Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls

We present a novel \textit{gauge-invariant and minimal} formation mechanism of primordial black holes in first-order phase transition and domain walls separately. The new analysis still awaits peer review, but it already lays out the central claim clearly.

The significance lies in astrophysics becomes persuasive only when an observed signal can be tied to a physically defensible explanation. Compact objects such as neutron stars and black holes are natural laboratories for extreme physics, but the distance and complexity of these systems make interpretation difficult without multi-wavelength coverage and careful modeling. A detection without a mechanism is only half a result. the other half comes from showing that the signal fits quantitatively inside a coherent physical picture rather than merely being consistent with a broad family of models. We present a novel \textit{gauge-invariant and minimal} formation mechanism of primordial black holes (PBHs) in first-order phase transition (FOPT) and domain walls (DW). This is based on the first-order tensor perturbations, generated during FOPT from bubble collisions \& sound waves, and from DW annihilation, sourcing curvature, at second-order.

We show that the PBH formation implies \textit{model-independent constraints} on FOPT parameters ($β/H, α, T_{\star}$) and on DW parameters, ($α_{\rm ann}, V_{\rm bias}, σ$). We find that asteroid mass PBHs can become the entire dark matter (DM) of the Universe, for $T_{\star} \in (4 \times 10^{2}, 10^{4})$ GeV, for $β/H \simeq 6$, involving.

The corresponding FOPT Gravitational Waves (GW) amplitude will have its characteristic peak at $Ω_{\rm GW}^{\rm p} h^2$ $\sim \mathcal{O}(10^{-8})$ between frequencies $f_{\rm p}. PBH as entire DM is possible for $σ^{1/3} \in [10^{6}.

10^{8}]$ TeV, for $V_{\rm bias}^{1/4} \in [10^7. 10^6] $) GeV within the reach in LISA and ET detectors.

The broader interest lies in turning an observational clue into something that can be weighed against competing models of the underlying physics. Astrophysics does not have the luxury of controlled experiments; everything is inferred from radiation that traveled across cosmic distances under conditions that cannot be reproduced in a terrestrial laboratory. This makes the interpretation chain longer and more uncertain than in bench science, but it also means that a well-constrained measurement of an extreme object carries theoretical information that no earthbound experiment can provide.

We also provide semi-analytical formulae for the tensor-induced density spectrum, $P_{δ^{(2)}}$, $M_{\rm PBH}$ and $f_{\rm PBH}$, relating them in terms of FOPT and DW parameters. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether independent datasets and physical modeling converge on the same interpretation. Multi-wavelength follow-up, combining X-ray, radio and optical data where possible, is typically what separates a compelling detection from a robust physical characterization. In high-energy astrophysics, results that initially looked definitive have been revised when data from a second messenger arrived; the current result should be read with that history in mind. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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