter \(k\) is reported to be weak compared with the effect of \(q\) and \(\delta\) [2503.21005].

A subsequent BBN-specific study sharpened the interpolation issue by comparing additive and multiplicative crossover rules with the same smooth \(\tanh\) profile [2606.04707]. 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
\[
10^{5}\,\mathrm{g}\lesssim M_i\lesssim 10^{10}\,\mathrm{g},
\]
the additive case can permit
\[
f_{\mathrm{PBH},0}\sim 10^{-1}
\]
where the multiplicative case gives
\[
f_{\mathrm{PBH},0}\lesssim 10^{-2}.
\]
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 [2606.04707].

## 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
\[
\Omega_{\rm GW}(f_{\rm peak})h^2 \simeq 7\times 10^{-9},
\qquad
f_{\rm peak} = 1\times 10^{3} \left(\frac{M_{\rm PBH}}{10^{10}\,\mathrm g}\right)^{-1/2}\,\mathrm{Hz},
\]
with the claim that PBH dark matter with initial mass above about \(10^7\,\mathrm g\) can be tested by future observations such as Cosmic Explorer [2409.06365]. The same work also discusses an ultra-high-frequency merger background with
\[
f_{\rm peak} = 2\times 10^{27} \left(\frac{M_{\rm PBH,ini}}{10^{10}\,\mathrm g}\right)^{-1}\,\mathrm{Hz},
\]
although it notes that there are currently no known realistic detection methods [2409.06365].

High-energy neutrinos provide a second class of probes. One PBH-focused study assumes a burdened two-stage history with \(q=\tfrac12\) and an entropy suppression \(S^{-k}\), and uses IceCube data to constrain the \((M_{\rm PBH},k,f_{\rm PBH})\) space [2410.07604]. In that framework, for \(k=2.0\) and \(f_{\rm PBH}=1\), viable PBH dark matter requires
\[
M_{\rm PBH} \gtrsim 2\times 10^5~{\rm g},
\]
and near the evaporation threshold neutrino observations improve bounds on \(f_{\rm PBH}\) by up to two orders of magnitude [2410.07604]. A different phenomenological deformation of the Hawking spectrum introduces an energy-dependent suppression
\[
\mathcal{S}(E,M;k)=\frac{1}{1+k(E/T_H)^2},
\]
which suppresses the high-energy tail while leaving the infrared behavior unchanged; in that model, IceCube-derived bounds at \(M\approx 10^8\,\mathrm g\) are weakened by a factor \(\approx 4.7\) for IceCube 2020 and \(\approx 6.0\) for HESE 2022 when going from \(k=0\) to \(k=1\) [2604.06858]. 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
\[
T_c=\left(\frac{\eta_M^2}{\eta_T}\right)^{1/3}T_{c,\mathrm{SC}},
\qquad
r_c=\left(\frac{\eta_T}{\eta_M}\right)r_{c,\mathrm{SC}},
\]
so that a suppressed mass-loss rate lowers the hot-spot temperature and enlarges the core [2511.17329]. In the “vanilla” rigid MB picture, hot spots form only if roughly
\[
10^5\mathrm{g}\lesssim qM_{\rm ini}\lesssim 5\times 10^{12}\mathrm{g}
\qquad\text{and}\qquad
k\lesssim 0.3,
\]
whereas a self-similar suppression can allow
\[
50\mathrm{g}\lesssim qM_{\rm ini}\lesssim 5\times 10^{15}\mathrm{g}
\qquad\text{and}\qquad
k\lesssim 1
\]
[2511.17329].

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 [2511.01848]. Under the adopted benchmarks, graviton-photon conversion excludes
\[
7.5\times 10^5\,{\rm g} \leq M_{\rm PBH}\leq 4.4\times 10^7\,{\rm g}
\]
with \(f_{\rm PBH}\geq 1\) and \(k=1\), while the merger scenario restricts PBH dark matter lighter than
\[
2.2\times10^{11}\,{\rm g}
\]
[2511.01848].

## 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 \(M,J,Q\) but different microscopic information loads need not ring down identically after merger [2509.22540]. In the effective description, the strength of the imprint is controlled by a memory-burden parameter
\[
\mu \equiv \frac{E_{\rm ms}}{pE_p},
\qquad
\mu \sim \frac{M}{E_P},
\]
and the paper argues that the relevant perturbative dynamics at frequencies \(\omega\sim 1/R\) can be shifted, suppressed, and driven toward the infrared when \(\mu\lesssim 1\) [2509.22540]. 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 [2510.19916]. In its minimal model, the SMB-induced ringdown shift is encoded through a gap-reopening parameter \(p\), and a Bayesian analysis of the \((220)\) and \((440)\) modes yields the lower bound
\[
\log_{10}p \gtrsim 2,
\]
while a Fisher forecast for a GW250114-like event in Cosmic Explorer gives
\[
\log_{10}p \gtrsim 5.
\]
The interpretation offered there is that current data already disfavour rapid gap reopening [2510.19916]. 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 [1810.02336], [2006.00011]. PBH applications show that such suppression can, under specific assumptions, reopen low-mass dark-matter windows [2402.14069], [2409.06365]. 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 [2503.21005]. 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.

Source: https://www.emergentmind.com/topics/memory-burden-scenario