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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Geometric entropies and their Hamiltonian flows

In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

AdS-CFT correspondence↗
DOE OSTI2020

Insights into the methanol synthesis mechanism via CO 2 hydrogenation over Cu-ZnO-ZrO2 catalysts: Effects of surfactant/Cu-Zn-Zr molar ratio

In this study, we evaluated aspects of the CO 2 hydrogenation mechanism, correlating structure-activity relationships of Cu-ZnO-ZrO 2 catalysts prepared by one-pot surfactant-assisted co-precipitation with different surfactant ratios. Identifying the CO 2 hydrogenation pathway intermediates is key to controlling the reaction selectivity. Experimental evidence shows that the CO 2 is dissociating into CO* and O* onto the surface of the Cu-ZnO-ZrO 2 catalyst. The adsorption and dissociation of CO2 were evidenced by a combination of in situ ambient-pressure X-ray Photoelectron Spectroscopy (AP-XPS) and Fourier Transform Infrared Spectroscopy (FTIR) with a transmission cell. AP-XPS showed that the catalysts are composed of a Cu 2+ , Zr 3+ , and Zr 4+ mixture and two kinds of Zn 2+ species. After the H 2 reduction process, only Cu 2+ was reduced to Cu0. The Zn and Zr species were oxidized by the dissociated O* species. In situ transmission FTIR showed that CO was adsorbed onto the Cu+/0 sites. The catalyst with the higher surfactant molar ratio exhibited the highest CO 2 conversion close to the equilibrium conversion, as well as a good methanol formation rate.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Ionic-like Superlattices by Charged Nanoparticles: A Step Toward Photonics Applications

Controlling interactions among nanoparticles is paramount to achieving assemblies vital to technologies seeking to exploit their cutting-edge collective properties. Although various techniques have been advanced, robust ones are necessary for upscaling nanoparticle assembly and crystallization. Here, we show that by grafting gold nanoparticles (AuNPs) with charge-end-group-thiolated poly(ethylene glycol), we control the charge of each AuNP. Such control facilitates the formation of various two-dimensional structures of oppositely charged binary constituents at vapor/liquid interfaces. Using surface-sensitive synchrotron X-ray diffraction techniques, we established the formation of distinct checkerboard square lattice structures at a range of pH values and molar ratios of the constituents. By regulating pH, the superlattices can transform from a square to a hexagonal lattice, or vice versa, and to a single-component superstructure at the interface. In conclusion, our recipe for the control of charges and their consequent interactions among nanoparticles can be readily exploited in the assembly of photonics and plasmonics devices in two and three dimensions.

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

Electrolyte Organization Leads to Potential-Dependence in Thermochemical Catalysis of Nonpolar Reactions

Electrochemical polarization is now known to play a key role in thermochemical catalysis at solid–liquid interfaces. However, existing frameworks cannot account for why even nonpolar, nonfaradaic reactions are sensitive to interfacial polarization. In order to uncover the molecular basis of this phenomenon, we herein study the potential-dependent reaction kinetics of ethylene and trans-2-butene hydrogenation at Pt–liquid interfaces. Measurements were performed in aqueous and ortho-difluorobenzene (o-DFB) solutions, spontaneously polarizing the Pt–liquid interfaces by, respectively, varying the pH or dissolving distinct metallocene redox buffers into solution. Here, we find that at comparable mechanistic regimes, the rates of both ethylene and trans-2-butene hydrogenation are maximized near the same electrochemical potential, E. Moreover, the potential-dependence, defined as $\frac{∂ln 𝑟}{∂𝐸}$, of trans-2-butene hydrogenation is approximately 2.2× greater than that of ethylene hydrogenation across the full potential range studied. These observations are all consistent with a model in which polarization of the Pt surface away from the local potential of zero free charge (E PZFC ) induces electrostatic organization of the polar solvent and charged ions near the interface, which impedes olefin adsorption and surface reaction because these surface reactions induce electrolyte displacement. Accordingly, interfacial polarization alters the free energy landscape and thus the rate of nonpolar heterogeneous catalysis by controlling the degree of electrostatic organization of polar and charged spectators at the interface, which do not in general need to be specifically chemisorbed onto the surface but could simply be close enough to the surface to be perturbed by the olefin adsorption. These results point toward electrochemical design handles, namely, the electrolyte, catalyst potential, and local E PZFC of the catalyst, with which to tune interfacial catalysis of thermochemical organic transformations.

adsorption↗
DOE OSTI2024

Complexities of urban impacts on long-term seasonal trends in a mid-sized arid city

