Gravitational Coupling Research Articles

The Einstein–Infeld–Hoffmann legacy in mathematical relativity I: The classical motion of charged point particles

Einstein, Infeld and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. This report identifies necessary conditions for a well-defined general-relativistic joint initial value problem of [Formula: see text] classical point charges and their electromagnetic and gravitational fields. Among them, in particular, is the requirement that the electromagnetic vacuum law guarantees a finite field energy–momentum of a point charge. This disqualifies the Maxwell(–Lorentz) law used by EIH. On the positive side, if the electromagnetic vacuum law of Bopp, Landé–Thomas and Podolsky (BLTP) is used, and the singularities equipped with a nonzero bare rest mass, then a joint initial value problem can be formulated in the spirit of the EIH proposal, and shown to be locally well-posed — in the special-relativistic zero-[Formula: see text] limit. With gravitational coupling (i.e. [Formula: see text]), though, changing Maxwell’s into the BLTP law and assigning a bare rest mass to the singularities is by itself not sufficient to obtain even a merely well-defined joint initial value problem: the gravitational coupling also needs to be changed, conceivably in the manner of Jordan and Brans–Dicke.

Nonaxisymmetric instabilities and star-disk coupling I. Moderate mass disks

We present results of an investigation of the effects massive circumstellar disks have on the stability properties of polytropic stars. We consider systems with moderate mass disks, $M_{d}/M_{*} = 0.2$ and 0.25 where $M_{d}$ and $M_{*}$ are the masses of the disk and star respectively, and with central stars in slow uniform rotation and central stars in rapid differential rotation. We study systems where the central stars are above the barlike mode secular and dynamic instability thresholds for rotating solitary stars and systems where the stars are below the barlike mode secular instability threshold for rotating solitary stars. Equilibrium systems composed of stars with massive circumstellar disks are calculated, and their stability properties determined using linear and nonlinear techniques. For the uniform rotation case, the central stars are in slow rotation in the sense that they are below barlike instability thresholds for rotating single stars. For the differential rotation case, the central stars span the range from slow rotation to rapid rotation where rapid rotation means the stars are unstable to dynamic barlike instabilities. Gravitational coupling between the star and disk drives one-armed instabilities in the slowly rotating central star case. The couple primarily forces orbital motion rather than spin-up of the star. For systems with differentially rotating central stars with slow rotation, star-disk coupling drives instability in one-armed and two-armed modes. At the fastest rotation considered, the central star becomes unstable to the barlike instability evolving in a manner similar to that found for single rapidly rotating stars. The central stars did not fission. Star-disk coupling does not strongly influence the development of the barlike mode for this case.

On the impact of Majorana masses in gravity-matter systems

We investigate the Higgs-Yukawa system with Majorana masses of a fermion within asymptotically safe quantum gravity. Using the functional renormalization group method we derive the beta functions of the Majorana masses and the Yukawa coupling constant and discuss the possibility of a non-trivial fixed point for the Yukawa coupling constant. In the gravitational sector we take into account higher derivative terms such as R2 and RμνRμν in addition to the Einstein-Hilbert term for our truncation. For a certain value of the gravitational coupling constants and the Majorana masses, the Yukawa coupling constant has a non-trivial fixed point value and becomes an irrelevant parameter being thus a prediction of the theory. We also discuss consequences due to the Majorana mass terms to the running of the quartic coupling constant in the scalar sector.

Planck mass and inflation as consequences of dynamically broken scale invariance

Classical scale invariance represents a promising framework for model building beyond the Standard Model. However, once coupled to gravity, any scale-invariant microscopic model requires an explanation for the origin of the Planck mass. In this paper, we provide a minimal example for such a mechanism and show how the Planck mass can be dynamically generated in a strongly coupled gauge sector. We consider the case of hidden $SU({N}_{c})$ gauge interactions that link the Planck mass to the condensation of a scalar bilinear operator that is nonminimally coupled to curvature. The effective theory at energies below the Planck mass contains two scalar fields: the pseudo--Nambu-Goldstone boson of spontaneously broken scale invariance (the dilaton) and a gravitational scalar degree of freedom that originates from the ${R}^{2}$ term in the effective action (the scalaron). We compute the effective potential for the coupled dilaton-scalaron system at one-loop order and demonstrate that it can be used to successfully realize a stage of slow-roll inflation in the early Universe. Remarkably enough, our predictions for the primordial scalar and tensor power spectra interpolate between those of standard ${R}^{2}$ inflation and linear chaotic inflation. For comparatively small gravitational couplings, we thus obtain a spectral index ${n}_{s}\ensuremath{\simeq}0.97$ and a tensor-to-scalar ratio as large as $r\ensuremath{\simeq}0.08$.

