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Recently discovered very metal-poor (VMP) star LAMOST J1010+2358 shows a peculiar abundance pattern that is remarkably well fit by a Pop III pair-instability supernova (PISN) of $\simeq 260$ M$_\odot$. Motivated by this, we investigate the nucleosynthetic characteristics of Pop III and Pop II PISNe to provide theoretical constraints for future observations. This paper is divided into two parts. First, we explore the evolution and nucleosynthesis of Pop III PISNe with initial masses of 130 - 300 M$_\odot$. Our main aim is to investigate how the uncertainty in $^{12}$C$(α,γ)^{16}$O and $^{16}$O+$^{16}$O reaction rates affect their explosion properties and nucleosynthesis. We find that the yields of odd-$Z$ elements are particularly sensitive to the $^{12}$C$(α,γ)^{16}$O rate, while the production of Fe-peak elements shows significant sensitivity to both rates. Second, we investigate the nucleosynthetic features of Pop II PISNe formed in gas enriched exclusively by Pop III PISN ejecta. By employing a time-dependent convection model during the explosion, we demonstrate that metal enrichment increases opacity and triggers vigorous convective mixing. This hydrodynamic effect significantly enhances the explosion energy and $^{56}\text{Ni}$ production. Consequently, Pop II PISNe exhibit distinct chemical signatures, including a weaker odd-even effect and enhanced Zn-Ge production, providing unique diagnostics for identifying PISN remnants in the early Universe.

We show that primordial quark pellets (PQP), ultra dense quark matter mini-stars formed at around 1 TeV, naturally arise in a radiation dominated universe if rare baryon overdensities are produced by collapsing Peccei-Quinn domain walls or similar superhorizon structures. Solving the Tolman-Oppenheimer-Volkoff equation with a hot quark equation of state, we find stable solutions with a maximum mass of $10^{-2}$ solar masses and radii of approximately 100 meters, although the formation mechanism favours much smaller objects. Once formed, PQPs cool and evolve intro mini neutron stars or stable strange matter nuggets, depending on the QCD ground state. Formation probabilities of $10^{-9}$ to $10^{-4}$ per horizon volume could suffice to reproduce the present dark matter density without altering Big Bang Nucleosynthesis or requiring entropy dilution. PQPs completely evade microlensing constraints if their mass is below $10^{-7}$ solar masses, a range that could easily accommodate most of the dark matter. PQPs thus potentially constitute a conservative, Standard-Model based, and observationally testable solution to the dark matter puzzle.

Reaction rate determination is an essential problem in the theories of cosmological and stellar nucleosynthesis. I investigate the closed-form analytic evaluation of thermonuclear reaction rates, which are necessary for both cosmic and celestial nucleosynthesis. An alternate velocity distribution to the Maxwell-Boltzmann distribution can be considered in nuclear fusion processes occurring in the interior of stars when there is a diversion from hydrostatic equilibrium. The extension of non-resonant reaction rate integrals in standard, cut-off, depletion, and screening instances is examined in this study, utilising the MacDonald distribution. This study is primarily on the use of generalized special functions that represent the extended non-resonant thermonuclear functions in mathematical physics. Moreover, an attempt is made to analyse the reaction probability integrals corresponding to the several forms of the slowly varying cross-section factor S(E).

The 220~PeV neutrino KM3-230213A, in tension with IceCube and Auger unless narrow, admits a two-body reading: relic decay $X \to ν\barν$ with $m_X \approx 4.4\times10^{8}$~GeV. Consistency with neutrino and $γ$-ray bounds sets $τ/f \approx 10^{29}$--$10^{30}$~s, lifetime over relic fraction. For a flavored $^1S_0$ onium, the operator scale lands in the Majorana-mass range of unified models: one Higgs insertion gives a singlet mediator, $M/|C_7|^{1/3} \approx 10^{14}$--$10^{16}$~GeV across the allowed relic fraction; two give the seesaw window; Dirac or Majorana neutrinos select the branch. We give the construction and its decisive tests.

