General Relativistic Effects Research Articles

IARD 2022 The 13th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Preface The International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president. Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remain the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge’s book, The Relativistic Gas, and in Balescu’s book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory. In recent years, highly accurate telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems, such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues.It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, foundations of relativity theory, and mathematical physics, with a common interest in relativistic dynamics, to investigate fundamental questions of this type, that this Association was founded. The second meeting took place in 2000 at Bar Ilan University in Israel, the third, in 2002, at Howard University in Washington, D.C., and the fourth, in 2004, in Saas Fee, Switzerland. Subsequent meeting took place in 2006 at the University of Connecticut Storrs, in 2008 at Aristotle University of Thessalonica, in 2010 at National Dong Hwa University, Hualien, Taiwan, in 2012 at the Galileo Galilei Institute for Theoretical Physics (GGI) in Florence, in 2014 as the University of Connecticut Storrs, Connecticut, in 2016 at Jožef Stefan Institute in Ljubljana, Slovenia, and in 2018 in Mérida, Yucatán, Mexico, under the sponsorship of the Instituto Politécnic Nacional. The 2020 meeting, planned for Czech Technical University in Prague, was successfully held online at the height of the Covid-19 pandemic, and the physical meeting in Prague was delayed to 2022.The 2022 meeting forms the basis for the Proceedings that are recorded in this issue of the Journal of Physics: Conference Series. Along with the work of some of the founding and newer but already much engaged members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, cosmological problems, and in the dynamics of systems subject to accelerations and the effects of general relativity. Topics treated in this issue include studies in general relativity and astrophysics, relativistic dynamics and electrodynamics, quantum theory and particles, and foundations of relativistic dynamics.This first physical meeting of the Covid-19 era took place 6 - 9 June at Czech Technical University in Prague, as originally planned for 2020. The meeting was divided into seven plenary sessions over four days. As a result of continued travel restrictions in some areas, a small number of talks were delivered by videoconferencing. The papers presented in this volume represent extensions and refinements to the conference talks, building on feedback and discussions associated with the lectures. We once again express our gratitude to Czech Technical University, and especially the local conference chair Petr Jizba, for their generous hospitality.List of Scientific Advisory Committee, International Organizing Committee and Editorial Board of the proceedings, Dedication are available in this Pdf.

Grgadget: an N-body TreePM relativistic code for cosmological simulations

ABSTRACT We present the merging of the Particle-Mesh (PM) relativistic gevolution code with the TreePM gadget-4 code, with the aim of studying general relativity effects in cosmology. Our code, called grgadget, is able to track the evolution of metric perturbations in the weak field limit by using gevolution’s implementation of a relativistic PM in the Poisson gauge. To achieve this, starting from gevolution, we have written a c++ library called libgevolution, which allows a code to access and use the same abstractions and resources that gevolution uses for its PM-only N-body simulations. The code works under the assumption that particle interactions at short distances can be approximated as Newtonian, so that we can combine the forces computed with a Newtonian Tree with those computed with a relativistic PM. The result is a TreePM simulation code that represents metric perturbations at the scales where they are relevant while resolving non-linear structures. We validate our code by closely matching gadget-4 forces, computed with the Tree switched off, with those computed with libgevolution in the Newtonian limit. With grgadget, we obtain a matter power spectrum that is compatible with Newtonian gadget-4 at small scales and contains GR features at large scales that are consistent with results obtained with gevolution. We demonstrate that, due to the better resolution of the highly non-linear regime, the representation of the relativistic fields sampled on the mesh improves with respect to the PM-only simulations.

ПРЕЦЕССИЯ ЛЕНЗЕ-ТИРРИНГА ЧЕРНЫМИ ДЫРАМИ В МОДЕЛИ РЭНДАЛЛА-САНДРАМА

The description of our universe on a brane suggests a large extra dimension and a fundamental scale of gravity, which can be several orders of magnitude lower than the Planck scale. An interesting consequence of the brane world scenario is the nature of spherically symmetric vacuum solutions of the brane gravitational field equations, which can represent black holes with properties quite different from those of ordinary black holes in 4 dimensions. The paper investigates the Lense-Thirring precession by black holes in the Randall-Sandrum model caused by the frame-dragging effect. Lense-Thirring precession is a general relativistic effect that occurs when a rotating particle is displaced vertically from the equatorial axis of a rotating body in such a way that the framedragging causes oscillations around the ecliptic and periapsis. The Randall-Sandrum model assumes that our universe is a negative tension domain wall separated from the positive tension wall by an anti-de Sitter space slab. The space-time of a black hole in the Randall-Sandrum model of the "brane world" theory is characterized by an induced tidal charge. In particular, a generalized expression for the Lense-Thirring precession rate in the case of a strong and weak gravitational field is obtained. Further, the precession of the gyroscope in the plane θ=0 is considered, the dependence of the Lense-Thirring precession rate for a stellar-mass black hole and a supermassive black hole is shown for different values of the tidal charge β. The results of numerical simulation are presented for various values of the tidal charge and the radial coordinate.