Dark energy, the swampland, and the equivalence principle

It has recently been argued that string theory does not admit de Sitter vacua. This would imply that the current accelerated expansion of the universe is not driven by a cosmological constant (or vacuum energy) but by other means such as a quintessential scalar field. Such a scalar field is in general expected to couple to at least some matter species, such as dark matter. Cosmological observations already constrain such dark matter couplings strongly. We argue that there are a number of interesting scenarios to be explored, such as coupling functions which possess a minimum at finite field values. In these theories, the effective gravitational coupling between dark matter particles grows with time and are consistent with observations of the anisotropies in the cosmic microwave background radiation and large scale structures. We argue that such couplings might also help to alleviate the tension between the swampland conjectures and the properties of the quintessential potential. Observational signatures of violations of the equivalence principle in the dark sector are expected in the non-linear regime on intermediate or small scales.

Double-logarithms in mathcal{N} = 8 supergravity: impact parameter description & mapping to 1-rooted ribbon graphs

The set of double-logarithmic (DL) contributions (α t ln2s)n to the 4-graviton amplitude in mathcal{N} = 8 supergravity (SUGRA), with α being the gravitational coupling and (s, t) the Mandelstam invariants, is studied in impact parameter (ρ) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as s increases, which is not present in mathcal{N} < 4 SUGRA theories, there exists a critical line ρc(s) above which the Born amplitude prevails. The short distance region ρ < ρc(s) is dominated by the DL terms. As a consequence, when studied in terms of an eikonal approach in the forward limit, the scattering angle linked to the bending of the semiclassical trajectory of the graviton shows a transition from attractive gravity at large distances to a region at small ρ characterized by a repulsive DL contribution to the gravitational potential due to the gravitino content of the theory. In the complex angular momentum plane, this DL high energy asymptotics is driven by the rightmost pole singularity of a parabolic cylinder function. The resummation of DL quantum corrections in mathcal{N} = 8 SUGRA can be understood in terms of the counting of 1-rooted maps on orientable surfaces.

Super-Higgs in Superspace

We determine the effective gravitational couplings in superspace whose components reproduce the supergravity Higgs effect for the constrained Goldstino multiplet. It reproduces the known Gravitino sector while constraining the off-shell completion. We show that these couplings arise by computing them as quantum corrections. This may be useful for phenomenological studies and model-building. We give an example of its application to multiple Goldstini.

Composite gravity from a metric-independent theory of fermions

We present a metric-independent, diffeomorphism-invariant model with interacting fermions that contains a massless composite graviton in its spectrum. The model is motivated by the supersymmetric D-brane action, modulated by a fermion potential. The gravitational coupling is related to new physics at the cutoff scale that regularizes UV divergences. We also speculate on possible extensions of the model.

An unified cosmological evolution driven by a mass dimension one fermionic field

An unified cosmological model for an Universe filled with a mass dimension one (MDO) fermionic field plus the standard matter fields is considered. After a primordial quantum fluctuation the field slowly rolls down to the bottom of a symmetry breaking potential, driving the Universe to an inflationary regime that increases the scale factor for about 71 e-folds. After the end of inflation, the field starts to oscillate and can transfer its energy to the standard model particles through a reheating mechanism. Such a process is briefly discussed in terms of the admissible couplings of the MDO field with the electromagnetic and Higgs fields. We show that even if the field loses all its kinetic energy during reheating, it can evolve as dark matter due a gravitational coupling (of spinorial origin) with baryonic matter. Since the field acquires a constant value at the bottom of the potential, a non-null, although tiny, mass term acts as a dark energy component nowadays. Therefore, we conclude that MDO fermionic field is a good candidate to drive the whole evolution of the Universe, in such a way that the inflationary field, dark matter and dark energy are described by different manifestations of a single field.

Overview of theoretical considerations and problems related to the putative existence of repulsive gravitation, charge-mass repulsive force and unification

We use a torsion balance scale to measure the attraction between two large lead balls and two smaller brass balls, connected with an up-side down T bar that is hung with a string. The vertical part of the T bar is attached with a mirror that reflects a laser beam to provide a light spot that shows how much the T bar has turned. It is observed that the gravitational forces between the lead balls and the brass balls are reduced when the temperature of the lead balls increased. Thus, this experiment shows clearly the existence of a repulsive gravitational force that increases as the temperature of the lead balls increase. This supports that the charge-mass interaction is the reason that the theories of Galileo, Newton, and Einstein failed to explain the Anomaly of the Space-Probes and flybys, and the fact that not all the neutral subjects necessarily fall with the same acceleration. In other words, the Newtonian law of gravitation is only approximately valid. Thus, the attempts such as J. Luo (罗俊)’s to obtain an accurate gravitational coupling constant with just improved skill are futile. The physical picture of Galileo, Newton, and Einstein on gravitation needs extension beyond the Standard Model (SM).