Autonomous radio arrays reconstruct air showers from trigger-selected ADC traces rather than from ideal electric-field footprints. We present a detector-level simulation-closure test that connects RF-chain-triggered ZHAireS event packages to direction, energy and quality labels. Geometry is reconstructed from voltage amplitudes and station timing. The ADC traces are then inverted through the RF chain, restricted to 50--200 MHz and reduced to the geomagnetic peak amplitude $|E_{x_π}|$ in a radio-core-recentered shower plane. Energy is obtained by fitting a fixed equal-prior mean of locked iron and proton template families. The estimator uses neither the simulated primary label nor an empirical amplitude or zenith scale. Of 972 event packages, 711 pass a common reconstructed-quality gate in the raw-noisy weighted, raw-hard-denoised equal-weight and clean-reference branches. Their mean fractional energy residuals are $+1.20\%$, $+0.55\%$ and $-0.10\%$, with event-to-event scatters of $14.51\%$, $14.40\%$ and $14.25\%$, respectively. The median truth-level opening-angle residual is $0.050^\circ$ in this selected simulated sample. These aggregate values conceal a zenith-dependent energy residual, from about $-8\%$ at $60^\circ$--$70^\circ$ to $+11\%$ at $80^\circ$--$85^\circ$, with substantially larger biases in sparsely populated edge bins. The results establish an internally consistent reconstruction baseline for selected simulated event packages, not a deployed-array resolution or exposure.

We investigate the implications of the interactions between ultralight dark matter (ULDM) and the Standard model particles for the effective self-interaction coupling constants of ULDM. Our analysis shows that one-loop quantum corrections can result in a substantial increase in the effective coupling constant, which is tightly constrained by cosmological observations. Our findings highlight the importance of considering quantum corrections in the detection of ULDM.

We investigate a mixed dark matter scenario comprising weakly interacting massive particles (WIMPs) and primordial black holes (PBHs). After PBH formation, WIMPs can accrete onto them, forming ultracompact minihalos (UCMHs). The resulting WIMP number density within UCMHs is significantly enhanced compared to classical dark matter halo models, leading to a higher WIMP annihilation rate. Previous studies have focused mainly on the associated gamma-ray flux, we investigate the extragalactic neutrino flux from such annihilation. Considering the annihilation channels $μ^{+}μ^{-}$, $τ^{+}τ^{-}$, and $ν_μ\barν_μ$, we analyze two classes of neutrino events: upward and contained events. By requiring the neutrino flux from WIMP annihilation around PBHs does not exceed the atmospheric neutrino background, we derive upper limits on the fraction of dark matter in PBHs ($f_{\rm PBH}$) for a one-year exposure of the IceCube experiment. These limits depend on the annihilation channel, the masses of the WIMP and PBH, and the neutrino event type. The strongest constraints come from the $ν_μ\barν_μ$ channel, yielding $f_{\rm PBH} \sim 10^{-4}$ ($4\times 10^{-5}$) for contained (upward) events with $m_χ=10^{3}$ GeV and $M_{\rm PBH}=10^{3} M_{\odot}$. Based on these bounds on PBHs, we further derive upper limits on the primordial curvature power spectrum $\mathcal{P}_{\mathcal{R}}$. From our strongest constraint, we obtain $\mathcal{P}_{\mathcal{R}} \sim 10^{-1.65}$ at the scale $k\sim 3\times 10^{12}~\mathrm{Mpc^{-1}}$.

