Energy Of Gravitational Field Research Articles

Mass-Charge Metric in Curved Spacetime

In the context of gravitational objects with spherical symmetry, we derive a solution to Einstein’s field equations using two methods leading to the same result. The first is based on a stress-energy tensor that takes into account both the electric field energy of the charge and the gravitational field energy of the mass. The second is based on the mass-energy equivalence and has more general validity. We show that the metric falls within the Weyl class of metrics, representing a static and axisymmetric solution to Einstein’s field equations. The metric, which has a form similar to that of Reisser-Nordström, is used for predictions in strong fields and possibly shows better agreement with observation in high z quasars.

Calculation of Dark Matter as a Feature of Space–Time

We derive the first analytical formula for the density of "Dark Matter" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to explain classically, with inclusion of the OM, the observed coherent gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρD = λgg′2 for the density ρD of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations.

Law of Conservation of Energy of Gravitational Fields and the Gravitational Field Equation

Law of Conservation of Energy of Gravitational Fields and the Gravitational Field Equation

Law of Conservation of Energy of Gravitational Fields and the Gravitational Field Equation

Law of Conservation of Energy of Gravitational Fields and the Gravitational Field Equation

New Capabilities of the Earth’s Gravitational Field Energy in Underground Ore Mining with Convergent Technologies

New Capabilities of the Earth’s Gravitational Field Energy in Underground Ore Mining with Convergent Technologies

New Capabilities of the Earth’s Gravitational Field Energy in Underground Ore Mining with Convergent Technologies

New Capabilities of the Earth’s Gravitational Field Energy in Underground Ore Mining with Convergent Technologies

Computer Modeling in the Application to Geothermal Engineering

In the article, investigation is given of the developed mathematical models of nonequilibrium in time and distributed in space thermodynamic state of Earth’s matter from its center to its surface depending on the cases of the presence and absence of an internal source of thermal energy concentrated in the center of mass taking into account known geophysical data about the nucleus, mantle, lithosphere and atmosphere, and endogenous and exogenous heat fluxes. The objects of research are as follows: mathematical models of geothermal energy of the Earth, its internal source, and heat balance of endogenous and exogenous heat fluxes on the Earth’s surface. Research methods used are as follows: thermometry in deep wells, ground and remote sensing of heat fluxes of the Earth and the planets of the Solar System, mathematical modeling of heat exchange and thermoelastic processes from compression of Earth’s matter by gravitational field energy information and classical physical and mathematical methods, and computer modeling. The aim of research: in computer modeling to provide new mathematical models that determine the geophysical parameters of geothermal energy, which are aimed on solving problems of energy, environmental and economic security of society, using modern technical means of calculating ground and remote sensing data development of geothermal resources, and regulation of the heat balance of the ecosystem, namely: (i) study of the geological structure of the lithosphere to a depth of 10 km by remote sensing to determine the physical parameters of its layers more accurately than ground methods; (ii) development of projects of geothermal power plants on the basis of single isolated wells of a given depth with a capacity of up to 2 ÷ 3 mW of electricity on continents of the globe; (iii) real-time monitoring and forecasting of the temperature field of the atmosphere according to its physical and chemical composition. The novelty of the obtained research results: (i) developed the mathematical model of the physical process of origin and distribution in the bowels of the density of geothermal energy of the Earth from the surface to its center, which is the density of internal energy of an elementary geological object, and which increases when approaching the center of the planet; (ii) developed the mathematical model of the thermal energy source of infrared (IR) waves of the elementary geophysical object of the Earth’s interior depending on the depth of its occurrence, which allows to determine the stable generation of geothermal energy by rocks in a deep well for extraction and conversion into electricity and to study the geological structure and physical properties of the Earth’s interior; (iii) the mathematical model of heat exchange between the layers of the Earth’s subsoil with the thermal energy of infrared waves according to the laws of Fourier thermal conductivity and Stefan–Boltzmann heat transfer, which together with the geothermal energy source model allows to determine a thermal capacity of rocks in a deep well; (iv) developed the mathematical model of stable action of a source of thermal energy in the center of mass of the Earth, in the absence of which it is hard to explain the power of its endogenous infrared heat flux, parameters of geothermal energy distribution in the Earth, and the current thermodynamic state of the atmosphere, and the change in temperature of which depends on the thermophysical parameters of the physical-chemical composition of the atmosphere more than on changes in the thermal activity of the Sun; (v) determination of new numerical values: thermophysical parameters of the Earth’s interior; kinetic, potential and own gravitational energy of the Earth and own gravitational energy of the planets of the Solar System.

