Gravitational Structure Research Articles

Precessing and periodic timelike orbits and their potential applications in Einsteinian cubic gravity

Einsteinian cubic gravity (ECG) is the most general theory up to cubic order in curvature, which has the same graviton spectrum as the Einstein theory. In this paper, we investigate the geodesic motions of timelike particles around the four dimensional asymptotically flat black holes in ECG, and discuss their potential applications when connecting them with recent observational results. We first explore the effects of the cubic couplings on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the periodic orbits around the Einsteinian cubic black hole. We find that comparing to Schwarzschild black hole in general relativity, the cubic coupling enhances the energy as well as the angular momentum for all the bound orbits of the particles. Then, we derive the relativistic periastron precessions of the particles and give a preliminary bound on the cubic coupling employing the observational result of the S2 star’s pericenter precession in SgrA*. Finally, after calculating the periodic orbits’ configurations, we preliminarily evaluate the gravitational waveform radiated from several periodic orbits in one complete period of a test object which orbits a supermassive Einsteinian cubic black hole. Our studies could be helpful for us to better understand the gravitational structure of the theory with high curvatures.

Reinforced soil retaining wall for ash handling facility Java 9 and 10 coal-fired steam power

The construction of coal ash handling facilities requires a large area to store large amounts of Fly Ash and Bottom Ash (FABA) material. Bund wall is proposed near the facility to be built FABA stockpile up to EL.+80.0. The area of the proposed bund wall is very limited, so a vertical earth retaining wall is proposed to maintain the FABA backfill as well as support the proposed Hauling Road. In this case, Geoforce Segmental Retaining Wall (GSRW) is adopted as one type of soil reinforcement, the construction is a combination of reinforcing elements in the form of geosynthetic strip (GI Strips) that interact with the filling material through friction and provide tensile capacity. The combination works as a gravitational structure capable of withstanding lateral ground pressure. This GI Strip material is produced in Indonesia so that it has a high “Tingkat Komponen Dalam Negeri” (TKDN) value. GSRW works are 820 m long with a height of 19.44 m. The analysis carried out was assisted by the PLAXIS 3D program to understand the deformation in the structure and obtain safety factors according to the requirements in “SNI Persyaratan Perancangan Geoteknik 8460:2017”.

Analysis of Spatiotemporal Changes in the Gravitational Structure of Urban Agglomerations in Northern and Southern Xinjiang Based on a Gravitational Model

The urban agglomeration plays a significant role in enhancing integrated regional development. Nevertheless, the expansion of urban agglomerations has demonstrated a lackluster ability to attract cities. Presently, finding solutions to stabilize the existing urban strength and effectively extend attraction to neighboring cities has become a crucial matter. This study adopts the enhanced comprehensive attraction model, fracture point model, and radiation radius model to examine the level of city attraction, intensity of radiation, and range of radiation in the northern and southern Xinjiang city clusters between 2010 and 2020. Based on the analysis, the following conclusions are drawn: (1) the comprehensive strength and city attraction of cities in the northern Xinjiang region is higher than that of the southern Xinjiang region; (2) the intensity of spatial connection between cities in the northern and southern Xinjiang regions is gradually increasing, and the intensity of spatial connection of cities in the northern Xinjiang region is significantly greater than that in the southern Xinjiang region. The intensity of spatial connection between cities in the northern and southern Xinjiang regions is significantly greater than that in the southern Xinjiang region; (3) the central role of the central cities in the northern and southern Xinjiang regions is weakening, the development of cities in the region is gradually becoming unified and coordinated, and regional integration is gradually being strengthened. This study reveals the similarities and differences in urban development in the north and south of Xinjiang and provides important theoretical reference value for regional urban development.

