On the possibility of gravitational collapse in the relativistic theory of gravity

In the example of dust matter, it is shown that a gravitational attractive force does not lead to the formation of “black holes” in the relativistic theory of gravity. It is proved that in the absence of matter, the gravitational field is also absent. Therefore, a vacuum is not a source of a gravitational field. The mechanism of energy production in the process of the accumulation of matter into massive objects is discussed.     

Relativistic theory of gravity and a Brans-Dicke scalar field

The natural generalization of the relativistic theory of gravity (RTG) by incorporating a Brans-Dicke scalar field is discussed. The equation for a scalar-tensor gravitational field in Minkowski space and the expression for the total energy-momentum metric tensor of a gravitational field and nongravitational matter is derived from the variational principle with a gravitational Lagrangian quadratic in the first derivatives of the scalar and tensor gravitational potentials. The two-parameter spherically symmetrical static solution for vacuum equations with a zero mass tensor graviton was obtained. This solution has a true singular Schwarzschild surface. In the case of a nonzero mass graviton, an approximate nonsingular solution for the beginning of the universe was obtained. It is noted that in the frame of the scalar-tensor generalization of RTG, a nonsingular homogeneous isotropic cosmology can be represented, not only by cyclic models, but also by models with an infinitely expanding universe and a simultaneously decreasing gravitational scalar.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 325–332, February, 1996.     

Basic equations for the massive gravitational field

The fundamental principles of the relativistic theory of gravitation are formulated, and equations of a gravitational field with nonzero mass are derived. The theory predicts the existence in the universe of dark matter.Physics Faculty, Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 2, pp. 191–206, August, 1992.     

Relativistic theory of gravity and a torsion field

The fundamentals of gravity theory are stated in a Minkowski space with an effective nonzero-torsion Riemann-Cartan space-time, which is more general than the Riemannian space. The theory presented thus includes a torsion field of the Einstein-Cartan type in the general concept of the relativistic theory of gravity. Expressions for the metric and canonical energy-momentum tensors of the gravitational field and nongravitational matter in the Minkowski space are found. Noncoordinate gauge transformations are introduced under which the variation of the density of the gravitational Lagrangian is a divergence expression. Translated from Teoreticheskaya i Matematischeskaya Fizika, Vol. 118, No. 1, pp. 126–132, January, 1999.     

Quintessence scalar field in the relativistic theory of gravity

We propose a variant of the quintessence theory in order to obtain an accelerated expansion of the Friedmann universe in the framework of the relativistic theory of gravity. The scalar field of dark energy creates the substance of quintessence. We show that the function V(Φ) that factors the Lagrangian of the scalar field Φ does not influence the evolution of the universe. We find some relations that allow finding the explicit time-dependence of Φ if only the function V(Φ) is chosen. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 551–560, September, 2007.     

Tensor-tensor model of gravity

The main problem with the standard gauge theory of the Poincaré group realized as a subgroup of GL(5, R) is that fields, whose physical sense is unclear, appear in connection with the non-Lorentz symmetries. Here, the Poincaré fields are treated as new Yang-Mills-type tensor fields and gravity is treated as a Higgs-Goldstone field. In this case, the effective metric tensor for matter is a hybrid of two tensor fields. In the linear approximation, the massive translation gauge field gives the Yukawa-type correction to the Newtonian potential. Also, corrections to the standard Einstein post-Newtonian formulas for light deflection and radar echo delay are obtained. A spherically symmetric solution to the equations of translation gauge fields is also found. The translation gauge field leads to the existence of a singular surface, which is impenetrable to matter and can prevent gravitational collapse of a large body, inside the Schwarzschild sphere. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 3, pp. 448–460, December, 1997. This work was supported in part by the Georgian Government and the International Science Foundation (ISF Grant No. MXL 200).     

The strength of Martin-Löf type theory with a superuniverse. Part II

Universes of types were introduced into constructive type theory by Martin-L?f [3]. The idea of forming universes in type theory is to introduce a universe as a set closed under a certain specified ensemble of set constructors, say ?. The universe then “reflects”?. This is the second part of a paper which addresses the exact logical strength of a particular such universe construction, the so-called superuniverse due to Palmgren (cf.[4–6]). It is proved that Martin-L?f type theory with a superuniverse, termed MLS, is a system whose proof-theoretic ordinal resides strictly above the Feferman-Schütte ordinal Γ₀ but well below the Bachmann-Howard ordinal. Not many theories of strength between Γ₀ and the Bachmann-Howard ordinal have arisen. MLS provides a natural example for such a theory. In this second part of the paper the concern is with the with upper bounds. Received: 8 December 1998 / Published online: 21 March 2001     

Theory of the classical gravitational field and Mach's principle

Equations for a massive gravitational field are found in the framework of the special theory of relativity on the geometrization principle. The existence of a graviton mass has fundamental significance for the construction of the theory. In accordance with this theory of gravitation, a homogeneous and isotropic universe evolves cyclically from a high density to a minimum density, etc., and can only be flat. The theory predicts the existence of an appreciable amount of dark matter in the universe. The existence of black holes in the universe is completely ruled out. The theory explains all known observational facts in the solar system.Institute of High Energy Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 1, pp. 3–27, October, 1994.     