The variability of surface air temperature is of great importance for both society and the environment, is impacted by global warming and local-scale changes. In the arid eastern part of Washington state of USA, substantial urbanization has transformed the Tri-cities into the state’s third-largest urban cluster. This study utilizes a combination of in situ observations and reanalysis datasets to investigate the influence of land use changes on the region’s 2-meter temperature, revealing local effects that compensate for the background global warming. Within the urban fabric, distinct microclimates have emerged due to varying land use, establishing unique relationships between greenness and temperature alterations caused by land use transitions. Notably, our findings demonstrate that the observed compensating signal in the temperature of farmland locations is primarily attributed to local vegetation increases. Through these observations, this research highlights the urban impacts on local climate, offering valuable insights into the complexities surrounding land use and its consequences on the environment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Coupling between plasmonic and photonic crystal modes in suspended three-dimensional meta-films

A complementary metal oxide semiconductor (CMOS) compatible fabrication method for creating three-dimensional (3D) meta-films is presented. In contrast to metasurfaces, meta-films possess structural variation throughout the thickness of the film and can possess a sub-wavelength scale structure in all three dimensions. Here we use this approach to create 2D arrays of cubic silicon nitride unit cells with plasmonic inclusions of elliptical metallic disks in horizontal and vertical orientations with lateral array-dimensions on the order of millimeters. Fourier transform infrared (FTIR) spectroscopy is used to measure the infrared transmission of meta-films with either horizontally or vertically oriented ellipses with varying eccentricity. Shape effects due to the ellipse eccentricity, as well as localized surface plasmon resonance (LSPR) effects due to the effective plasmonic wavelength are observed in the scattering response. The structures were modeled using rigorous coupled wave analysis (RCWA), finite difference time domain (Lumerical), and frequency domain finite element (COMSOL). The silicon nitride support structure possesses a complex in-plane photonic crystal slab band structure due to the periodicity of the unit cells. We show that adjustments to the physical dimensions of the ellipses can be used to control the coupling to this band structure. The horizontally oriented ellipses show narrow, distinct plasmonic resonances while the vertically oriented ellipses possess broader resonances, with lower overall transmission amplitude for a given ellipse geometry. We attribute this difference in resonance behavior to retardation effects. The ability to couple photonic slab modes with plasmonic inclusions enables a richer space of optical functionality for design of metamaterial-inspired optical components.

42 ENGINEERING↗
DOE OSTI2024

The Fragility of Bedform‐Induced Hyporheic Zones: Exploring Impacts of Dynamic Groundwater Table Fluctuations

Abstract Hyporheic zones are commonly regarded as resilient and enduring interfaces between groundwater and surface water in river corridors. In particular, bedform‐induced advective pumping hyporheic exchange (bedform‐induced exchange) is often perceived as a relatively persistent mechanism in natural river systems driving water, solutes, and energy exchanges between the channel and its surrounding streambed sediments. Numerous studies have been based on this presumption. To evaluate the persistence of hyporheic zones under varying hydrologic conditions, we use a multi‐physics framework to model advective pumping bedform‐induced hyporheic exchange in response to a series of seasonal‐ and event‐scale groundwater table fluctuation scenarios, which lead to episodic river‐aquifer disconnections and reconnections. Our results suggest that hyporheic exchange is not as ubiquitous as generally assumed. Instead, the bedform‐induced hyporheic exchange is restricted to a narrow range of conditions characterized by minor river‐groundwater head differences, is intermittent, and can be easily obliterated by minor losing groundwater conditions. These findings shed light on the fragility of bedform‐induced hyporheic exchange and have important implications for biogeochemical transformations along river corridors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Biotropic liquid crystal phase transformations in cellulose-producing bacterial communities

Biological functionality is often enabled by a fascinating variety of physical phenomena that emerge from orientational order of building blocks, a defining property of nematic liquid crystals that is also pervasive in nature. Out-of-equilibrium, “living” analogs of these technological materials are found in biological embodiments ranging from myelin sheath of neurons to extracellular matrices of bacterial biofilms and cuticles of beetles. However, physical underpinnings behind manifestations of orientational order in biological systems often remain unexplored. For example, while nematiclike birefringent domains of biofilms are found in many bacterial systems, the physics behind their formation is rarely known. Here, using cellulose-synthesizing Acetobacter xylinum bacteria, we reveal how biological activity leads to orientational ordering in fluid and gel analogs of these soft matter systems, both in water and on solid agar, with a topological defect found between the domains. Furthermore, the nutrient feeding direction plays a role like that of rubbing of confining surfaces in conventional liquid crystals, turning polydomain organization within the biofilms into a birefringent monocrystal-like order of both the extracellular matrix and the rod-like bacteria within it. We probe evolution of scalar orientational order parameters of cellulose nanofibers and bacteria associated with fluid-gel and isotropic-nematic transformations, showing how highly ordered active nematic fluids and gels evolve with time during biological-activity-driven, disorder-order transformation. In conclusion, with fluid and soft-gel nematics observed in a certain range of biological activity, this mesophase-exhibiting system is dubbed “biotropic,” analogously to thermotropic nematics that exhibit solely orientational order within a temperature range, promising technological and fundamental-science applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Photolytic Degradation of Water‐Soluble Organic Carbon in Snowmelts: Changes in Molecular Characteristics, Brown Carbon Chromophores, and Radiative Effects