We revisit the inter-detector cross-correlation criterion used in gravitational-wave validation by extending the analysis of Creswell et al.~\cite{Creswell2017} to nine LIGO--Virgo candidate events from the O2 and O3 observing runs. For each event, we analyze all three detector pairs (H1$\times$L1, H1$\times$V1, L1$\times$V1) and compare the normalized cross-correlation function $C(τ)$ in the event window with an empirical ensemble of $N=200$ surrounding off-source windows, using a band-pass-only pipeline. In 26 of 27 pair-measurements, the event peak is statistically indistinguishable from the corresponding noise ensemble, including all pairs involving the independent Virgo detector. The only exception is GW190412 in the H1$\times$L1 pair. We conclude that the cross-correlation statistic does not provide a robust standalone separation between event and noise. We interpret the persistence of comparable correlation structure in the LIGO--Virgo pairs as evidence that the strain data may contain a continuous correlated physical component, for which a stochastic gravitational-wave background is a plausible candidate.

A photon coupled non-minimally to the Weyl tensor propagates differently in its two linear polarization states: the vacuum around a black hole becomes a birefringent medium. On a Schwarzschild background the coupling $α$ splits the photon sphere and the critical impact parameter of the two polarizations, producing a double shadow and a polarization-dependent photon ring; the two shadow edges separate by $62\%$ of the shadow radius at $α/M^2=0.75$. We compute a unified set of wave-optical and geometric-optical observables for both polarizations across a range of $α$: greybody factors, absorption cross sections, differential cross sections and their glories, a backward birefringence signal, shadows, photon rings, and null trajectories. The two-polarization scattering matrices are extracted with a Riccati--Hankel matching scheme that keeps the phase-sensitive observables reliable, and the geometric-optics chain is cross-validated with three independent ray tracers. The cleanest diagnostic is the backward signal: it is protected by parity and vanishes identically at $α=0$.

We derive the complete first post-Newtonian (1PN) Lagrangian and corresponding equations of motion for the relativistic $N$-body system in Scalar-Tensor-Fourth-Order Gravity (STFOG), including the Non-Commutative Spectral Geometry (NCSG) sector as a special case. In the regime $Φ\sim Ψ$ ($γ\sim 1$), the linearized fourth-order field equations are solved in the Standard Post-Newtonian gauge, and the variational Lagrangian is built directly from the point-particle action. The resulting dynamics is governed by three Yukawa functions $ζ$, $\mathcal{W}$ and $Ξ$, which encode the scalar, gravitomagnetic and three-body sectors and depend on the effective masses $(m_R,m_Y,m_φ)$ of the additional propagating modes. In this context, we show that the nonlinear metric component ${}^{(4)}\!g_{00}$ plays no role at 1PN level. The 1PN orbital motion of the above extended theories is thus obtained in closed form, and the Einstein--Infeld--Hoffmann equations are recovered in the corresponding general-relativistic limit. The formalism provides a common framework for the relativistic celestial mechanics of the Solar System, binary pulsars such as PSR J0737-3039, Galactic-center stellar orbits and triple systems.

A localized enhancement of the primordial curvature spectrum can leave two distinct relics: gravitationally produced conformal-fermion dark matter and a scalar-induced stochastic gravitational-wave background. We show that the dark-matter abundance fixes the scalar normalization through the cubic moment of the curvature spectrum, while the induced tensor signal probes its quadratic convolution. This closes the usual normalization freedom in scalar-induced gravitational-wave templates and ties the MHz signal directly to the dark-matter mass, peak scale, and spectral width. A concrete single-field realization demonstrates this mechanism: a Mukhanov--Sasaki evolution produces a broad MHz background that sits safely below the Gaussian primordial-black-hole threshold. In this construction, a null high-frequency search becomes a lower bound on the conformal-fermion mass, while a detection has to reproduce the relic abundance, peak frequency, amplitude, and width from one primordial feature. The result is a testable link between small-scale inflationary structure, superheavy dark matter, and laboratory MHz gravitational-wave searches

