Eddington’s Prediction for General Relativity Revisited

Eddington’s prediction for general relativity (GR) is exemplified by three cases: a static spherically symmetric gravitational field, radiation of gravitational waves, and a homogeneous isotropic cosmological model. The results of GR for a static field are obtained using only Poisson’s equation instead of the Einstein–Hilbert equations. Degeometrization of GR will allow the gravitational interaction to be unified with others described in the framework of the Standard Model of particle physics.     

The Charge in a Lift. A Covariance Problem

We analyze the classical problemof a charge that falls in a gravitational field, Einstein’s famous Gedankenexperiment. The goal of this paper is to analyze an original approach developed by Soker and Harpaz (2000) based on what we have called Larmor “whiplash”. The authors consider the case of a charge freely falling in a uniform gravitational field and the case of a charge supported at rest in a gravitational field. Instead, starting from Thomson’s geometrical proof of the Larmor relation, we consider the case of a freely falling charge in a “real” gravitational field. In this case, we believe that tidal effects are present, and the charge will radiate. We also make some reflections about the equivalence principle, understood as general covariance, and about the metric construction according to Fock.     

Radial infall into a black hole in <Emphasis Type="Italic">R</Emphasis><Superscript>2</Superscript> gravity

We apply the formula for quadrupole gravitational loss of Einstein’s linearized theory to calculate the energy loss of an infalling pointlike mass into a black hole in the context of quadratic f(R) gravity.     

Gravitational waves in singular and bouncing FLRW universes

We investigate propagation of gravitational waves in two models belonging to the Friedman-Lemaître-Robertson-Walker (FLRW) class of cosmologies: the singular Einstein-Maxwell Universe (EMU), which has an electromagnetic field described by Maxwell’s electrodynamics as the source of its geometry, and the bouncing Nonlinear Electrodynamics Universe (NLEU), which has the electromagnetic field described by a nonlinear generalization of Maxwell’s electrodynamics as the source of its geometry. We work with an explicitly gauge-independent formulation of cosmological perturbations in FLRW models and analyze the qualitative features of the dynamical system that describes the propagation of primordial tensorial perturbations in both geometries. Based on this analysis, we show that gravitational waves generated near a singularity or a bounce exhibit qualitatively different behavior.     

Variations of α and G from nonlinear multidimensional gravity

To explain the recently reported large-scale spatial variations of the fine structure constant α, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities as compared with the Planck scale, the original theory reduces to a multiscalar field theory in four dimensions. On this basis, we consider different variants of isotropic cosmological models in both the Einstein and Jordan conformal frames. One of the models turns out to be equally viable in both frames, but in the Jordan frame themodel predicts simultaneous variations of α and the gravitational constant G, equal in magnitude. Large-scale small inhomogeneous perturbations of these models allow for explaining the observed distribution of α values.     

Gravitation and radiation

Gravitation is one of the most intriguing forces in space that govern all the interstellar spectacles motion in this universe. In this article we have shown there is a profound relationship between gravitational fields with respect to its converted energy. Since time is an inevitable element in every aspect of science; we have developed a partial differential equation from Einstein’s energy equation in which we show that gravitational field can be coupling with its diverging energy radiation. We have also shown that energy to mass conversion in principle is conceivable by means of energy convergent operation (i.e., in-flow) into a unit space. In fact this could have been happen by the eventuality of a black hole explosion, as remains to be observed.     

Multipolar Graviton in the Hydrogen Atoms

We derive multipolar gravitational radiation in the framework of quantum field theory in which the atomic states are treated nonrelativistically, and the gravitational waves are quantized. By relaxing the constraint e^ik·x ≈ 1, the multipolar transition rate is calculated when one graviton is emitted. As a consistency check, we recover the semiclassical result in the dipole approximation regime. Besides, we show that the dynamical mechanism that gives rise to spontaneous graviton emission by an atom, has a profound consequence on the lifetime of the atomic electron.     

