Source Of Gravity Research Articles

Insights on the structural framework of the Egyptian Eastern Desert derived from edge detectors of gravity data

Advanced geophysical techniques are used on Bouguer gravity data to unravel the structural complexity of the Eastern Desert. Using methods such as tilt angle (TA), enhanced horizontal gradient amplitude (EHGA), lineament analysis, and 2Dcrustal modeling, we are able to differentiate between deep and shallow gravity sources and delineate the area’s geologic features. Using fast Fourier transform, positive and negative anomalies are identified. The positive anomalies are interpreted as uplifted block, anticline features, or intrusive occurrences of denser rocks, whereas the negative anomalies are interpreted as downfaulted blocks, providing crucial insights. Lineament analysis suggests that the predominant tectonic force that shaped the area is in the northwest direction. Integration of TA and EHGA reveals nuanced structural patterns. The constructed structural map indicates a network of uplifted and downfaulted blocks intersected by strike-slip faults with a northeast trend. The 2D crustal modeling illustrates the diverse composition of granitic and basaltic rocks, with a discernible thinning of the continental crust toward the Red Sea offshore area. This significantly advances the understanding of the Eastern Desert’s geologic evolution, offering valuable insights into the tectonic processes and crustal dynamics.

The 3D Crustal Structure of the Wilkes Subglacial Basin, East Antarctica, Using Variation of Information Joint Inversion of Gravity and Magnetic Data

AbstractDirect geological information in Antarctica is limited to ice free regions along the coast, high mountain ranges, or isolated nunataks. Therefore, indirect methods are required to reveal subglacial geology and heterogeneities in crustal properties, which are critical steps toward interpreting geological history. We present a 3D crustal model of density and susceptibility distribution in the Wilkes Subglacial Basin (WSB) and the Transantarctic Mountains (TAM) based on joint inversion of airborne gravity and magnetic data. The applied “variation of information” technique enforces a coupling between inferred susceptibility and density, relating these quantities to the same gravity and magnetic sources to give an enhanced inversion result. Our model reveals a large body located in the interior of the WSB interpreted as a batholithic intrusive structure, as well as a linear dense body at the margin of the Terre Adélie Craton. Density and susceptibility relationships are used to inform the interpretation of petrophysical properties and the reconstruction of the origin of those crustal bodies. The petrophysical relationship indicates that the postulated batholitic intrusion is granitic, but independent from the Granite Harbor Igneous Complex described previously in the TAM area. Emplacement of a large volume of intrusive granites can potentially elevate local geothermal heat flow significantly. Finally, we present a new conceptual tectonic model based on the inversion results, which includes development of a passive continental margin with seaward dipping basalt horizons and magmatic underplating followed by two distinct intrusive events associated with the protracted Ross Orogen.

Evaluation of the Structural and Tectonic Boundaries Using Gravity Method at Diyala Government, NE Iraq

Gravity data were analyzed using the total horizontal derivative approach to locate fault lines at the NE of Diyala, Iraq. The results revealed that the structural tendencies of the investigated region are in parallel directions (NW-SE) and (NE-SW). The THD lineaments show that the dominated structures are in NW-SE, and low-presence structures are NE-SW trends with values of N15W, N35W, N45W, N65W, N15E, N33W, N43W, and N45E. The shallow source of gravity is approximately 4 km and may be associated with the sedimentary cover of the lower Miocene to Tertiary periods. THD approach map revealed three major subsurface structures (Al-Mansuriya, Khashim Al-Ahmer, and Injana), where Al-Mansuriya formed an asymmetrical fold and extended about 25 Km with a width of about 5 Km.