We develop a microscopic quantum membrane paradigm from the matrix quantum mechanics of black holes [1]. It was proposed that a quantum black hole is described by a fuzzy sphere together with a half-filled Fermi sea of horizon partons. We show that the topology of the fuzzy sphere induces a Berry monopole, providing a microscopic origin for the monopole appearing in the tunneling description of the decay of quantum black hole. Because the partons couple to the fuzzy sphere as fundamental degrees of freedom, they are sensitive to this monopole and form Lowest-Landau-Level (LLL) states rather than ordinary propagating two-dimensional fermions. Their guiding-center dynamics generates Ohmic, Hall, and polarization currents on the horizon. To couple these currents to an external electromagnetic field, we introduce a two-block matrix configuration comprising black-hole, environmental, and bifundamental link sectors. Off-diagonal link modes become tachyonic near the fuzzy sphere and condense, dynamically locking the horizon gauge field to the boundary value of the external Maxwell field. The parton current thereby becomes a physical boundary source for the exterior field. Our construction replaces the fictitious membrane of the classical paradigm with a dynamical quantum membrane populated by microscopic LLL degrees of freedom. The resulting boundary condition generalizes the classical ingoing membrane condition and yields explicit quantum, frequency-dependent, and helicity-dependent corrections, offering a possible probe of the microscopic quantum structure of the horizon.

GroundBIRD is a cosmic microwave background (CMB) experiment located at the Teide Observatory (altitude $\sim2400$ m, Spain) designed to measure large-angular-scale intensity and polarization anisotropies ($\ell \gtrsim 6$ to $\ell \sim 300$) to constrain the reionization optical depth, $τ$. The instrument employs a rapidly rotating telescope with a fixed elevation of $70$ deg and is equipped with 161 lenslet-coupled kinetic inductance detectors (KIDs): 138 at 145 GHz for CMB observations and 23 at 220 GHz for thermal dust characterization, all operated at $\sim280$ mK. This scan strategy provides daily coverage of $\sim$40% of the Northern Hemisphere sky. We present the first on-sky responsivity calibration model for GroundBIRD, derived from repeated observations of Jupiter using the twelve most stable KIDs from GroundBIRD array 6 (GB06). The analysis establishes and validates a calibration methodology for this detector subset while providing the first empirical characterization of detector responsivity as a function of precipitable water vapor (PWV). We find that the responsivity decreases by approximately 30% across the sampled PWV range and is well described by a linear PWV-dependent model. Comparison with Moon observations reveals distinct detector operating regimes associated with different optical loading conditions. The Jupiter-based calibration achieves better than 20% precision under typical observing conditions and better than 20% relative stability over a one-month timescale. These results establish the basis for extending the calibration methodology to the full GroundBIRD focal plane.

Asteroseismic observations of the interior rotation of main sequence stars have shown that angular momentum transport is much more efficient than expected. Which transport mechanisms are responsible for this is still unclear. Detections of radial differential rotation provide valuable constraints on these transport mechanisms. This has been detected in several massive main sequence $β$ Cep pulsators, even though fewer than ten $β$ Cep stars have been asteroseismically modelled in detail so far. We aim to expand the sample of asteroseismically forward modelled $β$ Cep pulsators to maximally exploit their potential to observationally constrain angular momentum transport mechanisms. To that end, we seek to constrain their rotation profiles. We searched for rotational splitting of non-radial modes in a large $β$ Cep sample with identified mode degrees. These were subjected to a novel forward modelling approach, which consistently accounts for second-order rotation effects using the state-of-the-art StORM oscillation code. We successfully modelled 36 $β$ Cep stars and constrained crucial parameters such as their initial mass, internal rotation frequency, convective core mass, and age. Like in intermediate-mass main sequence stars, the internal rotation rate globally decreases in $β$ Cep stars as they evolve along the main sequence. Radial differential rotation is constrained in 17 $β$ Cep stars. The rotation rate in at least 14 stars varies by more than 10%. Of these 14 stars, ten have their rotation rate decreasing from the core to the surface while it is the opposite in four of them. We affirm that radial differential rotation is common in $β$ Cep stars. Moreover, our constrained rotation profiles suggest that the typical $β$ Cep rotation profile may be non-monotonic.