On the canonical energy of weak gravitational fields with a cosmological constant varLambda in mathbb {R}

We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When varLambda >0 the energy diverges, but a renormalised formula with well defined flux is obtained. We show that the renormalised energy in the asymptotically off-diagonal gauge coincides with the quadratisation of the generalisation of the Trautman–Bondi mass proposed in Chruściel and Ifsits (Phys Rev D 93:124075, arXiv:1603.07018 [gr-qc], 2016).

Force and energy in gravitational field

This is the second paper of the induction theory of gravitational field. In the first paper, a new space-time view, which considers the influence of gravity, was constructed. In the new view of time and space, classical mechanics no longer holds. In this paper, the theory of mechanics and energy is established in the new space-time relation. In this paper, the basic mechanical law in the new space-time relationship is derived from the inertial force of the observed object relative to the reference object. Second, according to this basic law, the new formulas of gravitation and electromagnetic force in the space-time relationship are derived. Third, the influence of the moving of the observation object on the force is discussed. Finally, the new law of mass energy conversion is discussed.

<i>D’addio</i> to Blackness

It is assumed here that the energy of a strong gravitational field creates non-linear effects over enclosed masses. This idea and the rigorous rules of the General Theory of Relativity output a metric that covers strong and weak gravitational fields. The proposed metric could be correct because it included the Schwarzschild’s metric as a particular case and has no singularities. Additionally, it appears here that the massive condition of the gravitational fields has properties like the so-called Dark Matter.

Null second order corrections to Casimir energy in weak gravitational field: the Schwinger's approach

We show through Schwinger's approach that in a static weak gravitational background, the Casimir Energy for a real massless scalar field obeying Dirichlet boundary conditions on rectangular plates is unaltered from it's flat space-time value, at least to second order in the gravitational parameters. The result is obtained considering an rather general class of backgrounds, adding further generality and consistency test for the previous work. The proposed result has direct consequences on earlier works in the literature that found gravity related corrections for similar setups and in the measurability of future vacuum weight experiments. We also investigate higher order corrections using a simplified toy model geometry, finding nonzero corrections in this case.

Applied Physics and Technologies in Football, The Earth´s Gravitational Field and Gravitational Energy Emission, Effects of the velocity, air viscosity (Bernoulli Effect) and turbulence (Magnus Effect) on the Football ball and Effects of the Air Resistance, Atmospheric Pressure and Gravitation in Football and Players: The Variant Pressure and Variant Gravity respect to the altitude of the place above sea level:

