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Keywords = quadrupole moments

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20 pages, 432 KB  
Article
Magnetized Neutron Stars: Perturbative Versus Fully Numerical Approaches
by Debarati Chatterjee, Daw Guttmann, Jérôme Novak, Micaela Oertel and Martin Jakob Steil
Universe 2026, 12(6), 170; https://doi.org/10.3390/universe12060170 - 9 Jun 2026
Viewed by 289
Abstract
(1) Background: For the study of highly magnetized neutron stars observed as magnetars and to quantify the effect of this intense magnetic field on the star’s structure and shape, which can be particularly relevant for the study of the emission of continuous gravitational [...] Read more.
(1) Background: For the study of highly magnetized neutron stars observed as magnetars and to quantify the effect of this intense magnetic field on the star’s structure and shape, which can be particularly relevant for the study of the emission of continuous gravitational waves, both numerical and perturbative approaches have been developed. (2) Methods: We compare these two approaches in General Relativity with the limitation to the case where the magnetic field has a purely poloidal structure. The perturbative one assumes that the deformation induced by the magnetic field is small and that this field arises only from dipole currents. The fully numerical one is based on the lorene library. (3) Results: We used both approaches to compute the magnetic-field distribution and the deformation of the star, varying the value of the magnetic field at the pole, the compactness of the star and its equation of state. (4) Conclusions: Whereas the perturbative approach breaks down for very high polar magnetic-field values (typically above a few times 1016 G), it achieves very good results for observed values, even in magnetars. On the contrary, the numerical code exhibits resolution problems for relatively low magnetic-field values (typically 1010 G), which translates into imprecise computation of the star’s deformation and mass quadrupole moment. Full article
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10 pages, 420 KB  
Proceeding Paper
Atomic Structure Analysis and Radiative Properties with Einstein Coefficients for Ne-like Se (Se XXV)
by Malvika Singh, Richa Paijwar and Rinku Sharma
Phys. Sci. Forum 2026, 13(1), 6; https://doi.org/10.3390/psf2026013006 - 13 May 2026
Viewed by 326
Abstract
We present a detailed study of the atomic structure and radiative properties of highly charged neon-like selenium (Se XXV), motivated by its importance in plasma diagnostics, fusion research, and astrophysical spectroscopy. We calculated excitation energies and radiative parameters for the 50 lowest levels [...] Read more.
We present a detailed study of the atomic structure and radiative properties of highly charged neon-like selenium (Se XXV), motivated by its importance in plasma diagnostics, fusion research, and astrophysical spectroscopy. We calculated excitation energies and radiative parameters for the 50 lowest levels of fine structure using a fully relativistic multiconfiguration Dirac–Fock approach. We calculated transition wavelengths, radiative transition rates, oscillator strengths, and line strengths for electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among the specified levels. We also evaluated Einstein coefficients for spontaneous and stimulated emission, transition dipole moments, and radiative lifetimes of the low-lying states. To validate the results, we performed independent relativistic calculations using an alternative theoretical method and compared the datasets to examine internal consistency. The calculated excitation energies and radiative parameters agree well with values reported in the National Institute of Standards and Technology database (NIST) and other published theoretical results. The agreement between the independent approaches confirms the consistency of the present dataset. These results provide reliable atomic data for spectral line identification and quantitative plasma modeling in laboratory and astrophysical environments and support ongoing experimental and diagnostic studies of highly charged ions. Full article
(This article belongs to the Proceedings of The 1st International Online Conference on Atoms)
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22 pages, 1632 KB  
Article
Quantum Choreography of the Nucleus: Rotations, Vibrations, and Emergent Structure
by Ani Aprahamian, Kevin Lee, Shelly Lesher and Roelof Bijker
Symmetry 2026, 18(5), 812; https://doi.org/10.3390/sym18050812 - 9 May 2026
Viewed by 313
Abstract
Nuclei are complex many-body quantum systems where interactions of the neutrons and protons via the strong, the weak, and the electromagnetic forces lead to the emergence of simple patterns of energy states that have been described by various theoretical approaches. One of the [...] Read more.