The threshold of black hole formation in axisymmetric vacuum gravity is proving to be more complicated than had been anticipated but, following recent advances, a consensus between independent codes and methods is emerging. Building on earlier work we provide further details of a comparison between three independent numerical codes (the bamps, prague, and sphGR codes), paying special attention to the relative strengths and weaknesses of each and examining various features of near-threshold collapse of vacuum gravitational waves for the first time. In particular, we observe quasi-universal strong-field features appearing in curvature scalars. Focusing on geometric features on the symmetry axis, we construct reference coordinates to aid the comparison of strong-field data. We evolve, for the first time, time-asymmetric wave initial data within the bamps code. To the extent possible with current methods we compare apparent horizons and attempt to determine what causes difficulties in the classification of these strong-field and highly dynamical spacetimes. In all cases the results from the three codes agree very well.

We compute the stochastic background of gravitational waves (GWs) produced at second order in cosmological perturbation theory by a primordial curvature power spectrum that is flat in $\ln k$ over a finite band $[k_-,k_+]=[k_*e^{-Δ},k_*e^{+Δ}]$ and vanishes elsewhere. This logarithmic box interpolates between a monochromatic spectrum as $Δ\to0$ and a locally scale-invariant plateau as $Δ\to\infty$, and its sharp boundaries make the geometry of the source convolution unusually transparent. Working in the radiation era, we reduce the convolution to a compact integral over the overlap between the momentum triangle and the box, and evaluate it analytically in two regimes. For a narrow box we show that, to leading order in the width, the spectrum equals the Dirac-spectrum result multiplied by a purely geometric overlap factor $Φ_{\rm box}(κ,Δ)$; this factor turns the infrared slope from $k^{3}\ln^{2}k$ into $k^{2}\ln^{2}k$ at a break $k_b=2k_*\sinhΔ$. For a broad box we separate the lower edge, the scale-invariant interior, and the upper edge, derive the leading behaviour in each (an infrared $k^{3}\ln^{2}k$ rise, a scale-invariant plateau, and a quartic cut-off at the hard endpoint $k=2k_+$), and combine them into a single uniform formula cast as a product of two universal, $Δ$-independent edge functions. We also provide an integral-free closed-form surrogate for these edge functions for use in parameter scans.

We construct a new family of asymptotically flat static and rotating regular black holes characterized by a Minkowskian core and a finite two-horizon structure. The solutions are obtained within the framework of gravitational decoupling and provide an analytically tractable realization of non-singular black hole geometries with a regular interior and well-defined asymptotic properties. We investigate the optical appearance of the rotating spacetime through shadow observables and ray-traced images of geometrically thin, optically thin accretion disks. Despite the substantial differences between the interior geometry of these solutions and that of singular black holes, their optical signatures are found to remain remarkably close to those of Schwarzschild and Kerr spacetimes with the same asymptotic parameters. Our results show that markedly different black hole interiors may lead to nearly indistinguishable optical appearances, highlighting the challenges of probing the internal structure of compact objects using current shadow and imaging observations.

EY Cep is a detached eclipsing binary containing two F0 V stars in an orbit with a period of 7.97 d and an eccentricity of 0.440. We determine the physical properties of the system using light-curves from the Transiting Exoplanet Survey Satellite and published spectroscopic measurements. We find masses of 1.523 +/- 0.008 Msun and 1.494 +/- 0.014 Msun, radii of 1.491 +/- 0.004 Rsun and 1.446 +/- 0.004 Rsun, and temperatures of 7070 +/- 170 K and 6990 +/- 150 K. We calculate the system's distance to be 300.3 +/- 3.8 pc, in excellent agreement with the Gaia DR3 parallax, and estimate its age to be 220 Myr. We find no evidence for pulsations, but there are hints of variation in the eclipse times potentially attributable to a third body on a longer-period eccentric orbit.