The torsion of stellar streams and the overall shape of galactic gravity’s source

Context. Flat rotation curves, v(r), are naturally explained by elongated (prolate) dark matter (DM) distributions, and we have provided competitive fits to the SPARC database. To further probe the geometry of the halo, or the equivalent source of gravity in other formulations, one needs observables outside the galactic plane. Stellar streams, poetically analogous to airplane contrails, but caused by tidal dispersion of massive substructures such as satellite dwarf galaxies, would lie on their own plane (consistently with angular momentum conservation) should the DM-halo gravitational field be spherically symmetric. Tracks resembling entire orbits are seldom available because their periods are commensurable with Hubble time, with streams often presenting themselves as short segments. Aims. Therefore, we aim to establish stellar stream torsion, a local observable that measures the deviation from planarity in differential curve geometry, as a diagnostic providing sensitivity to aspherical DM distributions and ensuring the use of even relatively short streams. Methods. We performed small-scale simulations of tidally distorted star clusters to check that indeed a central force center produces negligible torsion, while distorted halos can generate it. Turning to observational data, we identified among the known streams those that are at the largest distance from the Galactic center, and that are likely not affected by the Magellanic clouds, as the most promising for the study, and by means of polynomial fits we extracted their differential torsion. Results. We find that the torsion of the few known streams that should be sensitive to most of the Milky Way’s DM halo is much larger than expected for a central spherical bulb alone. This is consistent with the nonsphericity of the halo. Conclusions. Future studies of stellar stream torsion with larger samples and further out of the galactic plane should be able to extract the ellipticity of the halo to see whether it is just a slight distortion of a spherical shape or whether it rather resembles a more elongated cigar.

The complete exterior spacetime of spherical Brans-Dicke stars

We derive the complete expression for the Brans Class I exterior spacetime explicitly in terms of the energy and pressures profiles of a stationary spherisymmetric gravity source. This novel and generic expression is achieved in a parsimonious manner, requiring only a subset of the Brans-Dicke field equation and the scalar equation. For distant orbiting test particles, this expression promptly provides a simple, closed and exact formula of the γ Eddington parameter, which reads γexact=ω+1+(ω+2)Θω+2+(ω+1)Θ, where Θ is the ratio of the star's “total pressure” integral over its energy integral. This non-perturbative result reproduces the usual Post-Newtonian ω+1ω+2 expression in the case of a “Newtonian star”, in which the pressure is negligible with respect to the energy density. Furthermore, it converges to the General Relativity value (γGR=1) as the star's equation of state approaches that of ultra-relativistic matter (in which case Θ approaches 1), a behavior consistent with broader studies on scalar-tensor gravity. Our derivation underscores the essence of these results involving (1) the key relevant portion of the Brans-Dicke field equations, (2) the uniqueness of the Brans Class I vacuum solution for the non-phantom action, viz. ω>−3/2, and (3) the involvement of only two free parameters in this solution, hence requiring two quantities (energy and pressure integrals) of the mass source to fully characterize the solution. From a practical standpoint, it elucidates how a given stellar interior structure model determines the star's exterior gravitational field and impacts the motions of light objects (such as planets and accretion disks) orbiting it.

A gravitational eye: a method for extracting maximum information from gravitational potentials

Gravity measurements have uses in a wide range of fields including geological mapping and mine-shaft inspection. The specific application under consideration sets limits on the survey and the amount of information that can be obtained. For example, in a conventional gravity survey at the Earth’s surface a gravimeter is translated on a two-dimensional planar grid taking measurements of the vertical component of gravity. If, however, the survey points cannot be chosen so freely, for example if the gravimeter is constrained to operate in a tunnel where only a one-dimensional line of data could be taken, less information will be obtained. To address this situation, we investigate an alternative approach, in the form of an instrument which rotates around a central point measuring the gravitational potential or its radial derivative on the boundary of a sphere. The ability to record additional components of gravity by rotating the gravimeter will give more information than obtained with a single measurement traditionally taken at each point on a survey, consequently reducing ambiguities in interpretation. We term a device which measures the potential, or its radial derivatives, around the surface of a sphere a gravitational eye. In this article we explore ideas of resolution and propose a thought experiment for comparing the performance of diverse types of gravitational eye. We also discuss radial analytic continuation towards sources of gravity and the resulting resolution enhancement, before finally discussing the possibility of using cold-atom gravimetry and gradiometry to construct a gravitational eye. If realised, the gravitational eye will offer revolutionary capability enabling the maximum information to be obtained about features in all directions around it.

