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DOE OSTI2024

The Penrose limit of the Weyl double copy

We embed the Penrose limit into the Weyl classical double copy. Thereby, we provide a lift of the double copy properties of plane wave spacetimes into black hole geometries and we open a novel avenue towards taking the classical double copy beyond statements about algebraically special backgrounds. In particular, the Penrose limit, viewed as the leading order Fermi coordinate expansion around a null geodesic, complements approaches leveraging asymptotic flatness such as the asymptotic Weyl double copy. Along the way, we show how our embedding of the Penrose limit within the Weyl double copy naturally fixes the functional ambiguity in the double copy for Petrov type N spacetimes. Here, we also highlight the utility of a spinorial approach to the Penrose limit. In particular, we use this spinorial approach to derive a simple analytical expression for arbitrary Penrose limits of four-dimensional, vacuum type D spacetimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Exploring life’s hidden majority: microbial dark matter symposium highlights

The Microbial Dark Matter Symposium held on August 28–29, 2025, in Laguna Beach, Orange County, CA, convened a multidisciplinary group of scientists to address the vast unknowns in microbial life—from uncultured taxa and uncharacterized proteins to elusive viruses and spacefaring microbes. Set against a scenic coastal backdrop, the symposium highlighted advances in single-cell genomics, proximity ligation sequencing, and artificial intelligence-ready bioinformatics, while also probing the limits of microbial persistence, metabolism, and ecological distribution. Sessions explored microbial dark matter from multiple dimensions: cultivability, where new strategies are enabling recovery of elusive microbes; functional ambiguity, where metagenomic dark zones are illuminated by computational annotation; and genomic representation, where single-cell methods bridge gaps left by shotgun community sequencing. Researchers shared breakthroughs in identifying atmospheric microbiomes, “dark oxygen” production in groundwater ecosystems, and microbial survival on the International Space Station. The symposium emphasized integration of methods, disciplines, and ecosystems, advancing a collective push to illuminate the microbial dark matter on Earth and beyond. By highlighting emerging tools, pressing questions, and cross-domain insights, the symposium underscored the need for collaborative, open, and adaptive approaches to study the microbial unknown. The meeting marks a pivotal moment in microbiology, where cultivating knowledge of the uncultivated promises transformative understanding of life, everywhere.

Podar, Mircea [ORNL] (ORCID:0000000327760205)↗

DOE OSTI2024

Transporter annotations are holding up progress in metabolic modeling

Mechanistic, constraint-based models of microbial isolates or communities are a staple in the metabolic analysis toolbox, but predictions about microbe-microbe and microbe-environment interactions are only as good as the accuracy of transporter annotations. A number of hurdles stand in the way of comprehensive functional assignments for membrane transporters. These include general or non-specific substrate assignments, ambiguity in the localization, directionality and reversibility of a transporter, and the many-to-many mapping of substrates, transporters and genes. In this perspective, we summarize progress in both experimental and computational approaches used to determine the function of transporters and consider paths forward that integrate both. Investment in accurate, high-throughput functional characterization is needed to train the next-generation of predictive tools toward genome-scale metabolic network reconstructions that better predict phenotypes and interactions. More reliable predictions in this domain will benefit fields ranging from personalized medicine to metabolic engineering to microbial ecology.

Casey, John↗

DOE OSTI2024

Exclusive J / ψ , ψ ( 2 s ) , and e + e - pair production in Au + Au ultraperipheral collisions at the BNL Relativistic Heavy Ion Collider

Measurements of exclusive J/ψ, ψ(2⁢s), and electron-positron (e + ⁢e - ) pair photoproduction in Au+Au ultraperipheral collisions are reported by the STAR experiment at $\sqrt{s_{NN}}$ = 200GeV. Here, we report several first measurements at the BNL Relativistic Heavy Ion Collider, which are (i) J/ψ photoproduction with large momentum transfer up to 2.2⁢(GeV/c) 2 , (ii) coherent J/ψ photoproduction associated with neutron emissions from nuclear breakup, (iii) the rapidity dependence of incoherent J/ψ photoproduction, (iv) the ψ⁡(2⁢s) photoproduction cross section at midrapidity, and (v) e + ⁢e - pair photoproduction up to high invariant mass of 6GeV/c 2 . For measurement (ii), the coherent J/ψ total cross section of γ + Au → J/ψ + Au as a function of the center-of-mass energy W γN has been obtained without photon energy ambiguities. The data are quantitatively compared with the Monte Carlo models STARlight, Sartre, BeAGLE, and theoretical calculations of gluon saturation with color glass condensate, nuclear shadowing with leading twist approximation, quantum electrodynamics, and the next-to-leading-order perturbative QCD. At the photon-nucleon center-of-mass energy of 25.0 GeV, the coherent and incoherent J/ψ cross sections of Au nuclei are found to be 71% ± 10% and 36% ± 7%, respectively, of that of free protons. These data provide an important experimental constraint for nuclear parton distribution functions and a unique opportunity to advance the understanding of the nuclear modification effect at the top RHIC energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Integrative Modeling and Analysis of Fungal Central Carbon Metabolism