In this paper, we consider possible corrections to the characteristics of inflationary models based on a specific parametrization of the non-minimal coupling between the scalar field and curvature. At the inflationary stage, these corrections lead to a deformation of the scalar field potential and a corresponding deviation in the determination of the cosmological perturbation parameters. At the same time, it is shown that the proposed parametrization yields a description of the reheating stage dynamics completely analogous to the case of Einstein gravity with minimal coupling between the scalar field and curvature. For a model-independent analysis of inflationary corrections induced by a non-minimal coupling, a classification of inflationary scenarios based on the expansion in series of the dependence of the tensor-to-scalar ratio on the spectral index of scalar perturbations is considered. It is also shown that this approach allows for the inclusion of well-known inflationary models as special cases.

Scalarizations of the Einstein-Euler-Heisenberg (EEH) black hole (EEHBH) with multiple horizons are investigated in the EEH-scalar theory by introducing a quadratic scalar coupling to the Maxwell term. For mass $M=1$ and Euler-Heisenberg parameter $μ=0.03$, the magnetically charged EEHBH admits four horizon families (low, cold, negative, and hot), with triple horizons appearing in the narrow band of magnetic charge $q\in[0.95,1.0065]$. The onset scalarization around the low, cold, and high horizons is then analyzed for the magnetic charge $q=0.5,\,1,\,2$, implying infinite branches of scalarized black holes for each case. We construct the three fundamental branches of scalarized black holes. From the positivity condition of their mass, we find the upper bounds on primary scalar charges $q_{s}$ for scalarized low and cold horizons. These bounds determine the allowable regions for the Hawking temperature and entropy. Furthermore, we perform a time-domain stability analysis and find that the instabilities arise only at small scalar charge regime. Therefore, stable and physically viable scalarized black holes exist in an intermediate window of the primary scalar charge for low and cold horizon solutions and a lower bound for hot horizon solution.

We propose a novel way to achieve the regularization of the JNW globally naked singularity sourced by the canonical Einstein minimally coupled scalar field (EMS). The key idea is to complexify (Wick rotate) the JNW parameters, which yields a regular metric that surprisingly represents a twice asymptotically flat regular traversable wormhole, famously known as the Ellis class III wormhole sourced by the ghost EMS. We begin by arguing that the JNW solution belongs to a hierarchy of actions describing different gravity theories, which indicates that a regularized version of JNW automatically adds corresponding regular versions to the hierarchy of gravity theories.

Recently, a new exact Ricci-flat rotating black-hole solution was constructed in four-dimensional general relativity, in which an additional parameter $B$ characterizes a spindle deformation of the Kerr geometry. We study geodesic motion and black-hole shadows in this spacetime. The Hamilton-Jacobi equation is not exactly separable for either timelike or null geodesics. Remarkably, however, at the leading nontrivial order, ${\cal O}(B^2)$, null but not timelike geodesics become separable. In the timelike sector, the spindle deformation shifts the innermost stable circular orbit and can give rise to an outermost stable circular orbit. In the null sector, exploiting the perturbatively separated equations, we analytically determine the photon region, equatorial photon orbits, and black-hole shadow, and compare the resulting predictions with direct ray tracing in the exact spacetime. The numerical results validate the perturbative treatment and quantify the deviations from Kerr.

