Curved Spacetime Research Articles

A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions

Following earlier works of Dereli and collaborators, we study a three dimensional toy model where we extend the topologically massive gravity with electrodynamics by the most general RF 2-type non-minimal coupling terms. Here R denotes the possible curvature terms and F denotes the electromagnetic 2-form. We derive the variational feld equations and look for exact solutions on constant negative curvature space-times with a constant, self-dual electromagnetic feld. The notion of self-dual electromagnetic felds in three dimensions is introduced by Dereli and collaborators in the study of exact solutions of models with gravity-electromagnetism couplings. We note the conditions that the parameters of the model have to satisfy for these self-dual solutions to exist.

Relativistic extended uncertainty principle from spacetime curvature

The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work that is recovered in the nonrelativistic limit. Applying the $3+1$ splitting in accordance with the ADM formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface. Its radius can then be understood as a measure of position uncertainty. Under the assumption of small position uncertainties in comparison to background curvature length scales, we obtain the corresponding corrections to the uncertainty relation in flat space. Those depend on the Ricci scalar of the effective spatial metric, the particle is moving on, and, if there are nonvanishing time-space components of the spacetime metric, there are gradients of the shift vector and the lapse function. Interestingly, this result is applicable not only to massive but also to massless particles. Over all, this is not a covariant, yet a consistently general relativistic approach. We further speculate on a possible covariant extension.

Polarization distortions of lensed gravitational waves

In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross polarization modes which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of sight can cause the apparent rise of additional polarizations due to GW-curvature interactions. In this paper, we continue the analysis by two of the authors of the present article, on lensing of gravitational waves beyond geometric optics. In particular, we calculate the lensing effect caused by a point-like lens, in the regime where its Schwarzschild radius $R_s$ is much smaller than the wavelength $\lambda$ of the signal, itself smaller than the impact parameter $b$. In this case, the curvature of spacetime induces distortions in the polarization of the wave such that effective scalar and vector polarizations may appear. We find that the amplitude of these apparent non-GR polarizations is suppressed by a factor $R_s\lambda/b^2$ with respect to the amplitude of the GR-like tensor modes. We estimate the probability to develop these extra polarization modes for a nearly monochromatic GW in the Pulsar Timing Arrays band traveling through a distribution of galaxies.

On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature

The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many approximation methods exploit the restrictive requirement of an explicit time-scale separation parameter. Most of those methods are also not formulated covariantly, i.e. in terms of tensorial constructions. We propose an intrinsically coordinate-free differential geometric approximation criterion approximating normally attracting invariant manifolds (NAIMs). We translate some ideas behind existing approximation approaches, the stretching based diagnostics (SBD) and the flow curvature method (FCM) to tensors of Riemannian geometry, specifically to spacetime curvature in extended phase space. For that purpose we derive from flow-generating smooth vector fields a metric tensor such that the original dynamical system is a geodesic flow on a Riemannian manifold. We apply the resulting method to test models.

Dimensional regularization for the particle transition amplitude in curved space

We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing dimensional regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work generalizes known results where DR was applied to the computation of one-loop effective actions, which in the worldline approach are linked to particle path integrals on the circle, i.e. with periodic boundary conditions. The main motivation of the present work comes from revived interest in particle transition amplitudes in curved space-times, due to their use in the recently proposed worldline quantum field theory (in curved space-time).

Non-minimally coupled vector boson dark matter

We consider a simple abelian vector dark matter (DM) model, where only the DM (X̃μ) couples non-minimally to the scalar curvature (R̃) of the background spacetime via an operator of the form ∼X̃μ X̃μ R̃. By considering the standard freeze-out scenario, we show, it is possible to probe such a non-minimally coupled DM in direct detection experiments for a coupling strength ξ∼\U0001d4aa(1030) and DM mass m X ≲ 55 TeV, satisfying Planck observed relic abundance and perturbative unitarity. We also discuss DM production via freeze-in, governed by the non-minimal coupling, that requires ξ ≲10-5 to produce the observed DM abundance over a large range of DM mass depending on the choice of the reheating temperature. We further show, even in the absence of the non-minimal coupling, it is possible to produce the whole observed DM abundance via 2-to-2 scattering of the bath particles mediated by massless gravitons.

New symmetry in higher curvature spacetimes

New symmetries have been found in Einstein-Maxwell spacetimes. New symmetries have also been found in imperfect fluid curved spacetimes. We will prove in this paper that we can extend these symmetries to spacetimes with higher curvature terms. Higher curvature theories are in many cases associated to dark energy for instance. We provide further justification for these higher curvature formulations through the existence of a new symmetry.