Over a thousand fungal genomes have been sequenced, yet manually curated genome-scale metabolic models (GEMs) are available for only a limited number of species. Moreover, these models have often been developed independently, leading to inconsistencies in namespaces, compartment definitions, and pathway representations that hinder comparative analysis, the systematic reuse of prior curation efforts, and the integration of consolidated metabolic knowledge. Here, we present the Consolidated Fungal Core Metabolism Model (CFCMM), constructed by integrating thirteen published fungal models spanning Ascomycota, Mucoromycota, and both Crabtree-positive and Crabtree-negative yeasts. We harmonized metabolites and reactions into a non-redundant shared ModelSEED ontological space, standardized compartmentalization, and refined gene–protein–reaction (GPR) rules. Using pathway-level visualization and systematic gap detection, we further improved the integrated network through literature-guided curation to correct stoichiometry, stereospecificity, and pathway architecture. Orthologous protein family reconstruction and functional annotation workflows were used to validate and inform GPR associations, with particular emphasis on ambiguous enzyme superfamilies and membrane-associated components. Using the resulting CFCMM, we built high-quality central carbon core models for each fungus and performed flux balance analysis to quantify ATP-yield variation under aerobic and anaerobic conditions, explicitly evaluating scenarios driven by differences in electron transport chain (ETC) composition. Simulations reproduced the expected fermentative yield of approximately 2 mmol ATP per mmol glucose under anaerobic conditions and separated the thirteen fungi into two bioenergetic groups under aerobic respiration based on Complex I status, with predicted yields of approximately 30 versus 22 mmol ATP per mmol glucose. Forcing flux through the alternative oxidase bypass further reduced ATP yields to approximately 12 and 4 mmol ATP per mmol glucose in Complex I-containing and Complex I-lacking fungi, respectively. Collectively, this work provides a manually curated, ModelSEED-consistent, and extensible fungal core metabolic template, deployed in DOE KBase as a resource for automated reconstruction of central carbon core models from any sequenced fungal genome. In addition, the CFCMM provides modular components for developing GEMs with more accurate energy predictions and enables robust comparative analyses of fungal bioenergetics and core metabolic diversity

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Polymer connectivity governs electrophotocatalytic activity in the solid state

The reductive functionalization of inert substrates such as chloroarenes is a critical yet challenging transformation relevant to both environmental remediation and organic synthesis. Combining electricity and light is an emerging strategy to access the deeply reducing potentials required for single electron transfer to chloroarenes, yet this approach is limited by poor stability and mechanistic ambiguity. Here, in this work, we demonstrate heterogeneous electrophotocatalysis using redox-active rylene diimide polymers for the reduction of chloroarenes. We find that the electrophotocatalytic activity varies dramatically as a function of the rylene diimide and the redox-inactive polymer backbone. In particular, a flexible, non-conjugated perylenediimide polymer outperforms all other tested electrophotocatalysts. Transient absorption spectroscopy reveals that precomplexation between the doubly reduced perylenediimide and the haloarene substrate is key to productive catalysis. Overall, this work highlights heterogeneous electrophotocatalysis using insoluble redox-active organic materials and provides critical structure–property insights into solid-state electrophotocatalytic activity, informing the development of next-generation materials for sustainable synthesis.

electrocatalysis↗

DOE OSTI2026

Mechanism of Tyrosine-Driven Deprotonation in Photosystem II Revealed by Multiscale Simulations

