Weak Gravitational Field Limit Research Articles

Shadow revisiting and weak gravitational lensing with Chern-Simons modification

Dynamical Chern-Simons (dCS) gravity has been attracting plenty of attentions due to the fact that it is a parity-violating modified theory of gravity that corresponds to a well-posed effective field theory in weak coupling approximation. In particular, a rotating black hole in dCS gravity is in contrast to the general relativistic counterparts. In this paper, we revisit the shadow of analytical rotating black hole spacetime in dCS modified gravity, based on which we study the shadow observables, discuss the constraint on the model parameters from the Event Horizon Telescope (EHT) observations, and analyze the real part of quasi-normal modes (QNMs) in the eikonal limit. In addition, we explore the deflection angle in weak gravitational field limit with the use of Gauss-Bonnet theorem. We find that the shadow related physics and the weak gravitational lensing effect are significantly influenced by the CS coupling, which could provide theoretical predictions for a future test of the dCS theory with EHT observations.

Nontrivial Isometric Embeddings for Flat Spaces

Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

Scalar field dark matter as an alternative explanation for the anisotropic distribution of satellite galaxies

In recent years, the scalar field dark matter (SFDM), also called ultralight bosonic dark matter, has received considerable attention due to the number of problems it might help to solve. Among these are the cusp-core problem and the abundance of small structures of the standard cold dark matter (CDM) model. In this paper we show that multi-state solutions of the low energy and weak gravitational field limit of field equations, interpreted as galactic halo density profiles, can provide a possible explanation to the anisotropic distribution of satellite galaxies observed in the Milky Way, M31 and Centaurus A, where satellites trajectories seem to concentrate on planes close to the poles of the galaxies instead of following homogeneously distributed trajectories. The core hypothesis is that multi-state solutions of the equations describing the dynamics of this dark matter candidate, namely, the Gross-Pitaevskii-Poisson equations, with monopolar and dipolar contributions, can possibly explain the anisotropy of satellite trajectories. In order to construct a proof of concept, we study the trajectories of a number of test particles traveling on top of the gravitational potential due to a multi-state halo with modes (1,0,0)+(2,1,0). The result is that particles accumulate asymptotically in time on planes passing close to the poles. Satellite galaxies are not test particles but interpreted as such, our results indicate that in the asymptotic time their trajectories do not distribute isotropically, instead they prefer to have orbital poles accumulating near the equatorial plane of the multistate halo. The concentration of orbital poles depends on whether the potential is monopolar or dipolar dominated.

Light bending by a slowly rotating source in quadratic theories of gravity

In this paper we study the light bending caused by a slowly rotating source in the context of quadratic theories of gravity, in which the Einstein--Hilbert action is extended by additional terms quadratic in the curvature tensors. The deflection angle is computed employing the method based on the Gauss--Bonnet theorem and working in the approximation of a weak lens; also, we assume that the source and observer are at an infinite distance. The formalism presented is very general and applies to any spacetime metric in the limit of weak gravitational field and slow rotation. We find the explicit formula for the deflection angle for several local and nonlocal theories, and also discuss some phenomenological implications.