A machian request for the equivalence principle in extended gravity and nongeodesic motion

Starting from the origin of Einstein’s general relativity (GR), the request of Mach on the theory’s structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of the Equivalence Principle (EP). TheMOND theory byMilgrom proposes a modification of Newtonian dynamics, and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a nongeodesic ratio m _i /m _g can be fixed and that Milgrom’s acceleration is retrieved at low energies.     

Filtration of the Gravitational Frequency Shift in Radio Link Communications with Earth’s Satellites

At present, the Radioastron (RA) Earth’s satellite has a very elliptic orbit, which is used to probe the gravitational redshift effect. The objective of this test is to enhance the accuracy of the measurement that will be used to check the correspondence value of the effect to EinsteinБ’s theory by an order of magnitude better than was done in the GP-A experiment (Vessot et al., 1980). There are two H-masers at our disposal: one on board the satellite and the other at the Land Tracking Station (LTS). It is possible to compare the satellite’s mutual time rates using communication radio links between RA and LTS. In contrast to the GP-A experiment, it is possible to measure the repetition and accumulation of data in the process of RA orbital circulation. In principle, this might result in an increase in the integral accuracy. In this paper, we investigate the achievable accuracy in the redshift extractionmethod associated with technical specifications of the RA mission.     

Analysis of optimal motion control for a material point in a central field with application of quaternions

This work is devoted to a survey and generalization of results obtained in the theory of optimal motion control for a material point in the central Newtonian gravitational field using the Pontryagin’s maximum principle and quaternion models of orbital motion. This theory is very important in space flight mechanics, being the background of the solution of optimal control problems of the motion of the center of mass of a space vehicle. In the first part of this work, a survey of quaternion models of the motion of a material point in a central Newtonian gravitational field is given, their advantages and disadvantages are analyzed. The formulation of the optimal control problem of the motion of a material point in the central Newtonian gravitational field and its correlation with the optimal control problem of the motion of the center of mass of a space vehicle is considered. The main problems arising in the solution of optimal control problems of the motion of a material point using the maximum principle, including instability in the Lyapunov’s sense of solutions to adjoint equations, are studied. It is shown that efficiency of analytical investigation and numerical solution of the corresponding boundary-value problems can be increased by the application of quaternion models of orbital motion.     

Rotating spin-polarized cylinder in Einstein–Cartan theory

The field equations of Einstein–Cartan theory are solved to describe the gravitational field due to a rotating spin-polarized cylindrical perfect fluid distribution with the proper choice of stress-energy-momentum tensor of Ray and Smalley. We show that the interior metric can be matched to an exterior vacuum using the Arkuszewski–Kopczynski–Ponomariev (AKP) matching conditions. We also discuss the nature of the singularity in the matter region.     

Quantizing gravity using physical states of a superstring

A symmetric zero-mass tensor of rank two is constructed using the superstring modes of excitation, which satisfies the physical state constraints of a superstring. These states have a one to one correspondence with the quantized field operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensor, using the quantum field theory method of quantization. The principle of equivalence makes the tensor identical to the metric tensor at any arbitrary space-time point. The propagator for the quantized field is deduced. The gravitational interaction is switched on by going over from ordinary derivatives to co-derivatives. The Riemann-Christoffel affine connections are calculated, and the weak field Ricci tensor R _μν ⁰ is shown to vanish. The interaction part R _μν ^int is found, and the exact R _μν of the theory of gravity is expressed in terms of the quantized metric. The quantum-mechanical self-energy of the gravitational field in vacuum is shown to vanish. By the use of a projection operator, it is shown that gravitons are quanta of the general relativity field which gives the Einstein equation G _μν = 0. It is suggested that quantum gravity may be renormalizable by the use of the massless ground state of this superstring theory for general relativity, and a tachyonic vacuum creates and annihilates quanta of quantized gravitational field.     

Relationship of gauge gravitation theory in Riemann-Cartan space-time and general relativity

We study the simplest version of a gauge gravitation theory in Riemann-Cartan space-time leading to the solution of the cosmological singularity problem and the dark energy problem. It is shown that this theory under certain restrictions on the indefinite parameters of the gravitational Lagrangian, in the case of usual gravitating systems, leads to Einstein gravitational equations with an effective cosmological constant.     