Optimising growth of structure constraints on modified gravity

We use growth of structure data to constrain the effective field theory of dark energy. Considering as case study Horndeski theories with the speed of gravitational waves equal to that of light, we show how constraints on the free parameters and the large-scale structure phenomenological functions can be improved by two ingredients: firstly by complementing the set of redshift-space distortions data with the three recent measurements of the growth rate f and the amplitude of matter fluctuations σ8 from the VIPERS and SDSS collaborations; secondly by applying a local Solar System bound on the variation of the Newton constant. This analysis allows us to conclude that: i) despite firmly restricting the predictions of weaker gravity, the inclusion of the Solar System bound does not prevent suppressed growth relative to the standard model ΛCDM at low redshifts; ii) the same bound in conjunction with the growth of structure data strongly restricts the redshift evolution of the gravitational slip parameter to be close to unity and the present value is constrained to one at the 10−3 level; iii) the growth of structure data favours a fifth force contribution to the effective gravitational coupling at low redshifts and at more than {two} sigma at present time.

Holographic subregion complexity of a (1+1)-dimensional $p$-wave superconductor

Abstract We analyze the holographic subregion complexity in a three-dimensional black hole with vector hair. This three-dimensional black hole is dual to a (1+1)-dimensional $p$-wave superconductor. We probe the black hole by changing the size of the interval and by fixing $q$ or $T$. We show that the universal part is finite across the superconductor phase transition and has competitive behaviors different from the finite part of the entanglement entropy. The behavior of the subregion complexity depends on the gravitational coupling constant divided by the gauge coupling constant. When this ratio is less than the critical value, the subregion complexity increases as temperature becomes low. This behavior is similar to that of the holographic (1+1)-dimensional $s$-wave superconductor [M. K. Zangeneh, Y. C. Ong, and B. Wang, Phys. Lett. B 771, 130 (2014)]. When the ratio is larger than the critical value, the subregion complexity has a non-monotonic behavior as a function of $q$ or $T$. We also find a discontinuous jump of the subregion complexity as a function of the size of the interval. The subregion complexity has a maximum when it wraps almost the entire spatial circle. Due to competitive behaviors between the normal and condensed phases, the universal term in the condensed phase becomes even smaller than that of the normal phase by probing the black hole horizon at a large interval. This implies that the condensate formed decreases the subregion complexity as in the case of the entanglement entropy.

Dynamical renormalization of black-hole spacetimes

We construct a black-hole spacetime which includes the running of the gravitational coupling in a self-consistent way. Starting from a classical Schwarzschild black hole, the backreaction effects produced by the running Newton’s coupling are taken into account iteratively. The sequence, described by a simple recurrence relation, flows towards a self-consistent solution that can be derived analytically. As a key result, if the gravitational renormalization group flow attains a non-trivial fixed point at high energies, the sequence converges to a “renormalized” black-hole spacetime of the Dymnikova-type, which is free of singularities.

Generalized framework for testing gravity with gravitational-wave propagation. III. Future prospect

The properties of gravitational-wave (GW) propagation are modified in alternative theories of gravity and are crucial observables to test gravity at cosmological distance. The propagation speed has already been measured from GW170817 so precisely and pinned down to the speed of light, while other properties of GW propagation have not constrained tightly yet. In this paper, we investigate the measurement precisions of the amplitude damping rate (equivalently, the time variation of the gravitational coupling for GWs) and graviton mass in the generalized framework of GW propagation with the future detectors such as Voyager, Cosmic Explorer, and Einstein Telescope. As a result, we show that the future GW observation can reach 1% error for the amplitude damping. We also study the time variation of the gravitational couplings in Horndeski theory by performing Monte Carlo-based numerical simulations. From the simulation results, we find that the current accelerating Universe prefers the models with less damping of GWs and that the equivalence principle can be tested at the level of 1% by the future GW observation.

Modified Gravity (MOG) fits to observed radial acceleration of SPARC galaxies

The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newton's gravitational acceleration law. In addition to the metric $g_{\mu\nu}$, MOG has a vector field $\phi_\mu$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $\alpha$, while parameter $\mu$ is the small effective mass of $\phi_\mu$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a radial acceleration relation (RAR) that relates accelerations derived from galaxy rotation curves to Newtonian accelerations derived from galaxy mass models. Using the same SPARC galaxy data, mass models independently derived from that data, and MOG parameters $\alpha$ and $\mu$ that run with galaxy mass, we demonstrate that adjusting galaxy parameters within $\pm 1$-sigma bounds can yield MOG predictions consistent with the given rotational velocity data. Moreover, the same adjusted parameters yield a good fit to the RAR of MLS, with the RAR parameter $a_0=(5.4\pm .3)\times 10^{-11}\,{\rm m/s^2}$.