It is possible to play Football on Earth because of Gravity and almost stable and suitable atmospheric conditions6,7,8. It is demonstrated at this article real gravitational interaction between objects with mass with Cavendish Experiment4 which is described by means of gravitational field g through a distance action interaction2,3,6. The gravitational energy emission and effect of gravitation as gravitational redshift, deflection of light passing close to Sun4 and Perihelion Precession of Mercury4 with discovered formulas obtained by myself are demonstrated at article4: “The Fundament of Mass and Effects of Gravitation on a Particle and Light”4. They are in agreement with experiment results and with Theory of General Relativity with high accuracy4. In addition, electromagnetic energy emission (photons) with corresponding decrease in mass for electron (Maxwell´s theory) with discovered formula obtained by myself is demonstrated at research article of Variant Mass for an accelerated charged particle5. Relating Football, it is investigated related applied Physics to Football as for example Free fall, Parabolic movement, Newton Laws, Work and Energy, Principle of energy conservation, Impulse and Momentum and Collisions1,2,3. Besides, it is researched effects of air resistance in maximum distance and height reached by ball in parabolic movement in a Free kick for example. However, main objective of this article is to research about effects of variable physics as air resistance, atmospheric pressure and gravity and climatic conditions (heavy rain, wind, snow, hail, high temperature or humidity) that influence in match and in Football ball: the ball does not bend and in Football players (effects of altitude in organism)6. It is obtained and demonstrated at this article formulas of variation of atmospheric pressure and gravity respect to altitude of place or city above sea level. For other hand, it is researched effects of air viscosity (Bernoulli Effect) and turbulence (Magnus Effect) on Football ball when player kicks with high velocity. Besides, it is researched effects of variations of atmospheric pressure and gravity in Football players and Physics of devices to measure atmospheric pressure and blood pressure which is important when they plays a Football match in a high altitude city or place6,7,8. It is also researched effects of climatic conditions in a Football match. Even weather conditions (high altitude, warm climates) and location can be used in favor to make result favorable. For other hand, weather conditions are very important for development of a good Football game. Many times matches are suspended due extreme climatic conditions as heavy rain, wind, snow, hail or severe weather conditions as high temperature or humidity. However, it has been possible to apply technology to build new stadiums that are suitable for these climates and to wear respective clothing that facilitates practice of Football6,7,8. Therefore, it is also researched at this article new technology that can be applied for normal development of a Football game and to get efficient performance of Football players and all best physical conditions on Football field 6. Thus, technologies have been incorporated to know characteristics of players that are very helpful to coach and physical trainer to obtain efficiency of player and of strategies applied in Football field. It is very important to use all advantages, characteristics and resources of team at appropriate time6. In this way, it is maximized important details that can contribute to win Football match. It helps a lot technical body such as Coach, Technical assistant, Physical trainer, Doctor, Managers, Scientists, who know very well all best that team has and physical conditions, strategies and player skills that can be used in a certain Football game. Thus, Teamwork is key to this beautiful sport: The Football6,7,8. Moreover, Medical Technologies have been incorporated in Football6,7,8 and in future, new technologies can also be incorporated to monitor player performance.

Quasi-local Casimir energy and vacuum buoyancy in a weak gravitational field

Casimir energy in presence of a weak gravitational field is discussed taking into account the issues related to energy and its conservation in a curved background. It is well-known that there are inherent difficulties in defining energy in general relativity, essentially due to its non-localizability. Using the concept of quasi-local mass and energy, it is shown that it is possible to attribute a Tolman mass to a massless scalar field confined to a Casimir cavity. Such non-local mass coincides—as expected—with the Casimir energy. The present approach offers an alternative derivation of the vacuum buoyancy force acting on a Casimir cavity, confirming the results presented by Calloni et al in a series of papers devoted to explore the possibility of experimentally weighting the Casimir vacuum (the so-called Archimedes experiment).

Some features of an interaction of electromagnetic radiation quantums with a gravitational field and a problem of graviton

The problems connected to propagation of a gravitational field are considered. The law of electromagnetic radiation frequency change in gravitational field is shown. The problem of a gravitational field quantization is investigated. Energy of a graviton is found by two ways. First, on the basis of use quantum gravitational eikonal and Lagrangian of a gravitational field the energy of a solitary graviton is found. It is shown that graviton has the mass proportional to its frequency. Second, due to refusal from symmetric stresses tensor in structure of an energy-impulse tensor the quantum form of the energy-impulse tensor in Einstein's equation is found. It has allowed found the energy of a solitary graviton. Both ways of an energy graviton finding has given the identical result. It is shown that the solution of the Einsteins equation with use of the quantum form of an energy-impulse tensor for the certain direction represents the sum of a gravitational wave and a graviton. It is found out that at approach of a graviton to the massive bodies (double stars) radiating gravitational waves there is a resonant pumping of the gravitational field energy of these bodies to the gravitons with increase in their mass and frequency. It enables registration of the gravitons with the help of the detector located near to massive bodies. The assumption is made that dark energy of a gravitational field is all set of the graviton energies of a space.