Photosystem II (PSII) drives light-induced water oxidation via stepwise redox transitions of its oxygen-evolving complex (OEC), a Mn 4 Ca cluster advancing through five intermediate S-states (S 0 –S 4 ). The S 2 → S 3 transition involves a redox event in which a Mn ion donates an electron to the redox-active tyrosine YZ, coupled to deprotonation of an OEC-bound water ligand─yet the underlying coupling mechanism remains unresolved. Time-resolved serial femtosecond crystallography (TR-SFX) has revealed transient electron density shifts near the redox-active tyrosine Y Z , interpreted as sequential oxidation and reduction, with reduction initiating ∼1 μs after excitation and substantially progressed by 30 μs. However, this interpretation conflicts with kinetics from photothermal beam deflection (PBD), time-resolved X-ray absorption spectroscopy (TR-XAS), and electron paramagnetic resonance (EPR), which place electron transfer at 190–400 μs and proton transfer around 30 μs. Here, we reconcile these discrepancies using quantum mechanics/molecular mechanics (QM/MM) and molecular dynamics (MD) simulations. We show that oxidation of P680 and Y Z breaks the symmetry of the nearby hydrogen bonds involving water molecule W4, displacing Y Z and replicating the TR-SFX features of Y Z and Q165 observed at 1 μs. This local perturbation propagates through a hydrogen-bond network, transmitting the electrostatic signal from Y Z to the E65-E312 dyad and triggering redox-coupled deprotonation via the Cl1 channel. By 30 μs, the hydrogen-bond symmetry is restored through deprotonation of W2 (or alternatively W1), reproducing the disappearance of TR-SFX density differences around Y Z and Q165 without requiring Y Z reduction. Our proposed mechanism also gives molecular insights into the O6* density, assigning it to water reorganization rather than a discrete Ca-bound hydroxide species. Here, our results reveal a detailed atomistic mechanism linking Y Z oxidation to long-range proton release and suggest a functional role for the nearby Cl – ion in proton transfer. More broadly, this study underscores the importance of hydrogen-bond dynamics in mediating redox-driven proton transport and demonstrates how integrative simulations can resolve mechanistic ambiguities.

Deprotonation↗

DOE OSTI2025

Influence of strain-rate on the response of elastomeric architected materials

Architected materials have shown substantial promise in impact mitigation and protective applications, and there has accordingly been great interest in better characterizing their response at elevated strain rates due to impact. There remains ambiguity regarding the contribution of inertial and material responses to strain rate sensitivity, and, in particular, when these effects begin to gain dominance in the impact response of an architected material. The response of soft polymer architected materials as a function of strain rate, in particular, has been little investigated. We characterize the experimental impact response of four soft polymer architected lattice geometries across varying strain rates in the intermediate strain rate regime (∼10 3 s −1 ) using split-Hopkinson pressure bar loading and high speed video characterization of the resulting deformation fields. In conclusion, our results highlight the interplay of influence between constituent material, lattice geometry, length scale, and strain rate in determining the onset of significant inertia effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Clarifying Terminology in Microbial Ecology: A Call for Precision in Scientific Communication

The rapid evolution of microbiology as a field of research has led to the introduction of new terminology and the adaptation of existing terms. However, inconsistencies in the use of these terms, including variations across different scientific disciplines, can lead to confusion and miscommunication within the scientific community. This article discusses the importance of precise terminology in microbiome research, highlighting examples where terms have been misused or redefined without clear justification. We also present a list of frequently used terms in microbial ecology along with their specific definitions. We argue that the misuse of terminology can hinder scientific progress by creating ambiguity and misunderstanding. To address this, we propose a set of guidelines for the consistent use of key terms and provide clear definitions for some of the most commonly misused or newly introduced terms in the field. The definitions provided herein will also function as a guide for young researchers new to the field of microbial ecology. Accurate and consistent use of terminology is crucial for effective communication and collaboration in microbiology research. By adhering to standardised definitions, researchers can ensure that their work is clearly communicated and contributes meaningfully to the progress of science.

definitions↗

DOE OSTI2024

Formally Verified ZTA Requirements for OT/ICS Environments with Isabelle/HOL

The clean energy transformation includes the integration of distributed energy resources with the power grid, which has led to a substantial increase in the complexity of power grids infrastructure and the underlying operational technology environment. Power grids infrastructure represents an operational technology environment that has become a system of systems, integrating heterogeneous devices which are both software-and hardware-intensive; as a result, there are increasing demands to exploit advances in the commodity of software-hardware infrastructures to improve energy systems requirements such as cybersecurity and resilience. In such a setting, system requirements at different levels mix, which leads to vulnerabilities and undesirable outcomes. The use of formal methods to characterize and prove system requirements removes ambiguity, increases automation, and provides high levels of assurance and reliability. In this paper, we contribute a methodology and a framework for the system-level verification of zero trust architecture requirements in operational technology environments. We define a formal specification for the core functionalities of operational technology environments, the corresponding invariants, and security proofs. Of particular note is our modular approach for the formal verification of asynchronous interactions in operational technology environments. The formal specification and the proofs have been mechanized using the interactive theorem proving environment Isabelle/HOL.

