Class Of Gravitational Theories Research Articles

Extension of Newton's classical theory of gravitation to the Universe: new law of cosmological force as an addition to Newton's law of gravitation

Extension of Newton's classical theory of gravitation to the Universe: new law of cosmological force as an addition to Newton's law of gravitation

Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory

We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time t constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite time-t interval, t being the cosmological time, i.e. the time of an observer located far away from the collapsing cloud. The presence of this vanishing lapse endpoint implies the necessity of a UV completion to describe the physics inside the resulting black hole. On the other hand, since the corresponding cosmic time t is infinite, VCDM can safely describe the whole history of the universe at large scales without knowledge of the unknown UV completion, despite the presence of the so-called shadowy mode.

Космология между физикой и философией

It is shown that the canonical cosmological model of the Universe – Big Bang Theory (BBT) contains unacceptably many unsolvable contradictions either to facts, or logic, or, finally, to physics. They can be categorized into several groups: 1) unacceptable, 2) unsubstantiated, and 3) multivalued. To the unac­ceptable fragments of the concept of BBT it is reasonable to include ideas about: a) “singularity”; b) “cosmological inflation”; c) “infinite death of Nature”. Un­reasonable include: a) hypothesis about materiality of space-time, b) recognition of the possibility of their birth and death. Among the interpretations admitting other ones with high probability are: a) the principle of equivalence of the iner­tial and gravitational masses, b) the gravitational redshift, c) the effect of deflec­tion of light near large masses. Among the interpretations, which do not cause doubts, it is possible to note an explanation of the black hole nature, following from Newton’s classical theory of gravitation. The source of insoluble contradic­tions of the BBT was Einstein’s General Theory of Relativity (GTR), which was created on the basis of strictly deterministic classical mechanics. The underde­velopment of quantum mechanics at the beginning of the twentieth century mis­led the author of the GTR about the equivalence of inertial and gravitational masses. A consequence of this delusion was the erroneous recognition of space-time as material substances. It, in turn, led to a lot of unexplained events in the past of the Universe, and fantastic predictions about its future. But the most striking thing that distinguishes GTR is its violation of the fundamental law of conservation of energy, which cosmological theorists turn a blind eye to. This allows us to consider it a legacy of classical physics of the nineteenth century, unsatisfactory from the perspective of probabilistic physics of the twenty-first century.

Gravitation, Density, Black Holes and Spatial Quantization

Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.

A Novel Explanation for the Arrangement of the Universe–Solar System–Planets–Earth. Part 3

New ideas are presented about the nature of the evolution of the Universe, which call for a deeper scientific understanding and reassessment of the existing views on the so-called Big Bang cosmological model. According to this model, the Universe has now been expanding for ~20 Ga, with the lightest elements forming during the first few seconds at T ~ 109 K as a result of nuclear fusion. These elements are H, D, and 3,4He; at first, hydrogen turns into helium, and then helium transforms into carbon, oxygen, nitrogen, etc., up to iron group elements. The probability is examined of the action of attraction forces due to electromagnetic interaction of rotating charged baryonic particles, instead of the classical Newton theory of gravitation, i.e., the law describing gravitational interaction in classical mechanics. A discussion is provided of the nature and role of black holes in the Universe, which are seen as an integral and obligatory part of all physical structures of the Cosmos. So far, no theory has been able to fully describe the internal structure of black holes; however, as follows from the Planck and Boltzmann laws, these holes are a perpetuum mobile of evolution for the entire Universe, controlling the transformation mechanism through electromagnetic resonance oscillations of the entire cosmic ether (like the human brain), which propagate across all structures of the Universe. Space objects are Earth-like planets with a solid core, liquid mantle, and a hard crust, above which the atmosphere immediately begins; gas giants with no solid surface (a substantial part of them is the atmosphere, which at low altitudes turns into a liquid due to increased pressure, while there is no clear boundary between the liquid ocean and the atmosphere); and stars, all of which have a solid core and poles synchronized with black holes. Although our conceptions about the existence of dark matter and dark energy in the Universe still remain the most mysterious ones, we argue that the bulk of matter and energy is concentrated in cosmic–plasma electromagnetic fields (>95%). All stars and planets must be increasing in volume with time while retaining their angular momentum and position in space. Both space and time are equivalent to each other and are the most uncertain and multivector universal functions of the Universe. They change simultaneously and proportionally with the form of existence of matter, which inevitably leads to the emergence of a fundamentally new quality—life. Living beings evolve and acquire spirituality, i.e., the ability to cognize not only themselves but the surrounding world. However, space–time is an extremely complex system, yet to be understood by new generations of scientists: physicists, cosmologists, and others.

