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DOE OSTI2023

Influence of MXene termination groups on hydrogen interactions

MXenes are a relatively new class of nanomaterial consisting of alternating layers of transition metals and carbon or nitrogen, capped off on either end by terminal groups, usually from the P-block. They have been considered for a wide range of purposes, including hydrogen storage. In this study, thermogravimetric analysis and mass spectrometry residual gas analysis are performed on Ti 3 C 2 T x and Ti 2 CT x to characterize their terminal groups. The hydrogen absorption capabilities of the heat-treated samples are measured using a Sievert apparatus and compared against untreated samples. This reveals that, during heating, the MXenes lose hydrogen, water, fluoride, hydrofluoric acid, and carbon dioxide. Isothermal absorption measurements suggest that the removal of termination groups might improve hydrogen uptake kinetics at high temperatures, but has little effect at room temperatures.

08 HYDROGEN↗
DOE OSTI2024

Safety Codes and Standards Review and Gap Analysis for Applicability to Hydrogen Rail Refueling, Defueling, Maintenance, and Storage

Hydrogen-powered locomotives may present an alternative to diesel for achieving transportation-related decarbonization, energy security, and resilience goals. As an emerging technology, hydrogen locomotives may not have adequate representation in current safety codes and standards. NFPA 2 and other appropriate codes and standards were reviewed to identify technical gaps in the code for hydrogen rail defueling, refueling, maintenance, and storage. Several technical gaps pertaining to setback distances, allowable quantities, ventilation rates, and grounding have been identified. Fueling requirements can be informed by road vehicle standards but may need to be revised for larger quantity hydrogen locomotive systems. Since there are no hydrogen-specific locomotive design and safety standards, some aspects of diesel-based locomotive standards may apply. CGA G- 5.5 currently provides the most guidance on height, placement, orientation, and design of vent systems, while other standards emphasize the importance of shielding vent stacks and provide requirements for orientation of their discharge.

08 HYDROGEN↗
DOE OSTI2022

Bioenergy: A Pathway to Decarbonization

An overview of BETO’s efforts to help engineer carbon reduction and decarbonize the atmosphere with improved carbon conversion technologies, along with bio-based alternatives to fossil fuels and petrochemical-related products.

biofuels, bioproducts, greenhouse gas, carbon foot↗
DOE OSTI2023

Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations

Background: Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here, we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022. Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported by a standardised source for 32 countries over the next 1–4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models’ predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models’ forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models’ past predictive performance. Results: Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models’ forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models’ forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models’ forecasts of deaths (N=763 predictions from 20 models). Across a 1–4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models. Conclusions: Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than 2 weeks. Funding: AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS-1633028, NSF Grant No.: OAC-1916805, NSF Expeditions in Computing Grant CCF-1918656, CCF-1917819, NSF RAPID CNS-2028004, NSF RAPID OAC-2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA1-19-D-0007, and respectively Virginia Dept of Health Grant VDH-21-501-0141, VDH-21-501-0143, VDH-21-501-0147, VDH-21-501-0145, VDH-21-501-0146, VDH-21-501-0142, VDH-21-501-0148. AF, AMa, GL funded by SMIGE - Modelli statistici inferenziali per governare l'epidemia, FISR 2020-Covid-19 I Fase, FISR2020IP-00156, Codice Progetto: PRJ-0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission - Directorate-General for Communications Networks, Content and Technology through the contract LC-01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018-095456-B-I00. DE., MGu funded by Spanish Ministry of Health / REACT-UE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021-021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID-19 ( https://www.nfdi4health.de/task-force-covid-19-2 ) within the framework of a DFG-project (LO-342/17-1). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for real-time monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17-043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16-013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Cold gas mass measurements for the era of large optical spectroscopic surveys