Magnetic switchbacks, characterized by reversals of magnetic field direction, are widely observed in the inner heliosphere by Parker Solar Probe (PSP). With PSP reaching perihelia near 10Rs, observations from the first 24 encounters enable studies of near-Sun switchback evolution at r > 10Rs. We construct a switchback catalog within 10 < r < 55Rs by identifying magnetic field reversals with stable field magnitude and strahl-electron polarity. Statistical analysis shows that switchback Alfvenicity decreases with increasing radial distance, consistent with solar wind evolution beyond the Alfven critical point. Meanwhile, switchback occurrence rate and spatial size increase with distance, suggesting continued generation and expansion during solar wind propagation. At a given radial distance, the fraction of solar wind containing switchbacks is positively correlated with background solar wind radial velocity (VR) and Alfven Mach number (MA), while the local occurrence rate is mainly controlled by MA. These results suggest that switchback patches preferentially form in faster and higher-MA solar wind. The spatial size of switchbacks shows no clear dependence on MA or VR, implying that their size evolution is probably not determined by source conditions. Solar activity influences switchback evolution through changes in background solar wind properties, with a larger fraction of higher-MA switchbacks during solar minimum. We further identify anisotropy relative to the background magnetic field direction: the local occurrence rate and spatial size are approximately 1.5 times as large in the perpendicular direction as in the parallel direction, indicating distinct magnetic topology of switchback patches

(Abridged) We investigate the behaviour of the electron temperature derived from [Ar IV] lines, Te([Ar IV]), in a sample of PNe to characterize the thermal structure of high-excitation gas and compare it with the predictions of standard photoionisation models. Using the DEep Spectra of ionised REgions Data Base Extended (DESIRED-E), we selected a sample of 57 PNe for which Te([Ar IV]), Te([O III]), and ne([Ar IV]) could be determined simultaneously and homogeneously. We performed a detailed comparison between these observational diagnostics and a suite of over 160000 photoionisation models from the Mexican Million Models Database (3MdB). We find that the observed Te([Ar IV]) values are systematically higher than those predicted by pure photoionisation models for a given Te([O III]), i.e. approximately 31 percent of the PNe sample exhibits a Te([Ar IV]) more than 2sigma higher than photoionization model predictions. This discrepancy persists regardless of the specific set of auroral lines used for the diagnostic or the choice of atomic data (transition probabilities and collision strengths) adopted in the calculations. Other high-ionisation Te diagnostics, compiled from the DESIRED database or from the literature, however, do not show such behaviour, though the statistics for these are much more limited. The fact that models succeed for the highest-ionisation species but fail specifically for [Ar IV] suggests that the discrepancy is not due to a global inner-nebula heating mechanism. Instead, it points toward a localized physical effect or a limitation in the current understanding of the ionisation stratification and atomic physics specific to the Argon ion stages. This "[Ar IV] anomaly" must be resolved to ensure the reliability of abundance determinations in high-excitation nebulae.

We study linear perturbations of static, spherically symmetric solutions of scalar-tensor theories (STT) of gravity from the Bergmann-Wagoner-Nordtvedt class, sourced by nonlinear electrodynamics (NED). We obtain a general expression for the effective potential $V_{\rm eff}$ governing the perturbation dynamics for theories with arbitrary scalar-electromagnetic interaction of the form $L(ψ, F)$, where $ψ$ is a scalar field and $F = F_{μν} F^{μν}$ the electromagnetic invariant. This consideration includes, in particular, arbitrary scalar self-interaction potentials and scalar fields that can be phantom in some regions of space-time (the so-called trapped ghosts). Only radial (monopole) perturbations are considered here as the most likely ones to cause an instability. It is shown, in particular, that if NED has a correct Maxwell weak field limit, the zero charge limit of $V_{\rm eff}$ does not contain any trace of NED, and the perturbation dynamics is the same as for vacuum STT solutions. The previously obtained stability results for STT-Maxwell solutions are shown to be extended without change to STT-NED solutions with equal electric and magnetic charges, implying $F =0$.

Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology of Schwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction \(ηE^3/E_P\). Enforcing physical constraints (\(S'(r_h) > 0\), \(T > 0\)) via the entropy-geometry correspondence, we find a single unstable branch with \(w = -1\) and \(W = -1\) for both signs of the correction parameter. A second root suggesting stability (\(w = +1\)) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.