Nuclei are complex many-body quantum systems where interactions of the neutrons and protons via the strong, the weak, and the electromagnetic forces lead to the emergence of simple patterns of energy states that have been described by various theoretical approaches. One of the goals of all the theoretical models is the development of a universal theory that can be applied across the entire chart of nuclides. Significant progress has been made by experiments as well as the increasing sophistication of models, but a universal theory has yet to be established. A recent reviewof nuclei in the Z = 50–82 region of the chart of nuclides has analyzed all the available compiled data from several decades of studies towards a clarification of the low-lying structure of nuclei. Other reviews have reported and explained the emergence of multiple different shapes in nuclei at somewhat higher excitation energies than the ground state. Somehave challenged the interpretation of the first excited Kπ =0+ band as a vibration of ground state. This work attempts to provide a guide to determining the nature of the first excited Kπ =0+ band in nuclei by the combined use of nuclear lifetimes, energy level evolutions, dynamic moments of inertia, and intrinsic quadrupole moments extracted from transition probabilities. The result is that for a subset of the nuclei in this region, the Kπ =0+ band is consistent with the traditional β-vibration description of an oscillation built on the ground state. Full article
(This article belongs to the Special Issue Advances in Nuclear Physics and Symmetry)
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17 pages, 6467 KB  
Article
The No-Hair Theorems at Work in the Tidal Disruption Event AT2020afhd
by Lorenzo Iorio
Universe 2026, 12(5), 120; https://doi.org/10.3390/universe12050120 - 23 Apr 2026
Viewed by 970
Abstract
Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and [...] Read more.
Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system’s parameter space which, as far as the hole’s dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole’s quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole’s mass yields the range 0.185–0.215 for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted. Some of the assumptions on which this work is based are critically examined. Full article
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18 pages, 667 KB  
Review
Reassessed Ability of Carbon-Based Physisorbing Materials to Keep Pace with Evolving Practical Targets for Hydrogen Storage
by Patrick L. Langlois, Chavdar P. Chilev and Farida D. Lamari
C 2026, 12(1), 9; https://doi.org/10.3390/c12010009 - 21 Jan 2026
Viewed by 1041
Abstract
This study provides a comprehensive overview of research and advancements on carbon materials with regard to practical targets for hydrogen storage in terms of gravimetric and volumetric capacities. For the sake of clarity, only the most relevant references on hydrogen storage by adsorption [...] Read more.
This study provides a comprehensive overview of research and advancements on carbon materials with regard to practical targets for hydrogen storage in terms of gravimetric and volumetric capacities. For the sake of clarity, only the most relevant references on hydrogen storage by adsorption are presented, although the study was conducted in the same exhaustive manner as the one initially carried out by Anne C. Dillon and Michael J. Heben in 2001 with a particular emphasis on emerging technologies and potential applications in various sectors. This study also focuses on the importance of carbon-based materials with high specific surface areas and porous structures optimised to maximise adsorption—including at high pressure—while primarily limiting references herein to experimentally validated results. It therefore offers insights into the porous materials, as well as the methodologies—including a fully comprehensive and so-far proven highly transferable intermolecular hydrogen model combining van der Waals’s and Coulomb’s forces—used to improve hydrogen solid storage efficiency. Full article
(This article belongs to the Special Issue 10th Anniversary of C — Journal of Carbon Research)
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20 pages, 2241 KB  
Article
Computational and Spectroscopic Investigation of Diaminomethane Formation: The Simplest Geminal Diamine of Astrochemical Interest
by Pravi Mishra, Parmanand Pandey, Rachana Singh, Manisha Yadav, Shivani, Aftab Ahamad, Alka Misra, Amritanshu Shukla and Poonam Tandon
Atoms 2025, 13(11), 91; https://doi.org/10.3390/atoms13110091 - 12 Nov 2025
Viewed by 1532
Abstract
A high-level ab initio characterization and formation of diaminomethane (DAM), the simplest geminal diamine, is presented to support its spectroscopic detection and astrochemical relevance in the interstellar medium. The C2v DAM conformer is identified as the global minimum, while C1 [...] Read more.
A high-level ab initio characterization and formation of diaminomethane (DAM), the simplest geminal diamine, is presented to support its spectroscopic detection and astrochemical relevance in the interstellar medium. The C2v DAM conformer is identified as the global minimum, while C1 DAM and C2 DAM represent higher-energy local minima. The proposed reaction pathways are exothermic and proceed without activation barriers. Simulated infrared spectrum reproduces accurate key spectral signatures with several vibrational modes exhibiting strong IR intensities (>80 km mol−1), particularly in the 800–3000 cm−1 range and band shapes. Dipole moments and accurate rovibrational spectroscopic parameters, including rotational constants, anharmonic vibrational frequencies, quartic and sextic distortion constants, and nuclear quadrupole coupling constants are reported to assist with high-resolution spectroscopic identification. This study provides significant theoretical benchmarks for its formation and offers guidance for future laboratory spectroscopy and molecular searches in interstellar environments. Full article
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23 pages, 5294 KB  
Article
CMB Parity Asymmetry from Unitary Quantum Gravitational Physics
by Enrique Gaztañaga and K. Sravan Kumar
Symmetry 2025, 17(7), 1056; https://doi.org/10.3390/sym17071056 - 4 Jul 2025
Cited by 4 | Viewed by 1663
Abstract
Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the [...] Read more.
Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity (P) and time-reversal (T) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data pM|D, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates pD|M, the likelihood of the data under the model, which undermines the importance of low- physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article
(This article belongs to the Special Issue Quantum Gravity and Cosmology: Exploring the Astroparticle Interface)
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17 pages, 5147 KB  
Article
Response Surface Optimization of Biodiesel Production via Esterification Reaction of Methanol and Oleic Acid Catalyzed by a Brönsted–Lewis Catalyst PW/UiO/CNTs-OH
by Xuyao Xing, Qiong Wu, Li Zhang and Qing Shu
Catalysts 2025, 15(5), 412; https://doi.org/10.3390/catal15050412 - 23 Apr 2025
Cited by 1 | Viewed by 1357
Abstract
In this study, a Brönsted–Lewis bifunctional acidic catalyst PW/UiO/CNTs-OH was synthesized via the hydrothermal method. The parameters for the esterification reaction of oleic acid with methanol catalyzed by PW/UiO/CNTs-OH were optimized using central composite design-response surface methodology (CCD-RSM). A biodiesel yield of 92.9% [...] Read more.
In this study, a Brönsted–Lewis bifunctional acidic catalyst PW/UiO/CNTs-OH was synthesized via the hydrothermal method. The parameters for the esterification reaction of oleic acid with methanol catalyzed by PW/UiO/CNTs-OH were optimized using central composite design-response surface methodology (CCD-RSM). A biodiesel yield of 92.9% was achieved under the optimized conditions, retaining 82.3% biodiesel yield after four catalytic cycles. The enhanced catalytic performance of PW/UiO/CNTs-OH can be attributed as follows: the [Zr6O4(OH)4]12+ anchored on the surface of multi-walled carbon nanotubes (MWCNTs) can serve as nucleation sites for UiO-66, not only encapsulating H3[P(W3O10)4] (HPW) but also reversing the quadrupole moment of MWCNTs to generate Lewis acid sites. In addition, introduction of HPW during synthesis of UiO-66 decreases the solution pH, inducing the protonation of p-phthalic acid (PTA) to disrupt the coordination with the [Zr6O4(OH)4] cluster, thereby creating an unsaturated Zr4+ site with electron pair-accepting capability, which generates Lewis acid sites. EIS analysis revealed that PW/UiO/CNTs-OH has higher electron migration efficiency than UiO-66 and PW/UiO. Furthermore, NH3-TPD and Py-IR analyses showed that PW/UiO/CNTs-OH possessed high densities of Lewis acidic sites of 83.69 μmol/g and Brönsted acidic sites of 9.98 μmol/g. Full article
(This article belongs to the Section Biomass Catalysis)
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22 pages, 3351 KB  
Article
Distinguishing Compact Objects in Extreme-Mass-Ratio Inspirals by Gravitational Waves
by Lujia Xu, Shucheng Yang, Wenbiao Han, Xingyu Zhong, Rundong Tang and Yuanhao Zhang
Universe 2025, 11(1), 18; https://doi.org/10.3390/universe11010018 - 13 Jan 2025
Cited by 5 | Viewed by 2221
Abstract
Extreme-mass-ratio inspirals (EMRIs) are promising gravitational-wave (GW) sources for space-based GW detectors. EMRI signals typically have long durations, ranging from several months to several years, necessitating highly accurate GW signal templates for detection. In most waveform models, compact objects in EMRIs are treated [...] Read more.