Gravity: Where Quantum Physics and Classical Physics finally merge

In this 3rd paper of a triptych on quantum theory regarding gravity, quantum, and classical physics are merged seamlessly-however with conclusions deviating from classical physics regarding singularities, space-curvature, and graviton. Mathematically, singularities (Schwarzschild, Droste) vanish by proper definition of the gravity source and field descriptions acquiring full validity at the Planck scale. Space(-time) curvature is shown to be geodesic-trajectory curvature by (energy) objects in the field of (a) gravity source(s). The gravity field is found to be a scalar field in which the trajectories are defined only by the principle of least action (LaGrange, Feynman) by compensation of accelerations due to different physical causal sources of acceleration. The graviton is argued to be a massive Higgs-type scalar boson with ubiquitous presence since the creation of quantum and clustered mass in the universe: the influence of a settled gravity field on mass (in) entering this field, therefore, is instantaneous, i.e., unlike a vector boson description. Gravity waves, occurring in mergers/transitions of mass, are defined by changes in time of the gravity field (at max. c m/s) in space and only become observable when substantial mass/energy is involved due to the weakness and spatial decay of gravity fields. All mathematics (e.g. integral transformations, vector space, etc) and related operators in the paper are part of the Abelian group for validity at the Planck scale. Results thus constitute the description of gravity on all scales.‎‎

Experimental research on the thermal performance of the dry conduction plate for multi-point electronic chips

This paper designs a dry conductive heat dissipation method using several parallel heat pipes to solve the difficulty of the thermal management problem of multi-point electronic chips. The heat sources are distributed along the heat pipe, whose heat is efficiently conducted from the middle to the cold plate on the two sides. The effect of gravity, flow rate, and heat source distributions on the heat transfer performance is studied. The testing data indicated that gravity has less effect on the conduction performance of heat pipes for the cooling on two sides. As the heat sources concentrate in the centre, the heat pipe temperature difference between the centre and the side increases under the same transmission power. The results demonstrated that the two-side cooling and multi-point distribution heat conduction method is conducive to improving the thermal management capability under different inclination angles.

Universe inflation and nonlinear electrodynamics

We analyse the inflation of the universe when the source of gravity is electromagnetic fields obeying nonlinear electrodynamics, with two parameters and without singularities. The cosmology of the universe with stochastic magnetic fields is considered, and the condition for universe inflation is obtained. It is demonstrated that singularities of energy density and pressure are absent as the scale factor approaches zero. When the scale factor goes to infinity, we have the equation of state for the ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of the universe shows that at large time scales, the scale factor corresponds to the radiation era. The duration of universe inflation is also analysed. We study the classical stability and causality by computing the speed of sound. Cosmological parameters including the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the running of the spectral index αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _s$$\\end{document} are evaluated.

Dimensionally continued black holes sourced by a conformally coupled scalar field and Chaplygin-like dark fluid

In this paper, we study the higher dimensional black holes of Lovelock gravity coupled with a conformal scalar field. The matter source of gravity is suggested to come from the Chaplygin-like dark fluid, i.e., the hybrid of a dark matter and dark energy. We primarily focus on dimensionally continued gravity where the coupling parameters are reduced into two independent parameters, i.e., the Newtonian and cosmological constants. In this specific case of Lovelock gravity, we derive the metric function that describes the hairy black holes surrounded by dark fluid. For these objects, the basic thermodynamic quantities are worked out. We discuss how the unified dark fluid affects both local and global thermodynamic stabilities. We also demonstrate that the radiation spectrum is proportional to the change in entropy of the hairy black holes. Lastly, the hairy black holes in the presence of Chaplygin-like dark fluid are briefly investigated within the context of generic Lovelock gravity.

Extension of the Schwarzschild black hole solution in f(R) gravitational theory and its physical properties