Abstract Water‐soluble organic carbon (WSOC) deposited in ambient snowpack play key roles in regional carbon cycle and surface energy budget, but the impacts of photo‐induced processes on its optical and chemical properties are poorly understood yet. In this study, melted samples of the seasonal snow collected from northern Xinjiang, northwestern China, were exposed to ultraviolet (UV) radiation to investigate the photolytic transformations of WSOC. Molecular characteristics and chemical composition of WSOC and its brown carbon (BrC) constituents were investigated using high‐performance liquid chromatography interfaced with a photodiode array detector and a high‐resolution mass spectrometer. Upon illumination, formation of nitrogen‐ and sulfur‐containing species with high molecular weight was observed in snow samples influenced by soil‐ and plant‐derived organics. In contrast, the representative sample collected from remote region showed the lowest molecular diversity and photolytic reactivity among all samples, in which no identified BrC chromophores decomposed upon illumination. Approximately 65% of chromophores in urban samples endured UV irradiation. However, most of BrC composed of phenolic/lignin‐derived compounds and flavonoids disappeared in the illuminated samples containing WSOC from soil‐ and plant‐related sources. Effects of the photochemical degradation of WSOC on the potential modulation of snow albedo were estimated. Apparent half‐lives of WSOC estimated as albedo reduction in 300–400 nm indicated 0.1–0.4 atmospheric equivalent days, which are shorter than typical photolysis half‐lives of ambient biomass smoke aerosol. This study provides new insights into the roles of WSOC in snow photochemistry and snow surface energy balance.

Meteorology & Atmospheric Sciences↗
DOE OSTI2021

Nucleation and growth of blue phase liquid crystals on chemically-patterned surfaces: a surface anchoring assisted blue phase correlation length

In condensed matter, the correlation length is an essential parameter which describes the distance over which a material maintains its structural properties. In liquid crystals, for the orientational order parameter this characteristic length is of the order of nanometers, while in solid crystals it can extend to macroscopic length scales. Here, we report the measurement of the correlation length, or persistence length, of the crystallographic orientation of blue phases (BPs)—chiral liquid crystals with long-range 3D-crystalline structures and submicron-sized lattice-parameters. These materials exhibit phase transformations that have been identified as the liquid analog of crystal-crystal martensitic transformations. In this work, we use liquid epitaxial growth to achieve spontaneous BP-crystal nucleation and subsequent growth. Specifically, we design patterned substrates made of a binary array of regions with different liquid crystal anchoring, which facilitate a uniform nucleation and growth of BP-crystals with (100)-lattice orientation and a simple cubic symmetry. Furthermore, our results indicate that this simple cubic BP, the so-called blue phase II (BPII), forms first on the patterned surface, thereby propagating the growth of domains in directions parallel or perpendicular to the patterned regions. These results are used to understand the emergence of a surface anchoring assisted BPII-correlation length, taken as the distance over which the BP preserves its lattice orientation, as a function of time and pattern characteristics. We found that BPII single crystals can be achieved on patterned regions whose lateral dimensions are equal to or larger than 10 μm, consistent with our measurements of the BPII-correlation length. This newly acquired understanding of the role of surfaces on the formation of BPs is then used to design processes that permit formation of macroscopically large mono-domain, single-crystal BPs by relying on significantly reduced patterned areas (only part of the area is patterned), a feature that could benefit the applications of this intriguing class of materials.

correlation length↗
DOE OSTI2023

Phase evolution during conventional and reactive flash sintering of (Mg,Ni,Co,Cu,Zn)O via in situ X-ray diffraction