New ideas regarding the geometry of space-time and gravitation

In the present survey on the basis of an analysis of the problem of the energy-momentum of the gravitational field in the general theory of relativity it is shown that this theory is unsatisfactory as a concrete realization of Einstein's idea of the connection of the geometry of space-time with matter. A new theory of gravitation is proposed which alters established ideas of space-time, makes it possible to describe all present gravitational experiments, and predicts a number of fundamental consequences.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 21, pp. 3–215, 1982.     

Theory of Dark Energy and Dark Matter

In (T. Ma and S. Wang. Gravitational field equations and theory of dark matter and dark energy, Discrete and Continuous Dynamical Systems, Ser. A, 34(2): 335-366, 2014; arXiv:1206.5078v2), a new set of gravitational field equations are derived based only on 1) the Einstein principle of general relativity, and 2) the principle of interaction dynamics, due to the the presence of dark energy and dark matter. With the field equations, we show that gravity can display both attractive and repulsive behavior, and the dark matter and dark energy are just a property of gravity caused by the nonlinear interactions of the gravitational potential $g_{μv}$and its dual field. The main objectives of this paper are two-fold. The first is to study the PID-induced cosmological model, and to show explicitly, as addressed in (T. Ma and S. Wang, Astrophysical dynamics and cosmology, Journal of Mathematical Study, 47(4): 305-378, 2014), that 1) dark matter is due to the curvature of space, and 2) dark energy corresponds to the negative pressure generated by the dual gravitational potential in the field equations, and maintains the stability of geometry and large scale structure of the Universe. Second, for the gravitational field outside of a ball of centrally symmetric matter field, there exist precisely two physical parameters dictating the two-dimensional stable manifold of asymptotically flat space-time geometry, such that, as the distance to the center of the ball of the matter field increases, gravity behaves as Newtonian gravity, then additional attraction due to the curvature of space (dark matter effect), and repulsive (dark energy effect). This also clearly demonstrates that both dark matter and dark energy are just a property of gravity.     

Newtonian limit in the stabilized Randall-Sundrum model

In the stabilized Randall-Sundrum model, we obtain and solve linearized equations of motion for gravitational and scalar fields in the case of matter on the brane. We find the Newtonian limit of an effective four-dimensional theory on branes with negative tension and explicitly isolate the radion field contribution. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 226–236, August, 2008.     

Dynamical symmetry breaking in hyperbolic 4D spacetime and in extra dimensions

We study the dynamical symmetry breaking in quark matter within two different models. First, we consider the effect of gravitational catalysis of chiral and color symmetries breaking in strong gravitational field of ultrastatic hyperbolic spacetime ℝ ⊗ H ³ in the framework of an extended Nambu-Jona-Lasinio model. Second, we discuss the dynamical fermion mass generation in the flat 4-dimensional brane situated in the 5D spacetime with one extra dimension compactified on a circle. In the model, bulk fermions interact with fermions on the brane in the presence of a constant abelian gauge field A ₅ in the bulk. The influence of the A ₅-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable.     

Large scale nonlinear effects of fluctuations in relativistic gravitation

The first fully nonlinear mean field theory of relativistic gravitation was developed in 2004. The theory makes the striking prediction that averaging or coarse graining a gravitational field changes the apparent matter content of space-time. A review of the general theory is presented, together with applications to black hole and cosmological space-times. The results strongly suggest that at least part of the dark energy may be the net large scale effect of small scale fluctuations around a mean homogeneous isotropic cosmology.     

Gravitation and Electromagnetism as Geometrical Objects of a Riemann-Cartan Spacetime Structure

In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the energy-momentum of the electromagnetic field can be derived from a geometrical Lagrangian proportional to the scalar curvature R of a particular kind of Riemann-Cartan spacetime structure. In our model the gravitational and electromagnetic fields are identified as geometrical objects of the structure.We show moreover that the contorsion tensor of the particular Riemann-Cartan spacetime structure of our theory encodes the same information as the one contained in Chern-Simons term ${{\bf A} \wedge {\it d}{\bf A}}$ that is proportional to the spin density of the electromagnetic field. Next we show that by adding to the geometrical Lagrangian a term describing the interaction of a electromagnetic current with a general electromagnetic field plus the gravitational field, together with a term describing the matter carrier of the current we get Maxwell equations with source term and Einstein equation having as source term the sum of the energy-momentum tensors of the electromagnetic and matter terms. Finally modeling by dust charged matter the carrier of the electromagnetic current we get the Lorentz force equation. Moreover, we prove that our theory is gauge invariant. We also briefly discuss our reasons for the present enterprise.     

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of α^3/2, α being the fine structure constant. A suitably chosen ground state vector depends analytically on α^3/2 and it is twice continuously differentiable with respect to the nuclear coordinates. Submitted: November 24, 2008. Accepted: March 4, 2009.     