The successes of f(R) gravitational theory as a logical extension of Einstein’s theory of general relativity (GR) encourage us to delve deep into this theory and continue our study to attempt to derive an extension of the Schwarzschild black hole (BH) solution. In this study, in order to solve the output nonlinear differential equation, we closed the form of the system by assuming the derivative of f(R) with respect to the scalar curvature R to have the form F(r)=df(R(r))dR(r)=1-αr4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(r)=\\frac{\ extrm{d}f(R(r))}{\ extrm{d}R(r)}=1- \\frac{\\alpha }{r^4}$$\\end{document}, where α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is a dimensional constant. Our study shows that when α→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 0$$\\end{document}, we obtain the Schwarzschild BH solution of GR assuming some constraints on the constant of integration, and if these constraints are bounded, we obtain the anti-de Sitter (AdS)/de Sitter (dS) spacetime. For the general case, i.e., when α≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e 0$$\\end{document}, we obtain a BH solution that tends asymptotically to AdS/dS spacetime. Moreover, we derive the timelike and null particle geodesics of the BH solution studied in this article. The equation of motion and effective potential of test particles are calculated to study the stability of radial orbits (trajectories). The energy and angular momentum are calculated to study the circular motion and stability of circular orbits. We also derive the stability condition using the geodesic deviation. Moreover, we discuss the physics of the output BH solutions through calculation of the thermodynamic quantities including entropy, the Hawking temperature, and Gibbs free energy. Finally, we check the validity of the first law of thermodynamics applied to the BH of this study. Although we can derive a Schwarzschild black hole solution in the lower order of f(R), specifically when f(R)=R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)=R$$\\end{document}, where the gravitational mass is generated from the source of gravity, we demonstrate that in the higher orders of f(R), when f(R)≠R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)\ e R$$\\end{document}, the source of gravity is attributed primarily to higher-order corrections, and the source of gravity that was originally derived from the Schwarzschild black hole has ceased to be dominant.

QUANTUM PARTICLE OF MATTER (CHARGE) AS A FUNDAMENTAL SOURCE OF GRAVITY AND MASS OF MATTER IN NATURE

One of the most intriguing problems of modern physics is the search of particles beyond the Standard Model and the creation of quantum theory of gravity. To these problems, namely to the problem of quantum description of gravitation the closest attention is paid. The importance of applying the Standard Model to describe three types of force physical interactions involving elementary particles is beyond doubt. These particles are active participants of physical processes of electromagnetism, strong and weak interactions. However, there is still an open question about the meaning and role in nature of gravitation. Moreover, it is not clear how gravity interacts with matter of any mass and what is the essence of these differences. Also, there is no answer to the question about the meaning in the nature of the discreteness factor and the possibility of real quantisation of gravitation. Besides, it is unknown whether in the surrounding world there exists a quantum of gravitational energy – graviton and what is its actual energy. To explain the significance of gravity on cosmic scales, the General Theory of Relativity of A. Einstein was applied, which describes the curvature of space around stars and planets. However, this theory affects only the interaction of large masses of matter and does not apply to quantum objects in the form of atoms and elementary particles. As for the objective application in the scientific literature of other known theories of gravity, including its quantum forms, they all use a mathematical apparatus where the criterion of quantum discreteness – Planck’s constant – is missing. The apparent incompleteness of research in the field of development and creation of an objective theory of gravitation and its quantum forms requires practical application of the existing apparatus of quantum mechanics for realisation of this scientific direction. Taking into account such a view, it is necessary to consider the possibility of applying the thermodynamic nature of the movement of gravity in nature, where it is necessary to raise the issue of the existence and manifestation of the quantum form of gravitational energy in nature, the source of which may be a quantum particle of matter (charge) outside the Standard Model. Due to the unique coincidence of physical properties of quantum particles of matter (charge) and physical principles inherent in the operation of any collider, it is possible to use the Large Hadron Collider to study the properties of quantum particles of matter (charge) as a source of gravity in nature. Keywords: gravity, quantum particle of matter (charge), energy and Planck’s constant, Schrödinger equation, Heisenberg uncertainty, graviton, oscillator of gravity of matter (charge), de Broglie wave, laws of gravity, converging effect of gravitational fields, standard model, collider

Inertia, gravity and the meaning of mass

Our concept of mass has evolved considerably over the centuries, most notably from Newton to Einstein, and then even more vigorously with the establishment of the standard model and the subsequent discovery of the Higgs boson. Mass is now invoked in various guises depending on the circumstance: it is used to represent inertia, or as a coupling constant in Newton’s law of universal gravitation, and even as a repository of a mysterious form of energy associated with a particle at rest. But recent developments in cosmology have demonstrated that rest-mass energy is most likely the gravitational binding energy of a particle in causal contact with that portion of the Universe within our gravitational horizon. In this paper, we examine how all these variations on the concept of mass are actually interrelated via this new development and the recognition that the source of gravity in general relativity is ultimately the total energy in the system.