formal methods↗

DOE OSTI2025

Resolving Lonsdaleite's decade-long controversy: Atomistic insights into a metastable diamond polymorph

Lonsdaleite, a theoretically proposed hexagonal diamond polymorph, has remained at the center of a five-decade scientific controversy since its 1967 identification. While some studies claim it exhibits superior hardness through compression-induced structural changes, others contend it is merely a stacking-faulted cubic diamond. Meteoritic samples and synthetic preparations have yielded conflicting evidence, with even advanced characterisation techniques like XRD and TEM failing to provide definitive proof. In this work, we employ first-principles density functional theory (DFT) and molecular dynamics (MD) simulations to generate unambiguous theoretical fingerprints through XRD, Raman, and SAED patterns that distinguish true Lonsdaleite from cubic diamond and its defective variants. Our atomistic approach quantifies the thermodynamic metastability of Lonsdaleite under realistic pressure-temperature conditions, reveals distinct spectral signatures through simulated Raman and resolves the structural ambiguity through generalised stacking fault energy analysis. By establishing clear criteria for definitive identification, this study provides long-awaited clarity to the Lonsdaleite debate while offering a robust computational framework for characterising metastable carbon phases in meteoritic, synthetic and industrial materials.

DFT↗

DOE OSTI2025

Tailoring MoS 2 for Small-Molecule Electroreduction: The Role of Metal Doping and Heterostructures

The electrification of chemical transformations central to sustainable fuel production and waste valorization, such as overall water splitting (OWS), hydrogen evolution reaction (HER), and electrochemical reduction of CO 2 (CO 2 R), presents a powerful opportunity to advance carbon-neutral energy technologies. Transition metal dichalcogenides (TMDs), particularly MoS 2 , have emerged as promising electrocatalyst candidates, owing to their abundance, tunable active sites, and defect-rich structures. This review highlights recent progress in leveraging metal doping and heterostructure engineering of MoS 2 to enhance the electrocatalytic activity and selectivity. By compiling insights from experimental studies and density functional theory (DFT) predictions, we examine how defect creation, electronic structure modification, and interface design contribute to improved charge transport and catalytic efficiency. Particular emphasis is placed on rational design principles, synthetic strategies, and operando characterization methods that provide a pathway to understanding and optimizing MoS 2 -based materials. We also discuss the challenges of stability, mechanistic ambiguity, and scaling while outlining opportunities to bridge theory and experiment. Collectively, this review underscores how defect and heterostructure engineering of MoS 2 can accelerate the development of efficient, sustainable electrocatalysts for both fuel generation and waste-to-value generation.

CO2 reduction↗

DOE OSTI2024

Bioleaching ion-unexchangeable rare earth in ion-adsorption type rare earth waste tailing

Ion-adsorption type rare earth ores (IREO) in China serve as the primary source of medium and heavy rare earth globally. With the rapidly growing demand for rare earth elements (REEs) and the dwindling supply of premium IREO, enhancing the recovery of REEs, especially the ion-unexchangeable REEs with ultra-low content and ambiguous speciation from IREO or its tailing, has become a critical trend and challenge. Here, this study identified the occurrences of ion-unexchangeable REEs, primarily detected in Fe-enriched minerals, xenotime, and monazite of IREO using TESCAN integrated mineral analyzer (TIMA) and laser ablation inductively coupled plasma mass spectrometer (LA-ICP-MS) analysis. To extract these elusive REEs, a bioleaching technique utilizing Aspergillus niger (A. niger) metabolites was proposed, achieving a leaching yield of 31.4 wt%. Complementary sequential chemical extraction methods (SCEM), X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations further elucidate the underlying mechanism, involving the carboxylic acid produced by the metabolic process of microbes that dissolves goethite by disrupting Fe—O bonds and liberating REEs, which complexed with carboxylate (R—COO—), to promote further dissolution. This work offers insight into enhancing the recovery of ion-unexchangeable REEs from IREO or its tailing, paving the way for sustainable and efficient rare earth mining practices.