Reactive flash sintering (RFS) enables the simultaneous synthesis and sintering of ceramics and has been shown to affect the reaction pathway of different materials. Herein, in situ synchrotron X-ray diffraction (XRD) is used to investigate the (Mg,Ni,Co,Cu,Zn)O entropy-stabilized oxide formation during: (i) conventional heating and (ii) RFS under current rate-controlled mode. The same reaction pathway is verified in both instances: the starting rock-salt (RS), spinel (Co 3 O 4 ), tenorite (CuO), and wurtzite (ZnO) phases transform into a single RS phase with a (1 1 1) to (2 0 0) intensity ratio of 0.67, consistent with a random distribution of the cations into the structure. Pt lattice peak shift from the XRD patterns is used as standard to monitor the sample surface temperature, revealing a strong endothermic reaction during the RS single-phase formation (Pt peaks shift toward higher angles while increasing sample temperature/current density). Furthermore, in RFS, the single-phase RS structure is formed in just 60 s at a furnace temperature of 600°C and a current rate of 220 mA mm -2 /min. Therefore, RFS greatly accelerates the synthesis of (Mg,Ni,Co,Cu,Zn)O, however, it does not play a role in the reaction pathway for this material formation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Columbia River Surface Water and Pore Water Unaligned FTICR-MS Data Associated with “Using Community Assembly Metrics from Metacommunity Ecology to Understand Environmental Metabolomes”

Surface water and pore water samples were collected at five sites along a shoreline transect of the Columbia River, southeastern WA, USA in 2017. This dataset is comprised of (1) high resolution characterization of dissolved organic matter via 12 Tesla Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) analyzed through the Environmental Molecular Sciences Laboratory (EMSL; https://www.pnnl.gov/environmental-molecular-sciences-laboratory) and (2) a metadata csv file. The FTICR-MS files are .xml, and the data package includes instructions for using Formularity (https://omics.pnl.gov/software/formularity) and an R script to process the data based on the user’s specific needs. The data are associated with the publication “Using community assembly metrics from metacommunity ecology to understand environmental metabolomes” that will be published in Nature Communications (Danczak et al.). The study aimed to investigate gaps in understanding the spatiotemporal organization of environmental metabolomes to improve the ability to predict ecosystem function. Associated sequencing data will be published via NCBI. The access information for NCBI and the publication DOI will be added to this abstract when they are available. Please use the data package’s DOI to cite the data package. We ask that you acknowledge the U.S. Department of Energy (DOE) Biological and Environmental Research (BER) Subsurface Biogeochemical Research (SBR) program when using the data. All data are free to be used for any purpose, such as for manuscripts, presentations, and grant proposals. There is no obligation to include data package authors as co-authors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Development Of A Photonic Doppler Velocimeter To Verify A Fabry-Perot Velocimeter

The laser shock system uses acoustic shockwaves to measure the interface strength of newly designed nuclear fuel plates. The quantitative measurement of interface strength will help understand fuel performance during irradiation. The laser shock technique imparts laser energy into a plate that then creates an acoustic shockwave. The amount of energy in the plate is proportional to the surface velocities measured on the back side of the plate. An accurate determination of surface velocity will enable better fuel performance predictions. The focus of this paper is on the implementation of a Photonic Doppler Velocimeter to corroborate the Fabry-Perot measurements from the laser shock system. Currently, a Fabry-Perot velocimeter takes the velocity measurements that are converted in stress. We have designed and implemented a Photonic Doppler Velocimeter to corroborate the Fabry-Perot measurements, which we discuss here along with implementing the short time fast Fourier transform to demodulate the heterodyne beat frequency into velocities. The Photonic Doppler Velocimeter has successfully corroborated the Fabry-Perot measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Metal ion dopant-induced famatinite to chalcostibite phase transformation of copper antimony sulphide colloidal nanostructures: effect on photophysical and pseudocapacitance properties