The big-bang started from nothing: Not the initially hot cosmic matter, but a positive vacuum pressure made the universe explode!

Mankind all over its past epochs did ask the question, how this huge and materially impressive universe could ever have started its existence. The standard dogmatic answer presently given by the majority of modern cosmologists is: By the Big-Bang! - i.e. that initial explosion of the central highly condensed world matter system! But why - it could be asked - should this system have exploded at all? Perhaps this popular BB-hypothesis of a general and global cosmic explosion creating the world is especially suggestive just in these days of wars and weapons all around. Nevertheless to declare such an initial event as the begin of the universe unexpectedly turns out to be extremely hard to explain when based on purely physical grounds. Though it is easy to envisage a granate explosion causing matter to fly apart in all directions from the center of the explosion, but as a total surprise it is extremely hard to explain which physically operating forces or pressures might be responsible to drive the initially highly compacted cosmic matter agglomeration apart of each other. If the explosion forces are imagined as due to acting thermal pressure forces of normal massive matter, then the needed pressures cannot be due to the extremely high temperatures of the condensed matter, because the thermal energy of relativistically hot matter, as relativity theory tells us, will act as an additional source of gravity, i.e. making matter even "heavier"! Hence this just impedes the initial mass agglomeration to explode and fly apart. As we shall show in the following article the explosive BB- event can only physically be explained, if the necessary pressure is not conventionally realized by the temperature of the gravitating matter, but to the contrary by the immaterial cosmic vacuum. In fact - as we shall demonstrate here - without a cosmic vacuum pressure, the so-called Big-Bang never at all could have happened. Certainly vacuum pressure up to the present days of cosmology still is a fully speculative subject, but it will become evident in the following article, that without this highly speculative, physically handable quantity a primordial Big-Bang would not have happened at all.

Constraining the Structure under Lunar Impact Basins with Gravity

The lunar gravity field is used to estimate and constrain the depth of mass anomalies under 19 major lunar impact basins. We use radial gravitational spectra, consisting of accelerations computed either per spherical harmonic degree or cumulatively, at surface locations to obtain the distribution of the gravity signal with spherical harmonic degree and, by implication, to the likely depth below the surface. The results provide estimates for the maximum likely depths of the primary component to the mass anomalies under 19 basins. We find that the maximum depths of the primary source of mascon gravity on the lunar nearside are deeper than the depths for those on the farside when South Pole–Aitken (SPA) is excluded. All basin mass anomalies on the lunar nearside are in the mantle. The maximum depth of the primary source of the mass anomalies is <80 km, with the exception of SPA, whose dominant mass signature lies at a maximum depth of >200 km beneath the surface. The upper 20 km under all basins is largely devoid of anomalies, reflecting predominantly mixing and relaxation associated with impact melt combined with ejecta fallback, as well as homogenization associated with post-basin formation impact bombardment. Except for SPA, all basin anomalies merge with the deep interior at ∼150 km or below, indicating the depth penetration of disruption of the density structure of the lunar interior associated with impact bombardment.

A linear low effort stabilization method for the Euler equations using discontinuous Galerkin methods

SummaryWe present a novel and simple yet intuitive approach to the stabilization problem for the numerically solved Euler equations with gravity source term relying on a low‐order nodal Discontinuous Galerkin Method (DGM). Instead of assuming isothermal or polytropic solutions, we only take a hydrostatic balance as a given property of the flow and use the hydrostatic equation to calculate a hydrostatic pressure reconstruction that replaces the gravity source term. We compare two environments that both solve the Euler equations using the DGM: deal.II and StormFlash. We utilize StormFlash as it allows for the use of the novel stabilization method. Without stabilization, StormFlash does not yield results that resemble correct physical behavior while the results with stabilization for StormFlash, as well as deal.II model the fluid flow more accurately. Convergence rates for deal.II do not match the expected order while the convergence rates for StormFlash with the stabilization scheme (with the exceptions for the L errors for momentum) meet the expectation. The results from StormFlash with stabilization also fit reference solutions from the literature much better than those from deal.II. We conclude that this novel scheme is a low cost approach to stabilize the Euler equations while not limiting the flow in any way other than it being in hydrostatic balance.