Einstein-Nordström theory as a frame for a theory of quantum gravity

The Einstein-Nordström theory is proposed as a framework for a theory of quantum gravity, dividing the space of physical reality into a part longer than the radius of a proton and described by Einstein’s classical field theory of gravitation and one smaller than the radius of a proton, for the Yang–Mills theories of elementary particles, with both of them separated by a common event horizon. This division of space is reflected into the division of classical Newtonian point particle dynamics and Helmholtz line vortex dynamics, leading to a non-dimensional number for stable vortex line configurations, as for the stability of the Karman vortex street in classical fluid dynamics, and here for the non-dimensional mass ratio, of the Higgs particle mass to the Planck mass. Setting the vortex core radius of the line vortices equal to the Planck length, Lorentz invariance is broken for energies larger than the Planck energy, whereby the underlying more fundamental symmetry is the Galilei group, establishing a preferred reference system. With the Hamiltonian operator there commuting with the particle number operator, this permits the existence of negative, as well as positive masses.

Selective Realism and the Framework/Interaction Distinction: A Taxonomy of Fundamental Physical Theories

Following the proposal of a new kind of selective structural realism that uses as a basis the distinction between framework and interaction theories, this work discusses relevant applications in fundamental physics. An ontology for the different entities and properties of well-known theories is thus consistently built. The case of classical field theories—including general relativity as a classical theory of gravitation—is examined in detail, as well as the implications of the classification scheme for issues of realism in quantum mechanics. These applications also shed light on the different range of applicability of the ontic and epistemic versions of structural realism.

Theoretical implications of a classical unitary theory of gravitation and the electromagnetism in the explaining of the planetary perihelion precession and the super-heavy astroparticles

The paper is based on the Galilean relativity and on a theory of cold genesis of matter and fields (CGT), which explains the gravitation and the electro-magnetic interaction by a charge model of static type, with spherical distribution of field quanta, compatible with the Fatio/LeSage model of gravitation and with the observations regarding the light beam deviation in the sun’s gravitic field. The planetary perihelion precession is explained as consequence of the dynamogene component of the gravitation force and of the high density of the sub-quantum medium, given by etheronic winds, in CGT, the electro-dynamic Lorentz’ force resulting as quantum Magnus force. It is shown that the principle of physics laws invariance may be maintained by considering also the d’Alembert paradoxe, without the conclusion of the light speed invariance, of the null rest mass of photons/bosons and of the Einsteinian speed –depending mass increasing, resulting also the possibility to explain the super-heavy astro-particles, experimentally detected, by a model of gammonic or mesonic Bose-Einstein condensate forming and pearlitizing, with the non-destructive collapsing of the formed sub-clusters, according to the cold genesis model of astroparticles of CGT.

Gravity in extreme regions based on noncommutative quantization of teleparallel gravity

In this paper, a noncommutative gravitational theory is constructed by applying Moyal deformation quantization and the Seiberg–Witten map to teleparallel gravity, a classical gravitational theory, as a gauge theory of local translational symmetry. Since our model is based on teleparallel gravity, it is an extremely simple noncommutative gravitational theory. We also clearly divide the role of the products, such that the metric is responsible for the rule of the inner product (which is calculated by taking the sum over the subscripts) and the Moyal product is responsible for tensor and field noncommutativity. This solves problems related to the order of the products and the relationship between the metric and the Moyal product. Furthermore, we analyze the cosmic evolution of the very early universe and the spacetime features around black holes using the constructed noncommutative gravitational theory, and find that gravity acts repulsively in the extreme region where its quantum effects become prominent.

Minimally modified theories of gravity: a playground for testing the uniqueness of general relativity

In a recent paper [1], it was introduced a new class of gravitational theories with two local degrees of freedom. The existence of these theories apparently challenges the distinctive role of general relativity as the unique non-linear theory of massless spin-2 particles. Here we perform a comprehensive analysis of these theories with the aim of (i) understanding whether or not these are actually equivalent to general relativity, and (ii) finding the root of the variance in case these are not. We have found that a broad set of seemingly different theories actually pass all the possible tests of equivalence to general relativity (in vacuum) that we were able to devise, including the analysis of scattering amplitudes using on-shell techniques. These results are complemented with the observation that the only examples which are manifestly not equivalent to general relativity either do not contain gravitons in their spectrum, or are not guaranteed to include only two local degrees of freedom once radiative corrections are taken into account. Coupling to matter is also considered: we show that coupling these theories to matter in a consistent way is not as straightforward as one could expect. Minimal coupling, as well as the most straightforward non-minimal couplings, cannot be used. Therefore, before being able to address any issues in the presence of matter, it would be necessary to find a consistent (and in any case rather peculiar) coupling scheme.

