Weak-field General Relativity Research Articles

The cosmological constant vs adiabatic invariance

The property of adiabatic invariance is studied for the generalized potential satisfying the condition of identity of sphere's and point mass's gravity. That function contains a second term corresponding to the cosmological constant as weak-field General Relativity and enables to describe the dynamics of groups and clusters of galaxies and the Hubble tension as a result of two flows, local and global ones. Using the adiabatic invariance approach we derive the orbital parameters via Weierstrass functions, including the formula for the eccentricity which explicitly reveals the differences from the Kepler problem.

On the origin of cosmic web

The emergence of one and two-dimensional configurations -- Zeldovich pancakes -- progenitors of the observed filaments and clusters and groups of galaxies, is predicted by means of a developed kinetic approach in analyzing the evolution of initial density perturbations. The self-consistent gravitational interaction described by Vlasov-Poisson set of equations with branching conditions is shown to predict two-dimensional structures as of layers of increased density and voids between them, i.e. the cellular macro-structure of the Universe. The modified potential of weak-field General Relativity is involved, which enables one to explain the Hubble tension, revealing the conceptual discrepancy in the local galactic flows and the cosmological expansion. This demonstrates the possible essential role of self-consistent gravity in the formation of the cosmic web.

Nonlocality and gravitoelectromagnetic duality

The weak-field Schwarzschild and NUT solutions of general relativity are gravitoelectromagnetically dual to each other, except on the positive $z$-axis. The presence of non-locality weakens this duality and violates it within a smeared region around the positive $z$-axis, whose typical transverse size is given by the scale of non-locality. We restore an exact non-local gravitoelectromagnetic duality everywhere via a manifestly dual modification of the linearized non-local field equations. In the limit of vanishing non-locality we recover the well-known results from weak-field general relativity.

Hubble tension vs two flows

The Hubble tension is shown to be solvable, without any free parameter, conceptually and quantitatively, within the approach of modified weak-field General Relativity involving the cosmological constant $\Lambda$. That approach enables one to describe in a unified picture both the dynamics of dark matter containing galaxies and the accelerated expansion of the Universe, thus defining a {\it local} Hubble constant of a local flow and the {\it global} one. The data on the dark matter content of peculiar galaxy samples are shown to be compatible to that unified picture. Future more refined surveys of galaxy distribution, hierarchical dynamics and flows within the vicinity of the Local group and the Virgo supercluster can be decisive in revealing the possible common nature of the dark sector.

Lense–Thirring precession and modified gravity constraints

The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $\Lambda$. It is shown that according to the current accuracy of satellite measurements the obtained error limits for $\Lambda$ is self-consistent with cosmological observations. The corrections of $\Lambda$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $\Lambda$-gravity we obtain constraints for $\Lambda$ in both relativistic and weak-field limits. Namely, for the latter we analyze several Keplerian systems at different scales. We find that the obtained constraints for the modified gravity corrections are several orders of magnitude tighter than those available for such effects as gravitational redshift, gravitational time delay and geodetic precession in Solar System.

On the Lambda-evolution of galaxy clusters

The evolution of galaxy clusters can be affected by the repulsion described by the cosmological constant. This conclusion is reached within the modified weak-field General Relativity approach where the cosmological constant varLambda enables to describe the common nature of the dark matter and the dark energy. Geometrical methods of theory of dynamical systems and the Ricci curvature criterion are used to reveal the difference in the instability properties of galaxy clusters which determine their evolutionary paths. Namely, it is shown that the clusters determined by gravity with varLambda -repulsion tend to become even more unstable than those powered only by Newtonian gravity, the effect to be felt at cosmological time scales.

The invalidity of “negative mass” description of the dark sector

It is shown that the concept of “negative mass” introduced by Farnes [Astron. Astrophys. 620, A92 (2018)] to describe the dark sector within a unifying theory with the negative cosmological constant contradicts both the essence of the General Relativity (GR) and the available observational data. A viable model with modified weak-field GR is mentioned.