Schrödinger and Klein–Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

The Schrödinger equation of the Schwarzschild black hole (BH) has been recently derived by the author and collaborators. The BH is composed of a particle, the ‘electron’, interacting with a central field, the ‘nucleus’. Via de Broglie’s hypothesis, one interprets the ‘electron’ in terms of BH horizon’s modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schrödinger equation and the Schrödinger equation of the s states of the hydrogen atom permits us to solve the same equation. The quantum gravitational quantities analogous of the fine structure constant and of the Rydberg constant are not constants, but the dynamical quantities have well-defined discrete spectra. The spectrum of the ‘gravitational fine structure constant’ is the set of non-zero natural numbers. Therefore, BHs are well-defined quantum gravitational systems obeying Schrödinger’s theory: the ‘gravitational hydrogen atoms’. By identifying the potential energy in the BH Schrödinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH described as a ‘gravitational hydrogen atom’ is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having a radius equal to the oscillating gravitational radius. Nontrivial consequences emerge from this result: (i) BHs have neither horizons nor singularities; (ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schrödinger equation give the BH Klein–Gordon equation and the corresponding eigenvalues.

Simulating gravitational motion, gas dynamics, and structure in the cosmos

We provide introductory explanations and illustrations of the N-body hydrodynamics code Charm N-body GrAvity solver (ChaNGa). ChaNGa simulates the gravitational motion and gas dynamics of matter in space with the goal of modeling galactic and/or cosmological structure and evolution. We discuss the algorithm for leapfrog integration and smoothed particle hydrodynamics and computer science concepts used by the program, including the binary data structure for the particle positions. Our presentation borrows from the doctoral dissertation of J. Stadel, U. Washington, 2001. Problems are provided in order to use ChaNGa to learn or solidify some cosmological concepts.

Measurement quantization

We present principles of Measurement Quantization (MQ) and approaches to measurement that support the discreteness of measure. Several claims are addressed. Notably, that measure is discrete with respect to the internal frame, non-discrete with respect to the system frame and that length is contracted due to the discreteness of measure. We address the relation of angular measure to momentum, the physical significance of count bounds and that the fundamental measures — more precise expressions for Planck’s units — are an emergent property of the internal frame. Quantum experiments by Shwartz, et. al and CODATA provide physical support. We predict and derive values for elementary charge and the gravitational, Hubble, reduced Planck, electric, magnetic, Coulomb, and fine structure constants. We then correlate gravity with electromagnetism (unification). We present expressions for galactic rotation, dark matter, dark energy, and accelerating expansion. MQ advances over Loop Quantum Gravity with two frames, the difference which leads to the physical constants and the laws of nature. We correlate the quantum and cosmological, describing an inflation free quantum epoch, why it ceases and expansion. Therein are solutions to the horizon problem and homogenous, isotropic properties of the universe. Predictions include length contraction unrelated to special or general relativity (SR/GR), 13-digit measures of the gravitational constant, the Planck momentum, and universal mass accretion. A calculation of CMB age, quantity, present-day density and temperature provides additional support. Also offered, discrete solutions to the size and age of the universe, ground state orbital, SR, GR, and equivalence.

Discovering gravitationally lensed gravitational waves: predicted rates, candidate selection, and localization with the Vera Rubin Observatory

ABSTRACT Secure confirmation that a gravitational wave (GW) has been gravitationally lensed would bring together these two pillars of General Relativity for the first time. This breakthrough is challenging for many reasons, including: GW sky localization uncertainties dwarf the angular scale of gravitational lensing, the mass and structure of gravitational lenses is diverse, the mass function of stellar remnant compact objects is not yet well constrained, and GW detectors do not operate continuously. We introduce a new approach that is agnostic to the mass and structure of the lenses, compare the efficiency of different methods for lensed GW discovery, and explore detection of lensed kilonova counterparts as a direct method for localizing candidates. Our main conclusions are: (1) lensed neutron star mergers (NS–NS) are magnified into the ‘mass gap’ between NS and black holes, therefore selecting candidates from public GW alerts with high mass gap probability is efficient, (2) the rate of detectable lensed NS–NS will approach one per year in the mid-2020s, (3) the arrival time difference between lensed NS–NS images is $1\, \rm s\lesssim \Delta \mathit{ t}\lesssim 1\, yr$, and thus well-matched to the operations of GW detectors and optical telescopes, (4) lensed kilonova counterparts are faint at peak (e.g. rAB ≃ 24–26 in the mid-2020s), fade quickly ($d\lt 2\, \rm d$), and are detectable with target of opportunity observations with large wide-field telescopes. For example, just ≲ 0.25 per cent of Vera C. Rubin Observatory’s observing time will be sufficient to follow up one well-localized candidate per year. Our predictions also provide a physically well-defined basis for exploring electromagnetically the exciting new ‘mass gap’ discovery space.