Tests of gravity theories with Galactic Center observations

An active stage of relativistic astrophysics started in 1963 since in this year, quasars were discovered, Kerr solution had been found and the first Texas Symposium on Relativistic Astrophysics was organized in Dallas. Five years later, in 1967–1968 pulsars were discovered and their model as rotating neutron stars (NSs) had been proposed, meanwhile Wheeler claimed that Kerr and Schwarzschild vacuum solutions of Einstein equations provide an efficient approach for astronomical objects with different masses. Wheeler suggested to call these objects black holes. NSs were observed in different spectral band of electromagnetic radiation. In addition, a neutrino signal had been found for SN1987A. Therefore, multi-messenger astronomy demonstrated its efficiency for decades even before observations of the first gravitational radiation sources. However, usually, one has only manifestations of black holes in a weak gravitational field limit and sometimes a model with a black hole could be substituted with an alternative approach which very often looks much less natural, however, it is necessary to find observational evidences to reject such an alternative model. At the moment, only few astronomical signatures for strong gravitational field are found, including a shape of relativistic iron [Formula: see text] line, size and shape of shadows near black holes at the Galactic Center (GC) and M87, trajectories of bright stars near the GC. After two observational runs, the LIGO–Virgo collaboration provided a confirmation for a presence of mergers for 10 binary black holes and one binary NS system where gravitational wave signals were found. In addition, in the last years, a remarkable progress has been reached in a development of observational facilities to investigate a gravitational potential, for instance, the number of telescopes operating in the Event Horizon Telescope network is increasing and accuracy of a shadow reconstruction near the GC is improving, meanwhile largest VLT, Keck telescopes with adaptive optics and especially GRAVITY facilities observe bright IR stars at the GC with perfect accuracy. More options for precision observations of bright stars will be available with creating extremely large telescopes Thirty Meter Telescope (TMT) and E-ELT. It is clear that the GC (Sgr [Formula: see text]) is a specific object for observations. Our solar system is located at a distance around 8 kpc from the GC. Earlier, theorists proposed a number of different models including exotic ones for GC such as boson star, fermion ball, neutrino ball, a cluster of NSs. Later, some of these models were ruled out or essentially constrained with consequent observations and theoretical considerations. Currently, a supermassive black hole with mass around [Formula: see text] is the most natural model for GC. Using results of observations for trajectories of bright stars in paper [A. F. Zakharov, P. Jovanović, D. Borka and V. B. Jovanović, J. Cosmol. Astropart. Phys. 05 (2016) 045] the authors got a graviton mass constraint which is comparable and consistent with constraints obtained recently by the LIGO–Virgo collaboration. Later, we consider opportunities to improve current graviton mass constraints with future observations of bright stars [A. F. Zakharov, P. Jovanović, D. Borka and V. B. Jovanović, J. Cosmol. Astropart. Phys. 04 (2018) 050]. Similarly, from an analysis of bright star trajectories, one could constrain a tidal charge which was predicted by a gravity theory with an additional dimension [A. F. Zakharov, Eur. Phys. J. C 78 (2018) 689].

To B or not to B: primordial magnetic fields from Weyl anomaly

The quantum effective action for the electromagnetic field in an expanding universe has an anomalous dependence on the scale factor of the metric arising from virtual charged particles in the loops. It has been argued that this Weyl anomaly of quantum electrodynamics sources cosmological magnetic fields in the early universe. We examine this long-standing claim by using the effective action beyond the weak gravitational field limit which has recently been determined. We introduce a general criteria for assessing the quantumness of field fluctuations, and show that the Weyl anomaly is not able to convert vacuum fluctuations of the gauge field into classical fluctuations. We conclude that there is no production of coherent magnetic fields in the universe from the Weyl anomaly of quantum electrodynamics, irrespective of the number of massless charged particles in the theory.

The Train Wreck Cluster Abell 520 and the Bullet Cluster 1E0657-558 in a Generalized Theory of Gravitation

A major hurdle for modified gravity theories is to explain the dynamics of galaxy clusters. A case is made for a generalized gravitational theory called Scalar-Tensor-Vector-Gravity (STVG) or MOG (Modified Gravity) to explain merging cluster dynamics. The paper presents the results of a re-analysis of the Bullet Cluster, as well as an analysis of the Train Wreck Cluster in the weak gravitational field limit without dark matter. The King- β model is used to fit the X-ray data of both clusters, and the κ -maps are computed using the parameters of this fit. The amount of galaxies in the clusters is estimated by subtracting the predicted κ -map from the κ -map data. The estimate for the Bullet Cluster is that 14.1 % of the cluster is composed of galaxies. For the Train Wreck Cluster, if the Jee et al. data are used, 25.7 % of the cluster is composed of galaxies. The baryon matter in the galaxies and the enhanced strength of gravitation in MOG shift the lensing peaks, making them offset from the gas. The work demonstrates that this generalized gravitational theory can explain merging cluster dynamics without dark matter.

Second-order Cosmological Perturbations Engendered by Point-like Masses

Abstract In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second‐order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second‐order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self‐consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.

Scalar and vector perturbations in a universe with discrete and continuous matter sources

We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The background spacetime geometry is defined by the FLRW metric. In the weak gravitational field limit, we develop the first-order scalar and vector cosmological perturbation theory. Our approach works at all cosmological scales (i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear effects with respect to energy density fluctuations. We demonstrate that the scalar perturbation (i.e. the gravitational potential) as well as the vector perturbation can be split into individual contributions from each matter source. Each of these contributions satisfies its own equation. The velocity-independent parts of the individual gravitational potentials are characterized by a finite time-dependent Yukawa interaction range being the same for each individual contribution. We also obtain the exact form of the gravitational potential and vector perturbation related to the discrete matter sources. The self-consistency of our approach is thoroughly checked. The derived equations can form the theoretical basis for numerical simulations for a wide class of cosmological models.