Hypothesis ofP-odd contribution to the gravitational interactions and its consequences

A generalized Lagrangian of spinor particles in a gravitational field containingP-odd terms is proposed. It is used to obtain a quasirelativistic equation of spinors in the field of a gravitational source with nonvanishing intrinsic angular momentum in both an inertial frame and in a frame rotating with the source. For these cases the quasirelativistic Hamiltonian of a test body with nonzero intrinsic angular momentum is obtained in the classical limit; it is shown that the presence in the Hamiltonian ofP-odd terms leads to the appearance of forces that, depending on the orientation of the intrinsic angular momentum of the test body, are attractive or repulsive. It is noted that theC noninvariance of the theory can in principle result in an evolution of the universe in which particles predominate over antiparticles. Other macroscopic consequences whose experimental verification would yield information about the values of the constants introduced in the theory are noted.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 2, pp. 309–319, May, 1992.     

New mechanism of energy release in astrophysical objects

Conclusions The above qualitative analysis of the evolution of astrophysical objects shows that in the field theory of gravitation with minimal coupling objects in the regionM/a<1/3 of values of the mean gravitational potential are stable to small perturbations of their radius with unchanged rest mass.However, the mean gravitational potential of these objects increases when they capture matter surrounding them. When the mean potential reaches the valueM/a=1/3, the object passes abruptly from an infinitely stable state to an infinitely unstable state (with respect to small perturbations of its radius). Therefore, even small perturbations in the radius of the object once the critical value of the mean gravitational potential has been reached necessarily lead to expansion of the matter, which may be accompanied by the ejection of mass of this object and the release of energy.Therefore, instead of gravitational collapse, the outcome of the instability of astrophysical objects in general relativity, in the present theory there is a new mechanism of energy release.Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 48, No. 3, pp. 275–283, September, 1981.     

The strength of Martin-Löf type theory with a superuniverse. Part I

Universes of types were introduced into constructive type theory by Martin-L?f [12]. The idea of forming universes in type theory is to introduce a universe as a set closed under a certain specified ensemble of set constructors, say . The universe then “reflects”. This is the first part of a paper which addresses the exact logical strength of a particular such universe construction, the so-called superuniverse due to Palmgren (cf. [16, 18, 19]). It is proved that Martin-L?f type theory with a superuniverse, termed MLS, is a system whose proof-theoretic ordinal resides strictly above the Feferman-Schütte ordinal but well below the Bachmann-Howard ordinal. Not many theories of strength between and the Bachmann-Howard ordinal have arisen. MLS provides a natural example for such a theory. Received: 14 October 1997     

Astrophysical Dynamics and Cosmology

First, the essence of a physical theory for a multilevel system is through coupling different physical laws in different levels by a symmetry-breaking principle, rather than through a unification using larger symmetry. In astrophysical dynamics, the symmetry-breaking mechanism and the coupling are achieved by prescribing the coordinate system so that the laws of fluid dynamics and heat conductivity are coupled with gravitational field equations. Another important ingredient in modeling fluid motion in astrophysics is to use the momentum density field to replace the velocity field as the state function of cosmic objects. Second, by applying the new symmetry-breaking mechanism and the new coupled astrophysical dynamics model, we rigorously prove a basic theorem on black holes: Assume the validity of the Einstein theory of general relativity, then black holes are closed, innate and incompressible. Third, we prove a theorem on structure of universes. Assume the Einstein theory of general relativity, and the principle of cosmological principle that the universe is homogeneous and isotropic. Then we show that 1) all universes are bounded, are not originated from a Big-Bang, and are static; and 2) The topological structure of our Universe can only be the 3D sphere. Also, thanks to the basic properties of black holes, we show that our results on our Universe resolve such fundamental problems as dark matter and dark energy, redshifts and CMB. Fourth, we discovered that both supernovae explosion and AGN jets, as well as many astronomical phenomena, are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Bénard convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to an huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.     

A proof of Price’s law for the collapse of a self-gravitating scalar field

A well-known open problem in general relativity, dating back to 1972, has been to prove Price’s law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation flux through the event horizon and null infinity with respect to appropriately normalized advanced and retarded time coordinates. It is intimately related both to astrophysical observations of black holes and to the fate of observers who dare cross the event horizon. In this paper, we prove a well-defined (upper bound) formulation of Price’s law for the collapse of a self-gravitating scalar field with spherically symmetric initial data. We also allow the presence of an additional gravitationally coupled Maxwell field. Our results are obtained by a new mathematical technique for understanding the long-time behavior of large data solutions to the resulting coupled non-linear hyperbolic system of p.d.e.’s in 2 independent variables. The technique is based on the interaction of the conformal geometry, the celebrated red-shift effect, and local energy conservation; we feel it may be relevant for the problem of non-linear stability of the Kerr solution. When combined with previous work of the first author concerning the internal structure of charged black holes, which had assumed the validity of Price’s law, our results can be applied to the strong cosmic censorship conjecture for the Einstein-Maxwell-real scalar field system with complete spacelike asymptotically flat spherically symmetric initial data. Under Christodoulou’s C⁰-formulation, the conjecture is proven to be false.