ABSTRACT Gas plays an important role in many processes in galaxy formation and evolution, but quantifying the importance of gas has been hindered by the challenge to measure gas masses for large samples of galaxies. Data sets of direct atomic and molecular gas measurements are sufficient to establish simple scaling relations, but often not large enough to quantify three-parameter relations, or second-order dependences. As an alternative approach, we derive here indirect cold gas measurements from optical emission lines using photoionization models for galaxies in the Sloan Digital Sky Survey (SDSS) main galaxy sample and the PHANGS-MUSE survey. We calibrate the gas surface density measurements using xCOLD GASS and PHANGS-ALMA molecular gas measurements to ensure that our measurements are reliable. We demonstrate the importance of taking into account the scale dependence of the relation between optical depth (τ V ) and gas surface density (Σ gas ) and provide a general prescription to estimate Σ gas from τ V , metallicity, and the dust-to-metal ratio, at any arbitrary physical resolution. To demonstrate that the indirect cold gas masses are accurate enough to quantify the role of gas in galaxy evolution, we study the mass–metallicity relation of SDSS galaxies and show that as a third parameter gas mass is better than star formation rate at reducing the scatter of the relation, as predicted by models and simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Comparative Effects of Radiation Sterilization Modality on Medical PVC Tubing

As the production volume of single-use, polymer-based medical devices increases each year, so does the need for throughput capacity to sterilize the devices. Around 80% of radiation-sterilized devices are processed using gamma-ray radiation from industrial cobalt-60 sources. Supply chain, security, and disposal concerns are prompting manufacturers and contract sterilizers to explore alternatives to irradiation using cobalt-60 gamma-rays, such as electron beam (E-beam) and X-ray radiation. Advantages of these ‘machine’ sources over radioisotope-based sources are that they do not decay, a characteristic that requires cobalt-60 to be replaced over time, they can be turned off when not in use, and they do not represent the same level of concern regarding misuse. One of the barriers to direct transition from gamma-ray sterilization to E-beam or X-ray sterilization is concern over the relatively unknown effects of sterilization dose of these alternative modalities on the performance of medical device polymers. Commercially available medical devices sterilized with gamma-ray irradiation exhibit acceptable device function, acceptable mechanical performance, and acceptable discoloration. To be viable, alternate sterilization methods must not only achieve acceptable sterilization, but the process must also result in a product with functional, mechanical, and visual effects acceptable to customers and the regulator. Flexible polyvinyl chloride (PVC) is a plastic material that is commonly found in single-use medical devices and is known for its sensitivity to radiation processing. For instance, transparent PVC is known to yellow upon irradiation. To encouraging sterilization alternatives to cobalt-60 gamma-ray, we directly compared the effects of gamma-ray, E-beam, and X-ray radiation exposure at similar sterilization-relevant doses on key properties of medical grade PVC tubing.

cobalt-60↗
DOE OSTI2026

Regional specialization in prefrontal cortex manifests in the reliability of task progression codes

The brain has the remarkable ability to guide the performance of complex tasks. Distinct prefrontal cortical areas make specific contributions to this ability, with the orbitofrontal cortex (OFC) critical for processing information related to trial outcomes and the dorsomedial prefrontal cortex (dmPFC) critical for sustained effort and selecting the right action at the right time. Yet, in both areas, neural activity represents both outcome- and action-related quantities. How similar neural representations support different functions remains unclear. Here, we compared OFC and dmPFC activity in rats performing a spatial alternation task. We show that, in contrast to other task-related variables, task progression is represented in both areas, but with distinct patterns of across-trial reliability that match each area’s previously documented functional specialization. Our results indicate that the engagement of reliable, task-phase-specific activity patterns differs across prefrontal regions in a manner well suited to engage different computations at different times.

Biological and medical sciences↗
DOE OSTI2026

Alternative Fuels for Public and Private Vehicle Fleets in Rural Areas

This fact sheet identifies opportunities for integration of alternative fuel vehicles in public and private fleets in rural areas, and was developed through the U.S. Department of Energy's Communities Local Energy Action Program (Communities LEAP). The project engaged community stakeholders, fleet operators, and local officials across ten rural counties in western Alabama to explore opportunities for expanding access to alternative transportation fuels. Guided by a regional coalition and supported by the National Laboratory of the Rockies (NLR), the effort emphasized challenges and related potential technical solutions. The fact sheet highlights different applications of alternative fuel vehicles and provides a framework for selecting the vehicle technology that meets a given stakeholder's needs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Biochemical and structural characterization of enzymes in the 4-hydroxybenzoate catabolic pathway of lignin-degrading white-rot fungi