42 ENGINEERING↗

DOE OSTI2026

Isolated and H 2 -reduced Anderson clusters catalyse low-temperature hydrogenation of CO 2 to methanol

CO 2 hydrogenation, especially to methanol, is crucial to establishing sustainable closed-loop systems for carbon utilization. However, the difficulties of CO 2 activation at low temperatures and the ambiguity of structure–activity correlations are obstacles to reducing the energy consumption of the hydrogenation process. Here we report that molecularly defined Anderson PtMo 6 O 24 clusters, sited within a robust metal–organic framework, are catalytic for low-temperature CO 2 hydrogenation. The performance of the cluster showed no signs of decay in either its activity or methanol selectivity over 3,600 h at 180 °C. It also achieves a per-pass yield exceeding that of state-of-the-art heterogeneous catalysts under similar conditions. Combined in situ spectroscopy and density functional theory calculations demonstrated that CH 3 OH formation is dominated by the reverse water–gas shift and subsequent CO* hydrogenation pathway, while the HCOO* pathway may serve as a supplementary route. The well-defined cluster structure offers an ideal model for elucidating structure–activity correlations and opens exciting avenues for the rational design of high-activity, low-temperature catalysts for CO 2 hydrogenation.

heterogeneous catalysis↗

DOE OSTI2026

High-throughput computation of electric polarization in solids via Berry flux diagonalization

Electric polarization in the absence of an externally applied electric field is a key property of polar materials, but the standard interpolation-based ab initio approach to compute polarization differences within the modern theory of polarization presents challenges for automated high-throughput calculations. Berry flux diagonalization [J. Bonini et al., Phys. Rev. B 102, 045141 (2020)] has been proposed as an efficient and reliable alternative, though it has yet to be widely deployed. Here, we assess Berry flux diagonalization using ab initio calculations of a large set of materials, introducing and validating heuristics that ensure branch alignment with a minimal number of intermediate interpolated structures. Our automated implementation of Berry flux diagonalization succeeds in cases where prior interpolation-based workflows fail due to band-gap closures or branch ambiguities. Benchmarking with ab initio calculations of 176 candidate ferroelectrics, we demonstrate the efficacy of the approach on a broad range of insulating materials and obtain accurate effective polarization values with fewer interpolated structures than prior automated interpolation-based workflows. Our real-space heuristics that can predict gauge stability a priori from ionic displacements enable a general automated framework for reliable polarization calculations and efficient high-throughput screening of chemically and structurally diverse polar insulators. These results establish Berry flux diagonalization as a robust and efficient method to compute the effective polarization of solids and to accelerate the data-driven discovery of functional polar materials.

Poteshman, Abigail N. [University of Chicago, IL (↗

DOE OSTI2024

Machine Learning Framework for Conotoxin Class and Molecular Target Prediction

Conotoxins are small and highly potent neurotoxic peptides derived from the venom of marine cone snails which have captured the interest of the scientific community due to their pharmacological potential. These toxins display significant sequence and structure diversity, which results in a wide range of specificities for several different ion channels and receptors. Despite the recognized importance of these compounds, our ability to determine their binding targets and toxicities remains a significant challenge. Predicting the target receptors of conotoxins, based solely on their amino acid sequence, remains a challenge due to the intricate relationships between structure, function, target specificity, and the significant conformational heterogeneity observed in conotoxins with the same primary sequence. We have previously demonstrated that the inclusion of post-translational modifications, collisional cross sections values, and other structural features, when added to the standard primary sequence features, improves the prediction accuracy of conotoxins against non-toxic and other toxic peptides across varied datasets and several different commonly used machine learning classifiers. Here, we present the effects of these features on conotoxin class and molecular target predictions, in particular, predicting conotoxins that bind to nicotinic acetylcholine receptors (nAChRs). We also demonstrate the use of the Synthetic Minority Oversampling Technique (SMOTE)-Tomek in balancing the datasets while simultaneously making the different classes more distinct by reducing the number of ambiguous samples which nearly overlap between the classes. In predicting the alpha, mu, and omega conotoxin classes, the SMOTE-Tomek PCA PLR model, using the combination of the SS and P feature sets establishes the best performance with an overall accuracy (OA) of 95.95%, with an average accuracy (AA) of 93.04%, and an f1 score of 0.959. Using this model, we obtained sensitivities of 98.98%, 89.66%, and 90.48% when predicting alpha, mu, and omega conotoxin classes, respectively. Similarly, in predicting conotoxins that bind to nAChRs, the SMOTE-Tomek PCA SVM model, which used the collisional cross sections (CCSs) and the P feature sets, demonstrated the highest performance with 91.3% OA, 91.32% AA, and an f1 score of 0.9131. The sensitivity when predicting conotoxins that bind to nAChRs is 91.46% with a 91.18% sensitivity when predicting conotoxins that do not bind to nAChRs.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Ladder symmetries and Love numbers of Reissner-Nordström black holes

It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner-Nordström black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