Relativistic composite-particle theory of the gravitational form factors of the pion: Quantitative results

We use a version of the instant-form relativistic quantum mechanics of composite systems to obtain the gravitational form factors of the pion in a common approach to its electroweak and gravitational properties. In the preceding work [Phys. Rev. D 103, 014029 (2021)], we formulated the mathematical background, presented the principal scheme of calculation and testified the obtained qualitative results to satisfy the general constraints given by the principles of the theory of hadron structure. In the present work, we give the detailed calculation of the gravitational form factors in the large range of momentum transfer, their static limits, and the slopes at zero value, the mean-square mass and mechanical radii of the pion. Now we take into account the gravitational structure of the constituent quarks. We show that the results are almost insensitive to the type of model two-quark wave function in a close analogy to the case of the pion electromagnetic form factor. We present a correct calculation of the form factor $D$ and corresponding matrix element of the energy-momentum tensor, going beyond the scope of the modified impulse approximation. Most of the parameters that we use for the calculation had been fixed even earlier in our works on the pion electromagnetic form factors. The only free parameter is the $D$-term of the constituent quark, which we fix by fitting the result for the slope at zero of the normalized to pion $D$-term form factor $D$ of the pion, to a chosen experimental value.

Sources of irregular energy density in energy–momentum squared gravity with charge

This manuscript studies the inhomogeneity in the energy density for the relativistic dynamical charged system by invoking the outcomes coming from the considered anisotropic distribution of radiating fluid. We use newly developed f(G,T2) theory, which was proposed by the addition of T2=TζξTζξ in the usual action of f(G,) gravity. We construct relativistic field equations for a specific model f(G,T2)=λT2+G(1+Gα), to examine the gravitational structure in the influence of electromagnetic filed. We use dynamical expressions and differential equations for Weyl tensor for the inspection of sources of irregularities. By exploring special cases in the non-radiating and radiating scenarios, the irregularity elements for a fluid are examined. These special cases show that modified terms and charge have a considerable impact on the fluid inhomogeneity.

The Planetary Theory of Solar Activity Variability: A Review

Commenting the 11-year sunspot cycle, Wolf (1859, MNRAS 19, 85–86) conjectured that “the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn.” The high synchronization of our planetary system is already nicely revealed by the fact that the ratios of the planetary orbital radii are closely related to each other through a scaling-mirror symmetry equation (Bank and Scafetta, Front. Astron. Space Sci. 8, 758184, 2022). Reviewing the many planetary harmonics and the orbital invariant inequalities that characterize the planetary motions of the solar system from the monthly to the millennial time scales, we show that they are not randomly distributed but clearly tend to cluster around some specific values that also match those of the main solar activity cycles. In some cases, planetary models have even been able to predict the time-phase of the solar oscillations including the Schwabe 11-year sunspot cycle. We also stress that solar models based on the hypothesis that solar activity is regulated by its internal dynamics alone have never been able to reproduce the variety of the observed cycles. Although planetary tidal forces are weak, we review a number of mechanisms that could explain how the solar structure and the solar dynamo could get tuned to the planetary motions. In particular, we discuss how the effects of the weak tidal forces could be significantly amplified in the solar core by an induced increase in the H-burning. Mechanisms modulating the electromagnetic and gravitational large-scale structure of the planetary system are also discussed.