White-rot fungi (WRF) are the most efficient lignin-degrading organisms in nature. However, their capacity to use lignin-related aromatic compounds, such as 4-hydroxybenzoate, as carbon sources has only been described recently. Previously, the hydroxyquinol pathway was proposed for the bioconversion of these compounds in fungi, but gene- and structure-function relationships of the full enzymatic pathway remain uncharacterized in any single fungal species. Here, we characterize seven enzymes from two WRF, Trametes versicolor and Gelatoporia subvermispora, which constitute a four-enzyme cascade from 4-hydroxybenzoate to β-ketoadipate via the hydroxyquinol pathway. Furthermore, we solve the crystal structure of four of these enzymes and identify mechanistic differences with the closest bacterial and fungal structural homologs. Overall, this research expands our understanding of aromatic catabolism by WRF and establishes an alternative strategy for the conversion of lignin-related compounds to the valuable molecule β-ketoadipate, contributing to the development of biological processes for lignin valorization.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗
DOE OSTI2023

Fast approximation to supershell partition functions: Explicit forms of the coefficients

In a previous work, we derived a formula for supershell partition functions, which are the cornerstone of the Super-Transition-Array approach to radiative-opacity calculations. The new expression takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients (denoted Γ $k$ ) for which we obtained a recursion relation. In the present short paper, as a complement of the previous one, we give an explicit formula for the coefficients Γ $k$ . Another recursion relation is also provided, as well as an alternative expression involving Bell polynomials. In conclusion, the connections with cycle indexes of permutation groups and with elementary symmetric polynomials are outlined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Synergistic Effect of Diatomic Mo-B Site Confined in Graphene-Like C 2 N Enables Electrocatalytic Nitrogen Reduction via Novel Mechanism

Structural modulation of active site with atomic-level precision is of great importance to meet the activity and selectivity challenges that electrocatalysts are commonly facing. In this work, we have designed a metal (M) - nonmetal (NM) diatomic site embedded in graphene-like C 2 N (denoted as Mo-B@C 2 N), where electrocatalytic N 2 reduction reaction (eNRR) was thoroughly explored using density functional theory combined with computational hydrogen electrode method. Compared to M-M diatomic sites, Mo-B site can generate pronounced synergistic effect that led to eNRR proceeding via a novel quasi-dissociative reaction mechanism that has not been reported relative to the conventional enzymatic, consecutive, distal, and alternating associative mechanism. This newly uncovered mechanism in which N-N bond scission takes place immediately after the first proton-coupled electron transfer (PCET) step (i.e., *NH-*N + H + + e – ® *NH 2 *N) has demonstrated much advantage in PCET process over the four conventional mechanism in terms of thermodynamic barrier, except that the adsorption of side-on *N 2 seemed thermodynamically unfavorable (DG ads = 0.61eV). Our results have revealed that the activation of inert NºN triple bond is dominated by π*-backdonation mechanism as a consequence of charge transfers from both B and Mo site, and unexpectedly, from the substrate C 2 N itself as well. Moreover, the hybrid Mo-B diatomic site demonstrated superior performance over either Mo-Mo or B-B site for driving eNRR. Furthermore, our study could provide insight into the delicate relationships among atomic site, substrate and electrocatalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Stacked reverberation mapping of high-redshift quasars in DESI. I. Feasibility analysis

The broad-line region of quasars has long been probed by reverberation mapping techniques that measure time lags between continuum and broad emission-line variations. Stacked reverberation mapping has been proposed as a less observationally expensive alternative to traditional methods. This ensemble approach also reduces biases from small-number statistics. The Dark Energy Spectroscopic Instrument (DESI) is conducting the most extensive spectroscopic survey of quasars to date. We create mock light curves emulating expected DESI quasar observations at redshifts $1.48\lt z\lt 5.2$ and luminosities $44.68 \le \log \lambda L_{1350 \mathring{\rm A}{}} / \mathrm{erg\, s^{-1}} \le 45.99$ to test stacked reverberation mapping feasibility using sparse spectroscopic data paired with well-sampled photometric data. The pipeline, using the lag estimation code JAVELIN (Just Another Vehicle for Estimating Lags In Nuclei), successfully recovers the simulated C IV lags within 1σ of the true values using spectroscopic light curves composed of only a few spectral epochs (2–10) with irregular cadences. We investigate how observational factors, including C IV flux error magnitude, number of stacked quasars, and spectral epoch count, affect performance. This work motivates a pathway for future stacked reverberation mapping projects with large-scale spectroscopic surveys of quasars having $\ge 2$ spectroscopic observations. Our results suggest an economical alternative for constraining and extending the radius–luminosity relation to higher redshifts and luminosities. Subsequently, this relation can be employed more reliably in single-epoch black hole mass measurements and quasar cosmology in these distant regimes.