Quantum flatness in two-dimensional quantum gravity

Flatness -- the absence of spacetime curvature -- is a well-understood property of macroscopic, classical spacetimes in general relativity. The same cannot be said about the concepts of curvature and flatness in nonperturbative quantum gravity, where the microscopic structure of spacetime is not describable in terms of small fluctuations around a fixed background geometry. An interesting case are two-dimensional models of quantum gravity, which lack a classical limit and therefore are maximally "quantum". We investigate the recently introduced quantum Ricci curvature in CDT quantum gravity on a two-dimensional torus, whose quantum geometry could be expected to behave like a flat space on suitably coarse-grained scales. On the basis of Monte Carlo simulations we have performed, with system sizes of up to 600.000 building blocks, this does not seem to be the case. Instead, we find a scale-independent "quantum flatness", without an obvious classical analogue. As part of our study, we develop a criterion that allows us to distinguish between local and global, topological properties of the toroidal quantum system.

Fermionic Bell violation in the presence of background electromagnetic fields in the cosmological de Sitter spacetime

The violation of the Bell inequality for Dirac fermions is investigated in the cosmological de Sitter spacetime, in the presence of background electromagnetic fields of constant strengths. The orthonormal Dirac mode functions are obtained and the relevant in-out squeezed state expansion in terms of the Bogoliubov coefficients are found. We focus on two scenarios here: strong electric field and heavy mass limits (with respect to the Hubble constant). Using the squeezed state expansion, we then demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Even though a background magnetic field alone cannot create particles, in the presence of background electric field and or spacetime curvature, it can affect the particle creation rate. Thus, our chief aim here is to investigate the role of the background magnetic field strength in the Bell violation. Qualitative differences in this regard for different maximally entangled initial states are shown. Further extension of these results to the so-called $\ensuremath{\alpha}$ vacua are also discussed.

Distinguishing Dark Energy models with neutrino oscillations

Dark Energy models are numerous and distinguishing between them is becoming difficult. However, using distinct observational probes can ease this quest and gives better assessment to the nature of Dark energy. To this end, the plausibility of neutrino oscillations to be a probe of Dark Energy models is investigated. First, a generalized formalism of neutrino (spinor field) interaction with a classical scalar field in curved space–time is presented. This formalism is then applied to two classes of Dark Energy models in a flat Friedman–Lemaître–Robertson–Walker metric: a Cosmological Constant and scalar field Dark Energy coupled to neutrinos. By looking at the neutrino oscillation probability’s evolution with redshift, these models can be distinguished, for certain neutrino and scalar field coupling properties. This evolution could be traced by neutrino flux measurements in future underground, terrestrial or extraterrestrial, neutrino telescopes which would assess probing Dark Energy models with this technique.

“Crooked Magnetism” of Maxwell (without real magnetic charges) as the age-old imprecation of Physical Science

Experimental and theoretical studies of the author (period: 1968 - present) have shown that magnetic fundamental particles (magnetic charges) are real structural components of atoms and substance. It is the magnetic charges, and not the electrons moving are the direct sources of all magnetic fields and magnetic manifestations in nature. Magnetic charges together with electric charges make up the shells of atoms which in reality are electromagnetic, and not electronic. It is the shells of atoms and nucleons that are the sources of the gravitational field, which is a vortex electromagnetic field. The main reason for ignoring magnetic charges, as well as true antielectronsа in physical science are the harsh conditions for their confinement in the structures of substance which is cardinally different from confinement of electrons. In addition, a very negative role in the “fate” of the noted problematic particles was played by Maxwell's vicious concept of electric magnetism, in which the great physicist, back in 1873, based on his superficial impressions of the famous Oersted Experiment declared moving electrons by the direct sources of the magnetic field. Paradoxically, the world physical community has accepted Maxwell's erroneous concept as the absolute truth and, for almost 150 years, his vicious electric magnetism largely determines the "development" of world fundamental physics. The article shows how the introduction of these problematic particles into basic physics radically changes the representation of most physical effects and manifestations. So, for example, the gravitational field in physics with magnetic charges is just the vortex electromagnetic field that has nothing to do with the ritual curvature of 4-dimensional space-time.  To obtain a gravitational field and use it in practice, it is necessary to legalize magnetic charges and learn how to work with them in superconductivity conditions.

Scalar-tensor theories within Asymptotic Safety

Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the Einstein-Hilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.

Enlightening the CSL model landscape in inflation

We propose a novel realization for the natural extrapolation of the continuous spontaneous localization (CSL) model, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL model to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory.

Interplay between Spacetime Curvature, Speed of Light and Quantum Deformations of Relativistic Symmetries

Recent work showed that κ-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincaré algebra of special-relativistic symmetries, one can toggle the curvature parameter Λ, the Planck scale quantum deformation parameter κ and the speed of light parameter c to move to the well-studied κ-Poincaré algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras and their curved versions. In this review, we survey the properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.