Bouguer and mantle gravity maps of Nigeria

We used global gravitational models together with topographic, bathymetric, and lithospheric density structure datasets to compile Bouguer and mantle gravity maps of Nigeria, and then used these gravity maps to interpret the crustal and upper mantle structure in this country. We applied methods for a spherical harmonic analysis and synthesis of gravitational and lithospheric density structure models to produce both gravity maps. Whereas existing Bouguer gravity datasets for different parts of Nigeria were computed by applying only a simple planar Bouguer gravity reduction and a planar terrain gravity correction, our approach took into consideration the Earth’s spherical approximation and the spherical terrain correction, the ocean density contrast as well as density variations within sediments and the underlying consolidated crust. This study also provides the first mantle gravity map of Nigeria. Our results show that the free-air gravity pattern reflects mainly a topographic relief with prevailing positive values over topographically elevated regions, while Cretaceous sedimentary basins are characterized by low negative values. The pattern in the Bouguer gravity map exhibits mainly a Moho signature, with low negative values associated with a regional Moho deepening beneath the Sokoto Basin and the North Shield Belt. The pattern in the mantle gravity map exhibits a thermal signature of the lithospheric mantle. The high values (≥ 1000 mGal) of the mantle gravity disturbances detected over the Benin-Nigerian Block and the Phanerozoic cover of the West African Mobile Zone are possibly associated with a thermal signature of the lithospheric mantle. Another thermal signature of the lithospheric mantle along the Cameroon Volcanic Line partially outlines margins between the Oubanguides Neoproterozoic Belt and the southern extension of the West African Mobile Zone.

True gravitational atoms: Spherical cloud of dilatonic black holes

Black hole as elementary particle is a fairly glamorous idea. For ordinary black holes, a surrounding particle inevitably penetrates into the interior of the hole since the center of the hole is an infinite potential well. For the first time we demonstrate that an extreme dilatonic black hole in spherical symmetry perfectly behaves as an atom, in the sense that its surrounding cloud of particles are completely stable. Thus we reach a spherical cloud of dilatonic black hole. We find exact wave functions of the cloud for arbitrary gravitational fine structure constant $\mu M$, and clear the underlying physical nature of the stability. Through careful studies of the exact wave function, we find the spectrum of this system. We discuss the physical meaning of this discovery especially from considerations of entropy, and the resultant possibility to explore quantization of gravitational waves from coming observations.

Evolution of cosmic structures in the expanding universe: Could not one have known it all before?

Most recent observations from the James Webb space telescope (JWST) have shown by highly resolved infrared observations of highest sensitivity that structure formation in the universe into the forms of early galaxies has already taken place at cosmic times less than 0.6 Gigayears after the Big-Bang. This is taken up with a big surprise in the whole astronomic community, though, as it seems, it could have been predicted from simple theoretical considerations. In this article, we are demonstrating that this result already would have clearly come out from theoretical considerations of gravitational structure formation processes in the early expanding universe just after the cosmic matter recombination period. While, however, it can be easily understood how matter structures of the order of 108 solar masses could evolve in the cosmic meantime, it nevertheless remains obscure, how galaxies of the type of the Milky way or more massive structures with 1011 or more solar masses can have evolved up to the present cosmic days without some not yet specified collapse-accelerating processes.

Gluon gravitational structure of hadrons of different spin

The gravitational form factors (GFFs) of hadrons encode the matrix elements of the energy momentum tensor of QCD. These quantities describe how energy, spin, and various mechanical properties of hadrons are carried by their quark and gluon constituents. We present the gluon GFFs of the pion, nucleon, $\rho$ meson, and $\Delta$ baryon as functions of the squared momentum transfer $t$ in the region $0 \leq -t < 2 \; \text{GeV}^2$, as determined in a lattice QCD study with pion mass $m_{\pi} = 450(5) \; \text{MeV}$. By fitting the extracted GFFs using multipole and z-parameter expansion functional forms, we extract various gluon contributions to the energy, pressure, and shear force distributions of the hadrons in the 3D and 2D Breit frames as well as in the infinite momentum frame. We also obtain estimates for the corresponding gluon mechanical and mass radii, as well as the forward-limit gluon contributions to the momentum fraction and angular momentum of the hadrons.