Gravity Application to Obtain the Subsurface Structures of Mafid Region, North Nasser Lake, Egypt

This study aims to define structures below the surface of the Mafid Area by using gravity data interpretation. Estimates were made for the contact density contrast and the gravity sources' depths. The source depths and contact locations were estimated using the Euler deconvolution method. Structures with shallow and deep seats were also assessed using power spectrum analysis. The structure at a shallow depth was between 0.032 km and 0.437 km. According to the Euler deconvolution method's outcomes, the basement may be below ground in the area's southernmost portion, and it has grown to between 200 and 300 meters in the area's northernmost portion. Multiple faults affect the region that most trends in the NW-SE, NNW-SSE, E-W, NE-SW, and NNE-SSW directions, according to the structural map that has been interpreted. Three-dimensional gravity modelling shows that the upper surface depth of crystalline rocks (Basement rocks ) ranges from 170 to 374 m.

The universe generated by the explosion of the primordial cosmic vacuum!

Over all its epochs mankind always has put the fundamental question: When and why at all did the universe start its existence? Most cosmologists univocally do answer this question with the standard dogmatic answer: By the Big-Bang! - namely by the initial explosion of an extremely concentrated world matter system! This standard paradigm of a general and global explosion creating this world obviously appears to be highly suggestive, though such an explosive event unexpectedly turns out to be extremely hard to understand on purely physical grounds. This is because it is extremely hard to explain which pressures might be responsible to drive the initially highly compacted cosmic matter apart. The somewhat naive idea that the required explosion forces in view of the extremely high temperatures and the extreme highly compacted primordial cosmic matter, are due to extreme initial pressure forces does not solve the problem, because relativistically hot matter will be just an additional source of gravity, hence just contrary to the expectations impedes matter to fly apart. It can, however, be shown that the expected explosive BB- event can only physically occur, if the required pressure is not established by the temperature of gravitating matter, but by the cosmic vacuum. In fact we show that without this cosmic vacuuum pressure, the so-called Big-Bang never could have happened, even though vacuum pressure up to the present days of cosmology, still may be a rather speculative subject. In the following article we shall demonstrate that with a revised understanding of this highly speculative quantity one can explain the present universe as an explosion of the primordial cosmic vacuum followed by a succesive materialisation of this vacuum into cosmic matter at the ongoing cosmic expansion.

Sectorial Paley–Wiener theorem

We consider the problem of restoring a two‐dimensional convex source of gravity based on values of its potential function on a union of half‐planes. With that aim we prove a Paley–Wiener type theorem for functions of exponential type in a sector. In particular, we find the maximal set of analytic continuation whose complement is convex inside a sector. Our result serves as a sectorial analog of G. Polya's indicator theorem. It corrects, simplifies, and extends a result of M. Morimoto. It also improves a related result of M. Dzhrbashyan and A. Avetisyan.

Never there would have been a cosmic big-bang without the action of a vacuum pressure!

The fundamental and always resurrecting question of mankind, how this universe could ever have started its existence, is answered by most cosmologists with the standard dogmatic answer: By the Big-Bang! - that initial explosion of the world matter system! Perhaps this standard paradigm of a general and global explosion creating the world, especially in these days of wars and weapons all around, seems to be highly suggestive. Nevertheless such an event unexpectedly turns out to be extremely hard to explain as based on purely physical grounds. It indeed seems easy to imagine a granate explosion causing matter to fly apart in all directions, but it is extremely hard to explain which pressures might be responsible to drive the initially highly compacted cosmic matter apart of eachother. If the explosion forces are imagined as due to pressure forces then these pressures cannot be due to extremely high temperatures of matter, because relativistically hot matter will be just an additional source of gravity, hence just impeding matter to fly apart. As we shall show in the following article the explosive BB- event can only physically be explained, if the necessary pressure is not manifested by the gravitating matter, but by the cosmic vacuum. In fact without the cosmic vacuuum pressure, the so-called Big-Bang never could have happened. Vacuum pressure, however, up to the present days of cosmology, still is a fully speculative subject, but it will become evident in the following article, that without this highly speculative quantity there could not have happened a Big-Bang at all.