Extreme-mass-ratio inspirals (EMRIs) are promising gravitational-wave (GW) sources for space-based GW detectors. EMRI signals typically have long durations, ranging from several months to several years, necessitating highly accurate GW signal templates for detection. In most waveform models, compact objects in EMRIs are treated as test particles without accounting for their spin, mass quadrupole, or tidal deformation. In this study, we simulate GW signals from EMRIs by incorporating the spin and mass quadrupole moments of the compact objects. We evaluate the accuracy of parameter estimation for these simulated waveforms using the Fisher Information Matrix (FIM) and find that the spin, tidal-induced quadruple, and spin-induced quadruple can all be measured with precision ranging from 102 to 101, particularly for a mass ratio of ∼104. Assuming the “true” GW signals originate from an extended body inspiraling into a supermassive black hole, we compute the signal-to-noise ratio (SNR) and Bayes factors between a test-particle waveform template and our model, which includes the spin and quadrupole of the compact object. Our results show that the spin of compact objects can produce detectable deviations in the waveforms across all object types, while tidal-induced quadrupoles are only significant for white dwarfs, especially in cases approaching an intermediate-mass ratio. Spin-induced quadrupoles, however, have negligible effects on the waveforms. Therefore, our findings suggest that it is possible to distinguish primordial black holes from white dwarfs, and, under certain conditions, neutron stars can also be differentiated from primordial black holes. Full article
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28 pages, 2099 KB  
Article
Electroweak Parameters from Mixed SU(2) Yang–Mills Thermodynamics
by Janning Meinert and Ralf Hofmann
Symmetry 2024, 16(12), 1587; https://doi.org/10.3390/sym16121587 - 27 Nov 2024
Cited by 4 | Viewed by 2273
Abstract
Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius r0a0, where a0 is the Bohr radius. This droplet is of [...] Read more.
Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius r0a0, where a0 is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of Tc=7.95 keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet’s charge at a value of the electromagnetic fine-structure constant α of α1134 for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle θW30°, which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales (Λe=3.6 keV and ΛCMB104 eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of θW. The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of r0. Full article
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13 pages, 4291 KB  
Article
Diffusion and Spectroscopy of H2 in Myoglobin
by Jiri Käser, Kai Töpfer and Markus Meuwly
Oxygen 2024, 4(4), 389-401; https://doi.org/10.3390/oxygen4040024 - 31 Oct 2024
Viewed by 2369
Abstract
The diffusional dynamics and vibrational spectroscopy of molecular hydrogen (H2) in myoglobin (Mb) is characterized. Hydrogen has been implicated in a number of physiologically relevant processes, including cellular aging or inflammation. Here, the internal diffusion through the protein matrix was characterized, [...] Read more.
The diffusional dynamics and vibrational spectroscopy of molecular hydrogen (H2) in myoglobin (Mb) is characterized. Hydrogen has been implicated in a number of physiologically relevant processes, including cellular aging or inflammation. Here, the internal diffusion through the protein matrix was characterized, and the vibrational spectroscopy was investigated using conventional empirical energy functions and improved models able to describe higher-order electrostatic moments of the ligand. Depending on the energy function used, H2 can occupy the same internal defects as already found for Xe or CO (Xe1 to Xe4 and B-state). Furthermore, four additional sites were found, some of which had been discovered in earlier simulation studies. Simulations using a model based on a Morse oscillator and distributed charges to correctly describe the molecular quadrupole moment of H2 indicate that the vibrational spectroscopy of the ligand depends on the docking site it occupies. This is consistent with the findings for CO in Mb from experiments and simulations. For H2, the maxima of the absorption spectra cover ∼20 cm−1 which are indicative of a pronounced Stark effect of the surrounding protein matrix on the vibrational spectroscopy of the ligand. Electronic structure calculations show that H2 forms a stable complex with the heme iron (stabilized by ∼−12 kcal/mol), but splitting of H2 is unlikely due to a high activation energy (∼50 kcal/mol). Full article
(This article belongs to the Special Issue Interaction of Oxygen and Other Gases with Haem Containing Proteins)
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24 pages, 7441 KB  
Article
Understanding Complex Interplay among Different Instabilities in Multiferroic BiMn7O12 Using 57Fe Probe Mössbauer Spectroscopy
by Iana S. Soboleva, Vladimir I. Nitsenko, Alexey V. Sobolev, Maria N. Smirnova, Alexei A. Belik and Igor A. Presniakov
Int. J. Mol. Sci. 2024, 25(3), 1437; https://doi.org/10.3390/ijms25031437 - 24 Jan 2024
Cited by 2 | Viewed by 2413
Abstract
Here, we report the results of a Mössbauer study on hyperfine electrical and magnetic interactions in quadruple perovskite BiMn7O12 doped with 57Fe probes. Measurements were performed in the temperature range of 10 K < T < 670 K, wherein [...] Read more.