On the Issue of the Gravitational Instability of the Solar Protoplanetary Disk

The gravitational instability of a homogeneous isotropic infinite gravitating gaseous medium is investigated in order to study the physical processes that take place during the formation of the solar planetary system. The analytical and numerical solutions of the motion equations of such a medium are considered in two approximations: cold gas and gas at a finite temperature. The real solutions describing the behavior of both wave density disturbances of a homogeneous medium and single disturbances are obtained. Waves of gravitational instability whose amplitude grows exponentially and whose highs and lows, as well as their nodal points, retain their positions in space follow the basic laws of Jean’s model. The authors interpret this wave of instability as an analogue of protoplanetary rings, which can be formed in protoplanetary disks. According to the numerical calculation results, the reaction of a homogeneous gravitating medium to the single initial perturbation of its density is significantly different from the laws of Jean’s model. The instability localized in single initial perturbations extends to the region λ < λ_J, although in this case the growth of the perturbation density is considerably less than for λ > λ_J. It is discovered that the gravitational instabilities in the region λ > λ_J suppress sound. It is shown that, without taking into account the rotation of the Sun’s protoplanetary disk medium, its critical density in the event of a large-scale gravitational instability is about four orders of magnitude smaller than the critical density in accordance with the theory of planet formation by the accumulation of solids and particles.     

Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors

A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source but also an arbitrary constant. In this work, we show that the constants appearing in the “temporal Schwarzschild”, “spatial Schwarzschild” and “Reissner-Nordströmlike” exteriors are not arbitrary but are completely determined by the star’s parameters, like the equation of state and the gravitational potential. Consequently, in the braneworld scenario, the gravitational field outside a star is no longer determined by the total mass alone but also depends on the details of the internal structure of the source. We show that the general-relativistic upper bound on the gravitational potential M/R < 4/9 for perfect fluid stars is significantly increased in these exteriors. Namely, M/R < 1/2, M/R < 2/3 and M/R < 1 for the temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordström-like exteriors, respectively. We find that stellar models embedded in such exteriors are very diverse and rich in structure: For stars like our Sun, the deviation from the Schwarzschild exterior metric is automatically negligible, but in other limits they allow the existence of new kinds of stellar models which have no general-relativistic counterpart. Regarding the surface gravitational redshift, we find that the general-relativistic Schwarzschild exterior as well as the braneworld spatial Schwarzschild exterior lead to the same upper bound, viz., Z < 2. However, when the external spacetime is the temporal Schwarzschild metric or the Reissner-Nordström-like exterior, there is no such constraint: Z < ∞. This infinite difference in the limiting value of Z is because for these exteriors the effective pressure at the surface is negative. The results of our work are potentially observable and can be used to test the theory.     

Strapdown inertial navigation systems for high precision near-Earth navigation and satellite geodesy: Analysis of operation and errors

Specific features of the solution of problems of near-Earth inertial navigation are described for applications in which geodetic-class precision is required, the connection of problems of autonomous inertial navigation and satellite gravimetry, their complementary and contradictory character are considered, navigation support of modern projects of satellite geodesy is analyzed. The architecture of a precise strapdown inertial navigation system is considered, the mathematical model for its operation with account of errors is proposed. Error equations are obtained in a general nonlinear form. The specific features of the constructed model are the account of variations of velocity of the Earth’s self rotation, the nonstationary character of the Earth’s gravitational field, the gravitational influence of the Sun, the Moon, planets, and the account of tidal, tectonic, seasonal motions of the navigation coordinate system whose origin is situated at the point of the surface of the elastic Earth with respect to the Earth’s geocentric coordinate system.     

A study of plane torsion waves in the Poincaré gauge theory of gravity

The variational equations of the gravitational field in Riemann-Cartan space are derived in the external forms formalism using the method of Lagrange indefinite multipliers for the Poincaré gauge theory of gravity with quadratic Lagrangians in the general form. The structure of the irreducible parts of torsion propagating in the form of plane waves in Riemann-Cartan spacetime is investigated.