Kronoseismology. VI. Reading the Recent History of Saturn’s Gravity Field in Its Rings

Abstract Saturn’s C ring contains multiple structures that appear to be density waves driven by time-variable anomalies in the planet’s gravitational field. Semiempirical extensions of density wave theory enable the observed wave properties to be translated into information about how the pattern speeds and amplitudes of these gravitational anomalies have changed over time. Combining these theoretical tools with wavelet-based analyses of data obtained by the Visual and Infrared Mapping Spectrometer on board the Cassini spacecraft reveals a suite of structures in Saturn’s gravity field with azimuthal wavenumber 3, rotation rates between 804° day−1 and 842° day−1, and local gravitational potential amplitudes between 30 and 150 cm2 s−2. Some of these anomalies are transient, appearing and disappearing over the course of a few Earth years, while others persist for decades. Most of these persistent patterns appear to have roughly constant pattern speeds, but there is at least one structure in the planet’s gravitational field whose rotation rate steadily increased between 1970 and 2010. This gravitational field structure appears to induce two different asymmetries in the planet’s gravity field, one with azimuthal wavenumber 3 that rotates at roughly 810° day−1 and another with azimuthal wavenumber 1 rotating three times faster. The atmospheric processes responsible for generating the latter pattern may involve solar tides.

Baikal\u2013Vilyui Paleoproterozoic Belt of The Siberian Platform: Regional Gold-Controlling Structure

The article demonstrates that the placer gold content of the Vilyui Syneclise is governed by the regional structure of the crystalline basement of the Siberian Platform—the Baikal–Vilyui Paleoproterozoic belt, the boundaries and tectonics of which are substantiated by analysis of the gravitational field structure. The belt includes a system of basement blocks with a common northeastern strike, which form horsts (of the Suntar type) and grabens (of the Kempendyai type). The gold-bearing placers of the Vilyui Syneclise are mainly confined to the Suntar, Tyukyan, and Chybyda blocks of the belt, the metamorphic and igneous rocks of which were the primary gold sources in the sedimentary cover. The suture zone of the Baikal–Vilyui belt was very permeable to deep fluids responsible for gold migration. The types of possible primary gold sources (gold–platinoid, low-sulfidation gold-quartz, and gold–silver) reflect the peculiarities in the evolution of Early Precambrian gold during sedimentation in the Vilyui Syneclise. The areas controlled by the Suntar, Kempendyai, Tyukyan, Chybyda, and Khapchagai blocks of Early Precambrian rocks, which may contain gold objects, should be considered promising for buried gold placers in the Vilyui Syneclise.

Gravitational footprints of black holes and their microstate geometries

We construct a family of non-supersymmetric extremal black holes and their horizonless microstate geometries in four dimensions. The black holes can have finite angular momentum and an arbitrary charge-to-mass ratio, unlike their supersymmetric cousins. These features make them and their microstate geometries astrophysically relevant. Thus, they provide interesting prototypes to study deviations from Kerr solutions caused by new horizon-scale physics. In this paper, we compute the gravitational multipole structure of these solutions and compare them to Kerr black holes. The multipoles of the black hole differ significantly from Kerr as they depend non-trivially on the charge-to-mass ratio. The horizonless microstate geometries (that are comparable in size to a black hole) have a similar multipole structure as their corresponding black hole, with deviations to the black hole multipole values set by the scale of their microstructure.