Impact of multiple modes on the black-hole superradiant instability

Ultralight bosonic fields in the mass range $\sim (10^{-20}-10^{-11})\,{\rm eV}$ can trigger a superradiant instability that extracts energy and angular momentum from an astrophysical black hole with mass $M\sim(5,10^{10})M_\odot$, forming a nonspherical, rotating condensate around it. So far, most studies of the evolution and end-state of the instability have been limited to initial data containing only the fastest growing superradiant mode. By studying the evolution of multimode data in a quasi-adiabatic approximation, we show that the dynamics is much richer and depend strongly on the energy of the seed, on the relative amplitude between modes, and on the gravitational coupling. If the seed energy is a few percent of the black-hole mass, a black hole surrounded by a mixture of superradiant and nonsuperradiant modes with comparable amplitudes might not undergo a superradiant unstable phase, depending on the value of the boson mass. If the seed energy is smaller, as in the case of an instability triggered by quantum fluctuations, the effect of nonsuperradiant modes is negligible. We discuss the implications of these findings for current constraints on ultralight fields with electromagnetic and gravitational-wave observations.

On the cutoff identification and the quantum improvement in asymptotically safe gravity

Applying the exact renormalization group method to search the non–Gaussian fixed points of gravitational coupling, is frequently followed by two steps: cutoff identification and improvement. Although there are various models for identifying the cutoff momentum by some physical length, saving the general covariance should be considered as an important property in the procedure. In this paper, use of an arbitrary function of curvature invariants for cutoff identification is suggested. It is shown that the field equations for this approach differs from the ones obtained from the conventional cutoff identification and improvement, even for non–vacuum solutions of the improved Einstein equations. Indeed, it is concluded that these two steps are correlated to each other.

Updated orbital ephemeris of the ADC source X 1822-371: a stable orbital expansion over 40 years

Aims. Source X 1822-371 is an eclipsing compact binary system with a period close to 5.57 h and an orbital period derivative Ṗorb of 1.51(7)×10−10 s s−1. The very high value of Ṗorb is compatible with a super-Eddington mass transfer rate from the companion star, as suggested by X-ray and optical data. The XMM-Newton observation taken in 2017 allows us to update the orbital ephemeris and verify whether the orbital period derivative has been stable over the past 40 yr. Methods. We added two new values obtained from the Rossi-XTE (RXTE) and XMM-Newton observations performed in 2011 and 2017, respectively, to the X-ray eclipse arrival times from 1977 to 2008. We estimated the number of orbital cycles and the delays of our eclipse arrival times spanning 40 yr, using as reference time the eclipse arrival time obtained from the RXTE observation taken in 1996. Results. Fitting the delays with a quadratic model, we found an orbital period Porb = 5.57062957(20) h and a Ṗorb value of 1.475(54)×10−10 s s−1. The addition of a cubic term to the model does not significantly improve the fit quality. We also determined a spin-period value of Pspin = 0.5915669(4) s and its first derivative Ṗspin = − 2.595(11) × 10−12 s s−1. Conclusions. Our results confirm the scenario of a super-Eddington mass transfer rate; we also exclude a gravitational coupling between the orbit and the change in the oblateness of the companion star triggered by the nuclear luminosity of the companion star.

4-Index theory of gravity and its relation with the violation of the energy–momentum conservation law

Recently, a 4-index generalization of the Einstein theory has been proposed by Moulin [F. Moulin, Eur. Phys. J. C 77, 878 (2017)]. Using this method, we find the most general 2-index field equations derivable from the Einstein–Hilbert action. The application of Newtonian limit, the role of gravitational coupling constant and the effects of the properties of ordinary energy–momentum tensor in obtaining a 4-index gravity theory have been studied. We also address the results of building Weyl free 4-index gravity theory. Our study displays that both the Einstein and Rastall theories can be obtained as the subclasses of a 4-index gravity theory which shows the power of 4-index method in unifying various gravitational theories. It is also obtained that the violation of the energy–momentum conservation law may be allowed in 4-index gravity theory, and moreover, the contraction of 4-index theory generally admits a non-minimal coupling between geometry and matter field in the Rastall way. This study also shows that, unlike the Einstein case, the gravitational coupling constant of 4-index Rastall theory generally differs from that of the ordinary 2-index Rastall theory.

A cosmological basis for E = mc2

The Universe has a gravitational horizon with a radius [Formula: see text] coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann–Lemaître–Robertson–Walker space–time, we see it retreating at proper speed [Formula: see text], giving rise to the eponymously named cosmological model [Formula: see text]. As of today, this cosmology has passed over 20 observational tests, often better than [Formula: see text]CDM. The gravitational radius [Formula: see text] therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass [Formula: see text] within the horizon and demonstrate that it is equal to [Formula: see text]. This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle’s escape energy when it approaches [Formula: see text]. In other words, a particle’s gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.