Here, the strategic doping of transition metal ions into copper antimony sulphide (CAS) semiconducting nanostructures can significantly influence their photophysical and pseudocapacitive properties, for which there are few reports and therefore is the focus of this study. Accordingly, highly crystalline metal ion (Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ and Zn 2+ ) doped off-stoichiometric copper rich/poor, antimony-rich/poor, and sulphur-poor CAS nanostructures (10–23 nm) were grown via colloidal (hot-injection) synthesis using metal diethyldithiocarbamate precursors. Importantly, metal ion doping significantly influences the structure and composition of the off-stoichiometric CAS nanostructures. Data from powder X-ray diffraction, Raman spectroscopy, high-resolution scanning/transmission electron microscopy, and energy dispersive X-ray spectroscopy confirm that the heavier metal ion dopants induce a novel phase transformation from famatinite (fCAS) to chalcostibite (cCAS) nanostructures. The influence of the metal ion dopants is also observed in the optical properties of as-synthesized nanostructures. This involves blue-shifted ultraviolet-visible absorption, reduced Urbach tailing, and tunable bandgaps between 2.17 and 2.38 eV. Also, the doped nanostructures display broad visible-near infrared photoluminescence via a triple radiative pathway with relatively short decay lifetimes between 0.2 and 6.1 ns. This is mediated by electronic transitions involving intrinsic (copper/antimony/sulphur interstitial) and extrinsic (metal ion interstitial) defect states. Additionally, electrodes prepared from Mn 2+ -doped fCAS nanostructures show enhanced pseudocapacitance via Na+ surface adsorption and intercalation relative to undoped fCAS electrodes, while Zn 2+ -doped cCAS electrodes exhibit pseudocapacitance via a combination of Na+ surface adsorption, intercalation, and redox reactions. These electrodes exhibit reduced charge transfer resistance, improved electronic conductivity and notably enhanced specific capacitance (∼222 F g −1 ), and charge transport, as measured in 1 M Na 2 SO 4 electrolyte via cyclic voltammetry and electrochemical impedance spectroscopy. To this end, the discovery of the metal ion-induced phase transformation presents a new avenue for optimizing the functional properties of fCAS and cCAS nanostructures, highlighting the critical role of metal ion-related defects in controlling the optical and electrochemical properties, towards potential solar absorption and energy storage applications.

25 ENERGY STORAGE↗
DOE OSTI2021

A holistic framework integrating plant-microbe-mineral regulation of soil bioavailable nitrogen

Abstract Soil organic nitrogen (N) is a critical resource for plants and microbes, but the processes that govern its cycle are not well-described. To promote a holistic understanding of soil N dynamics, we need an integrated model that links soil organic matter (SOM) cycling to bioavailable N in both unmanaged and managed landscapes, including agroecosystems. We present a framework that unifies recent conceptual advances in our understanding of three critical steps in bioavailable N cycling: organic N (ON) depolymerization and solubilization; bioavailable N sorption and desorption on mineral surfaces; and microbial ON turnover including assimilation, mineralization, and the recycling of microbial products. Consideration of the balance between these processes provides insight into the sources, sinks, and flux rates of bioavailable N. By accounting for interactions among the biological, physical, and chemical controls over ON and its availability to plants and microbes, our conceptual model unifies complex mechanisms of ON transformation in a concrete conceptual framework that is amenable to experimental testing and translates into ideas for new management practices. This framework will allow researchers and practitioners to use common measurements of particulate organic matter (POM) and mineral-associated organic matter (MAOM) to design strategic organic N-cycle interventions that optimize ecosystem productivity and minimize environmental N loss.

Environmental Sciences & Ecology↗
DOE OSTI2020

Probing Dopant Redistribution, Phase Propagation, and Local Chemical Changes in the Synthesis of Layered Oxide Battery Cathodes

Achieving the targeted control of layered oxide properties calls for more fundamental studies to mechanistically probe their evolution during their synthesis. Herein, dopant distribution, phase propagation, and local chemical changes as well as their interplay in multielement-doped LiNiO 2 materials are investigated using spectroscopic, imaging, and scattering techniques. It is shown that dopants undergo dynamic redistribution in the Ni(OH) 2 host lattice at the early stage of calcination (below 300 °C). Such redistribution behavior exhibits strong dopant-dependent characteristics, allowing for targeted surface and bulk doping control. The Ni oxidation process exhibits depth-dependent characteristics and the most rapid Ni oxidation takes place between 300 and 700 °C. Using Ni oxidation state as the proxy for the phase transformation, the buildup of heterogenous phase propagation in the early stage of calcination is shown, especially along the radial direction of secondary particles. Furthermore, the radial heterogenous phase distribution gradually decreases upon completing the calcination. However, a high degree of mosaic-like heterogeneity may still be present in the final product, departing from the perfect layered oxide. Overall, the present study offers fundamental insights into manipulating multiscale materials properties during calcination for obtaining stable, high-energy layered oxide cathodes.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Modification to the Hawking temperature of a dynamical black hole by a flow-induced supertranslation

One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the black hole evaporation, where the soft hairs on the horizon are induced by the absorption of a null anisotropic flow, generalizing the shock wave considered in [1, 2]. To do so we introduce two different time-dependent extensions of the diffeomorphism associated with the soft hair, where one is the backreaction of the anisotropic null flow, and the other is a coordinate transformation that produces the Unruh effect and a Doppler shift to the Hawking spectrum. Together, they form an exact BMS charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose surface gravity, i.e. the Hawking temperature, is found to be modified. The modification depends on an exponential average of the anisotropy of the null flow with a decay rate of 4M, suggesting the emergence of a new 2-D degree of freedom on the horizon, which could be a way out of the information loss paradox.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