quasars: general, quasars: supermassive black hole↗
DOE OSTI2025

Alternating and Gaussian Fermionic Isometric Tensor Network States

Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric tensor network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward; hence the name alternating isometric tensor network states. Second, we introduce a numerical tool—the isometric Gaussian fermionic TNS (isoGfTNS)—that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNSs represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNSs. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNSs mediate entanglement more efficiently than conventional isoTNSs. Second, alternating isoTNSs correspond to a deeper, and thus more representative, sequential-circuit construction of depth 𝒪⁢(𝐿𝑥 ⋅𝐿𝑦) compared to the original isoTNSs of depth 𝒪⁢(𝐿𝑥 +𝐿𝑦). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidence of better bond-dimension scaling and variational energy of alternating isoGfTNSs for ground states of various free-fermionic models, including the Fermi surface, the band insulator, and the 𝑝𝑥 +𝑖⁢𝑝𝑦 mean-field superconductor. Finally, benchmarking on the transverse-field Ising model, we demonstrate that an alternating isoTNS provides substantially improved performance and stability relative to the original isoTNS for the ground-state search algorithm in interacting systems.

Wu, Yantao [Chinese Academy of Sciences, Beijing (↗
DOE OSTI2024

Burton-Cabrera-Frank theory for the influence of off-cut direction on the growth of hcp crystals

The precise direction of the off-cut of a vicinal crystal surface determines the azimuth (in-plane angle) of the surface steps and thus their kink density. Here we develop a Burton-Cabrera-Frank (BCF) theory for step-flow crystal growth that includes the effects of step azimuth. We focus on the basal-plane surfaces of hexagonal close-packed (hcp) and related crystal structures, for which surface steps have alternating properties that depend on azimuth. We build on a previous treatment that considered only a single-step azimuth, 𝜙 = 0, that gives alternating steps of pure A and B type. As 𝜙 increases from zero, the density of kinks on the steps increases. For hcp-type crystals, in addition the structural difference between alternating steps decreases, until they become equivalent at 𝜙 = 30°. We consider the azimuth dependence of the step transparency, attachment, and repulsion parameters of the BCF model, including the effects of both geometrically required and thermally generated kinks. Example calculations are presented that demonstrate the overall effect of step azimuth on BCF predictions for step spacings during steady-state growth and for their dynamics during growth transients. Effects of symmetric and asymmetric step-step repulsion are discussed.

Ju, Guangxu↗
DOE OSTI2022

Detailed analysis of excited-state systematics in a lattice QCD calculation of 𝑔 𝐴

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations ≳ 1 fm are commonly used to combat these issues. In this work, focusing on g A , we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2–1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Lorentz symmetry in ghost-free massive gravity

The role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. Here, the result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

How do spherical black holes grow monopole hair?

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron star collapses to a black hole, scalar hair must grow until it settles to the stationary black hole solution with (monopole) hair. In this paper, we study this process in detail and show that the growth of scalar hair is tied to the appearance and growth of the event horizon (before an apparent horizon forms), which forces scalar modes that would otherwise (in the future) become divergent to be radiated away. We prove this result rigorously in general first for a large class of modified theories, and then we exemplify the results by studying the temporal evolution of the scalar field in scalar Gauss-Bonnet gravity in two backgrounds: (i) a collapsing Oppenheimer-Snyder background, and (ii) a collapsing neutron star background. In case (i), we find an exact scalar field solution analytically, while in case (ii) we solve for the temporal evolution of the scalar field numerically, with both cases supporting the conclusion presented above. Thus, our results suggest that the emission of a burst of scalar field radiation is a necessary condition for black hole formation in a large class of modified theories of gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