Bulk phase shift, CFT Regge limit and Einstein gravity

The bulk phase shift, related to a CFT four-point function, describes two-to-two scattering at fixed impact parameter in the dual AdS spacetime. We describe its properties for a generic CFT and then focus on large N CFTs with classical bulk duals. We compute the bulk phase shift for vector operators using Regge theory. We use causality and unitarity to put bounds on the bulk phase shift. The resulting constraints bound three-point functions of two vector operators and the stress tensor in terms of the gap o the theory. Similar bounds should hold for any spinning operator in a CFT. Holographically this implies that in a classical gravitational theory any non-minimal coupling to the graviton, as well as any other particle with spin greater than or equal to two, is suppressed by the mass of higher spin particles.

Alternative Reflections on Podkletnov's Gravity Experiments

In the 1990s Eugene Podkletnov published results of experiments which in his opinion proved the effect of gravity shielding. The present paper is concerned with the question, what results may be expected from such experiments on the basis of the "Alternative Reflections on Gravitation", (ARG). The results of these considerations are in excellent agreement with those experiments. There, however, appeared no gravity shielding, but the production of additional, highly focused repulsive forces. Such curious results can hardly be explained on the basis of classical gravitational theories, which deal with attractive forces and their strong decrease with distance.

The Mathematical Validity of the f(R) Theory of Modified Gravity

We investigate the Cauchy problem for the f(R) theory of modified gravity, which is a generalization of Einstein’s classical theory of gravitation. The integrand of the Einstein-Hilbert functional is the scalar curvature R of the spacetime, while, in modified gravity, it is a nonlinear function f(R) so that, in turn, the field equations of the modified theory involve up to fourth-order derivatives of the unknown spacetime metric. We introduce here a formulation of the initial value problem in modified gravity when initial data are prescribed on a spacelike hypersurface. We establish that, in addition to the induced metric and second fundamental form (together with the initial matter content, if any), an initial data set for modified gravity must also provide one with the spacetime scalar curvature and its first-order time-derivative. We propose an augmented conformal formulation (as we call it), in which the spacetime scalar curvature is regarded as an independent variable. In particular, in the so-called wave gauge, we prove that the field equations of modified gravity are equivalent to a coupled system of nonlinear wave–Klein-Gordon equations with defocusing potential. We establish the consistency of the proposed formulation, whose main unknowns are the conformally-transformed metric and the scalar curvature (together with the matter fields) and we establish the existence of a maximal globally hyperbolic Cauchy development associated with any initial data set with sufficient Sobolev regularity when, for definiteness, the matter is represented by a massless scalar field. We analyze the so-called Jordan coupling and work with the so-called Einstein metric, which is conformally equivalent to the physical metric —the conformal factor depending upon the unknown scalar curvature. A main result in this paper is the derivation of quantitative estimates in suitably defined functional spaces, which are uniform in term of the nonlinearity f(R) and show that spacetimes of modified gravity are ‘close’ to Einstein spacetimes, when the defining function f(R) is ‘close’ to the Einstein- Hilbert integrand R. We emphasize that this is a highly singular limit problem, since the field equations under consideration are fourth-order in the metric, while the Einstein equations are second-order only. In turn, our analysis provides the first mathematically rigorous validation of the theory of modified gravity.

Black Holes or Dark Stars—What Follows from the General Relativity Theory

The paper is concerned with spherically symmetric static problem of the Classical Gravitation Theory (CGT) and the General Relativity Theory (GRT). First, the Dark Stars, i.e. the objects that are invisible because of high gravitation preventing the propagation of light discovered in the 18th century by J. Michel and P. Laplace are discussed. Second, the Schwarzchild solution which was obtained in the beginning of the 20th century for the internal and external spaces of the perfect fluid sphere is analyzed. This solution results in singular metric coefficients and provides the basis of the Black Holes. Third, the general metric form in spherical coordinates is introduced and the solution of GRT problem is obtained under the assumption that gravitation does not affect the sphere mass. The critical sphere radius similar to the Black Hole horizon of events is found. In contrast to the Schwarzchild solution, the radial metric coefficient for the sphere with the critical radius referred to as the Dark Star is not singular. For the sphere with radius which is less than the critical value, the GRT solution becomes imaginary. The problem is discussed within the framework of the phenomenological theory which does not take into account the actual microstructure of the gravitating objects and, though the term “star” is used, the analysis is concerned with a model fluid sphere rather than with a real astrophysical object.