FIRST-ORDER COSMOLOGICAL PERTURBATIONS ENGENDERED BY POINT-LIKE MASSES

ABSTRACT In the framework of the concordance cosmological model, the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of these perturbations (inhomogeneities) are presented in the discrete form of a system of separate point-like gravitating masses. The expressions found for the metric corrections are valid at all (sub-horizon and super-horizon) scales and converge at all points except at the locations of the sources. The average values of these metric corrections are zero (thus, first-order backreaction effects are absent). Both the Minkowski background limit and the Newtonian cosmological approximation are reached under certain well-defined conditions. An important feature of the velocity-independent part of the scalar perturbation is revealed: up to an additive constant, this part represents a sum of Yukawa potentials produced by inhomogeneities with the same finite time-dependent Yukawa interaction range. The suggested connection between this range and the homogeneity scale is briefly discussed along with other possible physical implications.

Constraint equations in Einstein-aether theories and the weak gravitational field limit

We discuss the set of constraints for Einstein-aether theories, comparing the flat background case with what is expected when the gravitational fields are dynamic. We note potential pathologies occurring in the weak gravitational field limit for some of the Einstein-aether theories.

Effects of structure formation on the expansion rate of the Universe: An estimate from numerical simulations

General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this paper, we propose a new scheme that utilizes numerical simulations to make a realistic estimate of the magnitude of these corrections for general inhomogeneities in (3+1) spacetime. We then quantitatively calculate the volume averaged expansion rate using N-body large-scale structure simulations and compare it with the expansion rate in a standard FRW cosmology. We find that in the weak gravitational field limit, the converged corrections are slightly larger than the previous claimed 10^{-5} level, but not large enough nor even of the correct sign to drive the current cosmic acceleration. Nevertheless, the question of whether the cumulative effect can significantly change the expansion history of the Universe needs to be further investigated with strong-field relativity.

Studies of strong gravitational fields near super-massive black hole horizons with space missions

General relativity (GR) can be probed by several tests in the weak gravitational field limit. On the contrary, very poor information exists about GR tests in strong gravitational fields. Here, we focus on the interaction of light rays with the strong gravitational field of a massive black hole and show that relativistic images may form. Hence, we calculate the shapes of shadows (mirages) forming just near BH horizons and discuss the possibility to estimate the black hole parameters (mass, spin and charge) by future astrometric missions. In 2007, the Radioastron space telescope will be launched and it will allow to evaluate those parameters for the black hole hosted at the center of our Galaxy.

Gyroscopic precession in non-circular orbits: a phase-locked tetrad approach

We deduce the explicit form of a phase-locked (PL) tetrad, adapted to a small spinning particle (a test gyroscope) following an arbitrary geodesic orbit in the Schwarzschild geometry of a gravitational source. We subsequently obtain the analytic expression of the gyroscopic precessional velocity Ω in a non-circular orbit, by means of the Fermi rotation coefficients related to the tetrad’s transport law. As an application, we compute the orbital shift in the spin vector, considering a spinning test particle (the gyroscope) in a slightly non-circular orbital motion in the weak gravitational field limit. We compare our results with those of other previous works.

Schwarzschild-Type Solutions in Dilaton Gravity

In the D-dimensional dilaton gravity model, we obtain and study stationary Schwarzschild-type solutions, i.e., centrally symmetric solutions in a vacuum. They form a two-parameter family of solutions: one of the parameters is an analogue of the gravitational radius, and the second parameter characterizes the intensity of the dilaton field. If the second parameter is zero, which means that the dilaton field is constant, then the expression obtained for the metric becomes the well-known Schwarzschild solution describing a black hole. But if this parameter is nonzero, then the black hole horizon does not appear. We find the parameters of quasielliptic orbits of test particles for the obtained solutions in the weak gravitational field limit.

Action principle formulation for the motion of extended bodies in general relativity

We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments.

ASYMPTOTICAL CONFORMAL INVARIANCE IN “FINITE” SU(2) GAUGE THEORIES IN CURVED SPACE-TIME

The behavior of effective coupling constants in one-loop “finite” SU(2) gauge theories in curved space-time is investigated. It is shown that in strong gravitational field the effective coupling constants, corresponding to the parameters of non-minimal interaction of scalars and gravitational field, tend to the conformal values (asymptotical conformal invariance) or increase in an exponential fashion. The weak gravitational field limit is also considered in the same models.