Localizing energy in Fierz-Lanczos theory

We calculate energy carried by the massless spin-2 field using Fierz-Lanczos representation of the theory. For this purpose Hamiltonian formulation of the field dynamic is thoroughly analyzed. Final expression for the energy is very much analogous to the Maxwell energy in electrodynamics (spin-1 field) and displays the locality property. Known as a ``super-energy'' in gravity theory, this quantity differs considerably from the well understood gravitational field energy (represented in linear gravity by the quadratic term in Taylor expansion of the A.D.M. mass) which cannot be localized.

Buchdahl compactness limit and gravitational field energy

The main aim of this paper is essentially to point out that the Buchdahl compactness limit of a static object is given by gravitational field energy being less than or equal to half of its non-gravitational matter energy. It is thus entirely determined without any reference to interior distribution by the unique exterior solutions, the Schwarzschild for neutral and the Reissner-Nordström for charged object. In terms of surface potential, it reads as Φ(R) = (M−Q2/2R)/R ⩽ 4/9 which translates to surface red-shift being less than or equal to 3. It also prescribes an upper bound on charge an object could have, Q2/M2 ⩽ 9/8 > 1.

Null second order corrections to Casimir energy in weak gravitational field

The discussion of vacuum energy is currently a subject of great theoretical importance, specially concerning the cosmological constant problem in General Relativity. From Quantum Field Theory, it is stated that vacuum states subject to boundary conditions may generate tensions on these boundaries related to a measurable non-zero renormalized vacuum energy: the Casimir effect. As such, investigating how these vacuum states and energy behave in curved backgrounds is just natural and might provide important results in the near future. In this paper we revisit a model of the Casimir effect for a massless scalar field in a weak gravitational field background, with rectangular Dirichlet boundaries, which has been proposed and further generalized in the literature. A trick originally used to simplify calculations is shown to lead to a inconsistent value for the energy shift, and by performing explicit mode expansion we arrive at an unexpected result: null gravitational correction even at order (M/R)2, in opposition to earlier results.

AtmoFlow - Investigation of Atmospheric-Like Fluid Flows Under Microgravity Conditions

The main objective of the AtmoFlow experiment is the investigation of convective flows in the spherical gap geometry. Gaining fundamental knowledge on the origin and behavior of flow phenomena such as global cells and planetary waves is interesting not only from a meteorological perspective. Understanding the interaction between atmospheric circulation and a planet’s climate, be it Earth, Mars, Jupiter, or a distant exoplanet, contributes to various fields of research such as astrophysics, geophysics, fluid physics, and climatology. AtmoFlow aims to observe flows in a thin spherical gap that are subjected to a central force-field. The Earth’s own gravitational field interferes with a simulated central force-field with the given parameters of the model which makes microgravity conditions of $\mathrm {g}<10^{-3} \mathrm {g}_{0}$ (e.g. on the ISS) necessary. Without losing its overall view on the complex physics, circulation in planetary atmospheres can be reduced to a simple model of a central gravitational field, the incoming and outgoing energy (e.g. radiation) and rotational effects. This strongly simplified assumption makes it possible to break some generic cases down to test models which can be investigated by laboratory experiments and numerical simulations. Varying rotational rates and temperature boundary conditions represent different types of planets. This is a very basic approach, but various open questions regarding local pattern formation or global planetary cells can be investigated with that setup. A concept has been defined for developing a payload that could be installed and utilized on-board the International Space Station (ISS). This concept is based on the microgravity experiment GeoFlow, which has been conducted successfully between 2008 and 2016 on the ISS. This paper addresses the scientific goals, the experimental setup, the concept for implementation of the AtmoFlow experiment on the ISS and first numerical results.

RETRACTED ARTICLE: Development of a safe antiparasitic against scuticociliates (Miamiensis avidus) in olive flounders: new approach to reduce the toxicity of mebendazole by material remediation technology using full-overlapped gravitational field energy

RETRACTED ARTICLE: Development of a safe antiparasitic against scuticociliates (Miamiensis avidus) in olive flounders: new approach to reduce the toxicity of mebendazole by material remediation technology using full-overlapped gravitational field energy

The Relationship between the Energy of Gravitational Field and the Representative Pseudotensor

The Relationship between the Energy of Gravitational Field and the Representative Pseudotensor