MOND-like behavior in the Dirac–Milne universe

Aims.Observational data show that the observed luminous matter is not sufficient to explain several features of the present universe, from gravitational structure formation to the rotational velocities in galaxies and clusters. The mainstream explanation is that the missing mass, although gravitationally active, interacts very weakly with ordinary matter. Competing explanations involve changing the laws of gravity at low accelerations, as in MOdified Newtonian Dynamics (MOND). Here, we suggest that the Dirac-Milne cosmology, a matter-antimatter symmetric cosmology where the two components repel each other, is capable of accounting for such an apparent modification of the Newtonian law, without invoking dark matter.Methods.Using a simple analytical approximation and 1D and 3D simulations, we study rotation curves and virial velocities and compare the mass observed in the simulations to the mass derived assuming Newtonian gravity. Using a modified version of theRAMSEScode, we study the Faber-Jackson scaling relation and the intensity of the additional gravitational field created by antimatter clouds.Results.We show that, in the Dirac-Milne universe, rotation curves are generically flat beyond a characteristic distance of ≈2.5 virial radii, and that the Tully-Fisher and Faber-Jackson scaling relations with an exponent ≈3 are satisfied. We show that the mass derived from the rotation curves assuming Newtonian gravity is systematically overestimated compared to the mass really present. In addition, the Dirac-Milne universe, featuring a polarization between its matter and antimatter components, presents a behavior similar to that of MOND, characterized by an additional surface gravity compared to the Newtonian case. We show that in the Dirac-Milne universe, at the present epoch, the intensity of the additional gravitational fieldgamdue to the presence of clouds of antimatter is on the order of a few 10−11m s−2, similar to the characteristic acceleration of MOND. We study the evolution of this additional accelerationgamand show that it depends on the redshift, and it is therefore not a fundamental constant.Conclusions.Combined with its known concordance properties on the SNIa luminosity distance, age, nucleosynthesis, and structure formation, the Dirac-Milne cosmology may then represent an interesting alternative to the standard cosmological model ΛCDM, MOND, and other scenarios for explaining the dark matter (or missing gravity) and dark energy conundrum.

Quasibound states of charged dilatonic black holes

Investigation of quasibound states of black holes is significant for expected ultralight particles, as well as black holes through gravitational waves. We first investigate quasibound states of a massive scalar field for dilatonic charged black holes via numerical analysis. We study the complex eigenfrequencies of the massive scalar field in a wide range of gravitational fine structure constant $\ensuremath{\mu}M$ in detail, and show the effects of charge. Further, we study the eigenfrequencies of the massive field through an analytical approach by matching the near horizon solution and far field solution, and find its spectra for excited states by the iteration method. We demonstrate that the numerical solution and analytical solution perfectly agree with each other in the region where charge of the black hole is large, both for real and imaginary parts of the eigenfrequencies.

Joint Suzaku and Chandra observations of the MKW4 galaxy group out to the virial radius

ABSTRACT We present joint Suzaku and Chandra observations of MKW4. With a global temperature of 1.6 keV, MKW4 is one of the smallest galaxy groups that have been mapped in X-rays out to the virial radius. We measure its gas properties from its centre to the virial radius in the north, east, and north-east directions. Its entropy profile follows a power law of ∝r1.1 between R500 and R200 in all directions, as expected from the purely gravitational structure formation model. The well-behaved entropy profiles at the outskirts of MKW4 disfavour the presence of gas clumping or thermal non-equilibrium between ions and electrons in this system. We measure an enclosed baryon fraction of 11 per cent at R200, remarkably smaller than the cosmic baryon fraction of 15 per cent. We note that the enclosed gas fractions at R200 are systematically smaller for groups than for clusters from existing studies in the literature. The low baryon fraction of galaxy groups, such as MKW4, suggests that their shallower gravitational potential well may make them more vulnerable to baryon losses due to active galactic nucleus feedback or galactic winds. We find that the azimuthal scatter of various gas properties at the outskirts of MKW4 is significantly lower than in other systems, suggesting that MKW4 is a spherically symmetric and highly relaxed system.