On the force caused by a null Einstein-Maxwell field with the plane symmetry

The article shows that a large flat platform with a constant current, which flows over its surface, accelerates time. It is also shown that if an alternating current flows along the surface of a flat platform while creating a null electromagnetic field then a force repelling from the platform acts on the test particle located near it. This force has no gravitational nature and arises as a result of the curvature of space-time by the electromagnetic field of a flat platform with an alternating current.

What can we learn from the conformal noninvariance of the Klein–Gordon equation?

It is well known that the Klein–Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully relativistic regime, then in the nonrelativistic regime leading to the Schrödinger equation, and then within the de Broglie–Bohm causal interpretation of quantum mechanics. The conformal noninvariance of the Klein–Gordon equation coupled to a vector potential is confronted with the conformal invariance of Maxwell’s equations in the presence of a charged current. The conformal invariance of the nonminimally coupled Klein–Gordon equation to gravity is then examined in light of the conformal invariance of Maxwell’s equations. Finally, the consequence of the noninvariance of the equation on the Aharonov–Bohm effect in curved space–time is discussed.

Electromagnetic potentials in curved spacetimes

Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potentials. We provide a general relativistic analysis of these potentials, by deriving their wave equations in an arbitrary Riemannian spacetime containing a generalised imperfect fluid. Some of the driving agents in the resulting wave formulae are explicitly due to the curvature of the host spacetime. Focusing on the implications of non-Euclidean geometry, we look into the linear evolution of the vector potential in Friedmann universes with nonzero spatial curvature. Our results reveal a qualitative difference in the evolution of the potential between the closed and the open Friedmann models, solely triggered by the different spatial geometry of these spacetimes. We then consider the interaction between gravitational and electromagnetic radiation and the effects of the former upon the latter. In so doing, we apply the wave formulae of both potentials to a Minkowski background and study the Weyl–Maxwell coupling at the second perturbative level. Our solutions, which apply to low-density interstellar environments away from massive compact stars, allow for the resonant amplification of both the electromagnetic potentials by gravitational-wave distortions.

GPS, GLONASS, and Galileo orbit geometry variations caused by general relativity focusing on Galileo in eccentric orbits

Three main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In the apogee, the semimajor axis decreases but eccentricity increases, and thus, the orbit becomes more eccentric. Hence, the orbital size variabilities for eccentric orbits are greatly compensated by the orbital shape changes, and thus the total effect of satellite height change is much smaller than the effects for the size and shape of the orbit, individually. The mean semimajor axis offset based on all GPS, GLONASS, and Galileo satellites is − 17.41 ± 2.90 mm, which gives a relative error of 0.36% with respect to the theoretical value.

Dirac–Kratzer problem with spin and pseudo-spin symmetries in curved space–time

In this work, the Dirac–Kratzer problem with spin and pseudo-spin symmetries in a deformed nucleus is analyzed. Thus, the Dirac equation in curved space–time was considered, with a line element given by [Formula: see text], where [Formula: see text] is a scalar potential, coupled to vector [Formula: see text] and tensor [Formula: see text] potentials. Defining the vector and scalar potentials of the Kratzer type and the tensor potential given by a term centrifugal-type term plus a term cubic singular at the origin, we obtain the Dirac spinor in a quasi-exact way and the eigenenergies numerically for the spin and pseudo-spin symmetries, so that these symmetries are removed due to the coupling of an Coulomb-type effective tensor potential coming from the curvature of space, however, when such potential is null the symmetries return. The probability densities were analyzed using graphs to compare the behavior of the system with and without spin and pseudo-spin symmetries.

Modified general relativity and quantum theory in curved spacetime

With appropriate modifications, the multi-spin Klein–Gordon (KG) equation of quantum field theory can be adapted to curved space–time for spins 0, 1, 1/2. The associated particles in the microworld then move as a wave at all space–time coordinates. From the existence in a Lorentzian space–time of a line element field [Formula: see text], the spin-1 KG equation [Formula: see text] is derived from an action functional involving [Formula: see text] and its covariant derivative. The spin-0 KG equation and the KG equation of the outer product of a spin-1/2 Dirac spinor and its Hermitian conjugate are then constructed. Thus, [Formula: see text] acts as a fundamental quantum vector field. The symmetric part of the spin-1 KG equation, [Formula: see text], is the Lie derivative of the metric. That links the multi-spin KG equation to Modified General Relativity (MGR) through its energy–momentum tensor of the gravitational field. From the invariance of the action functionals under the diffeomorphism group Diff(M), which is not restricted to the Lorentz group, [Formula: see text] can instantaneously transmit information along [Formula: see text]. That establishes the concept of entanglement within a Lorentzian formalism. The respective local/nonlocal characteristics of MGR and quantum theory no longer present an insurmountable problem to unify the theories.