Derivation of Specific Velocity of Body Moving under Gravity with Zero Total Energy

Mathematical solutions predict abstract conditions that indicate limits or bounds for physical processes. Generally, experimental verifications and physical observations on physical processes validate the mathematical predictions. Sometimes these predictions lead to new theories and concepts that form basis of better understanding of the natural processes. Gravitational interactions between bodies are natural physical processes. A smaller body moves under the influence of gravity, due to the gravitational effect of another large body. Newton’s classical gravitational theory addresses the interactions at low velocities. Einstein’s general relativity provides firm basis for gravitational interactions. Observations over past 100 years prove the mathematical precision and predictions of general relativity. Einstein’s special relativity forms the foundation of quantum physics. In this paper, the author applies concepts of special relativity to classical two body Newtonian gravitational problem. The study predicts a new mathematically viable condition that when a body moves at a specific velocity derived in this paper, the total energy of the moving body is zero. The specific velocity is a constant. At velocities far less than specific velocity, the total energy is negative and is equal to classical value of half the potential energy. At velocities, greater the specific velocity the total energy is positive. The specific velocity condition also enables determination of specific mass of gravitating body, as well as the specific distance of the moving body from gravitating body, at which the total energy of moving body is zero.

Metric measure space as a framework for gravitation

In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar f, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in both relativistic and non-relativistic regimes, a relation between density function f and the quantum potential is proposed. This suggests metric measure space to be considered as a suitable framework for geometric description of Bohm’s quantum mechanics. On the other hand, as it is known, Weyl geometry is one of the main approaches to construct conformally invariant gravitational models. Regarding the fact that the connection in the integrable Weyl space is modified and in metric measure space remains the same as it is in the Riemann space, the mathematical analogy between these two spaces is also discussed.

On the Escape Velocity in General Relativity and the Problem of Dark Matter

The paper is concerned with analysis of the escape velocity for a spherical star within the framework of the Classical Gravitation Theory (CGT) and the General Theory of Relativity (GTR). In GTR, two possible results corresponding to the classical and the generalized Schwarzschild solutions are obtained. For the latter solution which, in contrast to the former one, is not singular, the critical radius of the star for which the particle cannot leave the surface even if the initial velocity of the particle is equal to the velocity of light is found and is associated with the radius of the Dark Star introduced in the 18-th century by J. Michel and P. Laplace. As shown, the radius of the largest visible star, i.e., the red supergiant UY Scutti, is much larger than the obtained critical radius. If the Dark Stars whose radii are smaller than the critical radius exist, they are hypothetically not visible and can concentrate the matter that cannot be observed.

Emergent gravity paradigm: Recent progress

Research during the last one decade or so suggests that the gravitational field equations in a large class of theories (including, but not limited to, general relativity) have the same status as the equations of, say, gas dynamics or elasticity. This paradigm provides a refreshingly different way of interpreting spacetime dynamics and highlights the fact that several features of classical gravitational theories have direct thermodynamic interpretation. I review the recent progress in this approach, achieved during the last few years.

Beables/Observables in Classical and Quantum Gravity

Observables 'are observed' whereas beables just 'are'. This gives beables more scope in the cosmological and quantum domains. Both observables and beables are entities that form 'brackets' with 'the constraints' that are 'equal to' zero. We explain how depending on circumstances, these could be, e.g., Poisson, Dirac, commutator, histories, Schouten-Nijenhuis, double or Nambu brackets, first-class, gauge, linear or effective constraints, and strong, weak or weak-effective equalities. The Dirac-Bergmann distinction in notions of gauge leads to further notions of observables or beables, and is tied to a number of diffeomorphism-specific subtleties. Thus we cover a wide range of notions of observables or beables that occur in classical and quantum gravitational theories: Dirac, Kucha\v{r}, effective, Bergmann, histories, multisymplectic, master, Nambu and bi-. Indeed this review covers a representatively wide range of such theories: general relativity, loop quantum gravity, histories theory, supergravity and M-theory.

Super-accelerating bouncing cosmology in asymptotically free non-local gravity

Recently, evidence has been collected that a class of gravitational theories with certain non-local operators is renormalizable. We consider one such model which, at the linear perturbative level, reproduces the effective non-local action for the light modes of bosonic closed string-field theory. Using the property of asymptotic freedom in the ultraviolet and fixing the classical behavior of the scale factor at late times, an algorithm is proposed to find general homogeneous cosmological solutions valid both at early and late times. Imposing a power-law classical limit, these solutions (including anisotropic ones) display a bounce, instead of a big-bang singularity, and super-accelerate near the bounce even in the absence of an inflaton or phantom field.