The cosmological constant derived via galaxy groups and clusters

The common nature of dark matter and dark energy is argued in Gurzadyan (Eur Phys J Plus 134:14, 2019) based on the approach that the cosmological constant varLambda enters the weak-field General Relativity following from Newton theorem on the “sphere-point mass” equivalency (Gurzadyan and Stepanian in Eur Phys J C 78:632, 2018). Here we probe the varLambda -gravity description of dark matter in galaxy systems, from pairs up to galaxy clusters using the data of various sources, i.e. of Local Supercluster galaxy surveys, gravity lensing and Planck satellite. The prediction that the cosmological constant has to be the lower limit for the weak-field varLambda obtained from galaxy systems of various degree of virialization is shown to be supported by those observations. The results therefore support the varLambda -gravity nature of dark matter in the studied systems, implying that the positivity of the cosmological constant might be deduced decades ago from the dynamics of galaxies and galaxy clusters far before the cosmological SN surveys.

Exponential metric represents a traversable wormhole

For various reasons a number of authors have mooted an "exponential form" for the spacetime metric: \[ ds^2 = - e^{-2m/r} dt^2 + e^{+2m/r}\{dr^2 + r^2(d\theta^2+\sin^2\theta \, d\phi^2)\}. \] While the weak-field behaviour matches nicely with weak-field general relativity, and so also automatically matches nicely with the Newtonian gravity limit, the strong-field behaviour is markedly different. Proponents of these exponential metrics have very much focussed on the absence of horizons --- it is certainly clear that this geometry does not represent a black hole. However, the proponents of these exponential metrics have failed to note that instead one is dealing with a traversable wormhole --- with all of the interesting and potentially problematic features that such an observation raises. If one wishes to replace all the black hole candidates astronomers have identified with traversable wormholes, then certainly a careful phenomenological analysis of this quite radical proposal should be carried out.

The power of weak-field GR gravity

While general relativity (GR) is our premier theory of gravity, galactic dynamics from the outset has been studied with Newtonian gravity (NG), guided by the long-held belief in the idea of the “Newtonian-limit” of GR. This maintains that when the gravitational field is weak and the velocities are nonrelativistic, NG is the appropriate theory, apart from small corrections at best (such as in GPS tracking). However, there are simple examples of phenomena where there is no NG counterpart. We present a particularly simple new example of the stark difference that NG and weak-field GR exhibit for a modified van Stockum source, which speaks to the flat galactic rotation curve problem. We note that the linear GR compatibility equation in the literature is incomplete. Its completion is vital for our case, leading to a stark contrast between GR and NG for totally flat van Stockum rotation curves.

The confrontation between general relativity and experiment

We review the experimental evidence for Einstein’s general relativity. Tests of the Einstein equivalence principle support the postulates of curved space-time and bound variations of fundamental constants in space and time, while solar system experiments strongly confirm weak-field general relativity. The binary pulsar provides tests of gravitational wave damping and of strong-field general relativity. Future experiments, such as the gravity probe B gyroscope experiment, a satellite test of the equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser Interferometric Gravitational Wave Observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves.

The Confrontation between General Relativity and Experiment

We review the experimental evidence for Einstein's general relativity. Tests of the Einstein Equivalence Principle support the postulates of curved spacetime and bound variations of fundamental constants in space and time, while solar-system experiments strongly confirm weak-field general relativity. The Binary Pulsar provides tests of gravitational-wave damping and of strong-field general relativity. Future experiments, such as the Gravity Probe B Gyroscope Experiment, a satellite test of the Equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves.

A new gauge-invariant Hamiltonian formulation of weak-field general relativity

Presents a new Hamiltonian formulation of weak-field general relativity, based on canonical variables completely analogous to the electric and magnetic field strengths of Maxwell theory. This formulation displays with particular clarity and duality invariance of weak-field general relativity. The author computes the generator of these duality symmetries, and thereby arrives at a new conserved quantity associated with weak gravitational fields.