Here, we report the results of a Mössbauer study on hyperfine electrical and magnetic interactions in quadruple perovskite BiMn7O12 doped with 57Fe probes. Measurements were performed in the temperature range of 10 K < T < 670 K, wherein BiMn6.9657Fe0.04O12 undergoes a cascade of structural (T1 ≈ 590 K, T2 ≈ 442 K, and T3 ≈ 240 K) and magnetic (TN1 ≈ 57 K, TN2 ≈ 50 K, and TN3 ≈ 24 K) phase transitions. The analysis of the electric field gradient (EFG) parameters, including the dipole contribution from Bi3+ ions, confirmed the presence of the local dipole moments pBi, which are randomly oriented in the paraelectric cubic phase (T > T1). The unusual behavior of the parameters of hyperfine interactions between T1 and T2 was attributed to the dynamic Jahn–Teller effect that leads to the softening of the orbital mode of Mn3+ ions. The parameters of the hyperfine interactions of 57Fe in the phases with non-zero spontaneous electrical polarization (Ps), including the P1 ↔ Im transition at T3, were analyzed. On the basis of the structural data and the quadrupole splitting Δ(T) derived from the 57Fe Mössbauer spectra, the algorithm, based on the Born effective charge model, is proposed to describe Ps(T) dependence. The Ps(T) dependence around the ImI2/m phase transition at T2 is analyzed using the effective field approach. Possible reasons for the complex relaxation behavior of the spectra in the magnetically ordered states (T < TN1) are also discussed. Full article
(This article belongs to the Special Issue Physical Inorganic Chemistry in 2024)
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14 pages, 332 KB  
Review
The Distributional Stress–Energy Quadrupole and Gravitational Waves
by Jonathan Gratus and Spyridon Talaganis
Universe 2023, 9(12), 518; https://doi.org/10.3390/universe9120518 - 15 Dec 2023
Cited by 1 | Viewed by 2193
Abstract
In this overview, we discuss the (Schwartz) distributional stress–energy quadrupole and show it is a source of gravitational waves. We provide an explicit formula for the metric of linearised gravity in the case of a background Minkowski spacetime. We compare and contrast the [...] Read more.
In this overview, we discuss the (Schwartz) distributional stress–energy quadrupole and show it is a source of gravitational waves. We provide an explicit formula for the metric of linearised gravity in the case of a background Minkowski spacetime. We compare and contrast the two different representations for quadrupoles taken by Dixon and Ellis, present the formula for the dynamics of the quadrupole moments, and determine the number of free components. We review other approaches to the dynamics of quadrupoles, comparing our results. Full article
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20 pages, 2961 KB  
Article
Observable Properties of Thin Accretion Disk in the γ Spacetime
by Bobur Turimov and Bobomurat Ahmedov
Symmetry 2023, 15(10), 1858; https://doi.org/10.3390/sym15101858 - 3 Oct 2023
Cited by 6 | Viewed by 2946
Abstract
We study matter accretion in a static, axially symmetric and vacuum geometry describing the exterior gravitational field of a black hole mimicker called the γ metric. We evaluate the thermal and optical properties of thin accretion disks, including the emission rate, luminosity and [...] Read more.
We study matter accretion in a static, axially symmetric and vacuum geometry describing the exterior gravitational field of a black hole mimicker called the γ metric. We evaluate the thermal and optical properties of thin accretion disks, including the emission rate, luminosity and shadow, in the gamma spacetime. Also, we explore the radial accretion of polytropic matter fields onto the central source and evaluate the thermal and optical properties of the infalling gas, such as temperature and luminosity. The results are discussed in the context of evaluating the possibility that the true nature of astrophysical black hole candidates may not be a black hole but some exotic compact object possessing a non-vanishing mass quadrupole moment. Full article
(This article belongs to the Section Physics)
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16 pages, 388 KB  
Article
Conditions for Graviton Emission in the Recombination of a Delocalized Mass
by Alessandro Pesci
Quantum Rep. 2023, 5(2), 426-441; https://doi.org/10.3390/quantum5020028 - 22 May 2023
Cited by 3 | Viewed by 2673
Abstract
In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles [...] Read more.
In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles with the superposed locations, a proposed resolution being graviton emission from quadrupole moments. Here, we focus on the delocalized particle (forgetting about the probe and the gedanken experiment) and explore the conditions (in terms of mass, separation, and recombination time) for graviton emission. Through this, we find that the variations of quadrupole moments in the recombination are generically greatly enhanced if the field is entangled compared to if it is sourced instead by the energy momentum expectation value on the delocalized state (moment variation md2 in the latter case, with m mass, d separation). In addition, we obtain the (upper) limit recombination time for graviton emission growing as m in place of the naive expectation m. In this, the Planck mass acts as threshold mass (huge, for delocalized objects): no graviton emission is possible below it, however fast the recombination occurs. If this is compared with the decay times foreseen in the collapse models of Diósi and Penrose (in their basic form), one finds that no (quadrupole) graviton emission from recombination is possible in them. Indeed, right when m becomes large enough to allow for emission, it also becomes too large for the superposition to survive collapse long enough to recombine. Full article
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