Extremely Relativistic Tidal Disruption Events

Extreme tidal disruption events (eTDEs), which occur when a star passes very close to a supermassive black hole, may provide a way to observe a long-sought general relativistic effect: orbits that wind several times around a black hole and then leave. Through general relativistic hydrodynamics simulations, we show that such eTDEs are easily distinguished from most tidal disruptions, in which stars come close, but not so close, to the black hole. Following the stellar orbit, the debris is initially distributed in a crescent, it then turns into a set of tight spirals circling the black hole, which merge into a shell expanding radially outwards. Some mass later falls back toward the black hole, while the remainder is ejected. Internal shocks within the infalling debris power the observed emission. The resulting lightcurve rises rapidly to roughly the Eddington luminosity, maintains this level for between a few weeks and a year (depending on both the stellar mass and the black hole mass), and then drops. Most of its power is in thermal X-rays at a temperature ∼(1–2) × 106 K (∼100–200 eV). The debris evolution and observational features of eTDEs are qualitatively different from ordinary TDEs, making eTDEs a new type of TDE. Although eTDEs are relatively rare for lower-mass black holes, most tidal disruptions around higher-mass black holes are extreme. Their detection offers a view of an exotic relativistic phenomenon previously inaccessible.

Nonrelativistic limit of scalar and Dirac fields in curved spacetime

We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays experimentally accessible. We believe that the ever-improving measurement accuracy and the theoretical interest in finding general relativistic effects in quantum systems require the introduction of corrections to the Schr\"{o}dinger-Newtonian theory. We rigorously determine these corrections by the non-relativistic limit of fully relativistic quantum theories in curved spacetime. For curved static spacetimes, we show how a non-inertial observer (equivalently, an observer in the presence of a gravitational field) can distinguish a scalar field from a Dirac field by particle-gravity interaction. We study the Rindler spacetime and discuss the difference between the resulting non-relativistic Hamiltonians. We find that for sufficiently large acceleration, the gravity-spin coupling dominates over the corrections for scalar fields, promoting Dirac particles as the best candidates for observing non-Newtonian gravity in quantum particle phenomenology.

Hidden Quantum Effect in General Relativity

Hidden Quantum Effect in General Relativity

General relativistic effects and the near-infrared and X-ray variability of Sgr A* I

The near-infrared (NIR) and X-ray emission of Sagittarius A* shows occasional bright flares that are assumed to originate from the innermost region of the accretion flow. We identified 25 4.5 μm and 24 X-ray flares in archival data obtained with the Spitzer and Chandra observatories. With the help of general relativistic ray-tracing code, we modeled trajectories of “hot spots” and studied the light curves of the flares for signs of the effects of general relativity. Despite their apparent diversity in shape, all flares share a common, exponential impulse response, a characteristic shape that is the building block of the variability. This shape is symmetric, that is, the rise and fall times are the same. Furthermore, the impulse responses in the NIR and X-ray are identical within uncertainties, with an exponential time constant τ ∼ 15 m. The observed characteristic flare shape is inconsistent with hot-spot orbits viewed edge-on. Individually modeling the light curves of the flares, we derived constraints on the inclination of the orbital plane of the hot spots with respect to the observer (i ∼ 30° , < 75°) and on the characteristic timescale of the intrinsic variability (a few tens of minutes).

More direct methods to evaluate general relativity effects. The influence of the age of the Universe

More direct methods are given to evaluate the general relativity effects by simplifying the solving the solution of the extremum of variational problem to one variable only. The influence of the age of the Universe is mainly related to the variation of the coefficient of gravity the age of the Universe.

Structure and evolution of ultra-massive white dwarfs in general relativity

Context. Ultra-massive white dwarfs (M⋆ ≳ 1.05 M⊙) are of utmost importance in view of the role they play in type Ia supernovae explosions, merger events, the existence of high-magnetic -field white dwarfs, and the physical processes in the super asymptotic giant branch phase. Aims. We aim to present the first set of constant rest-mass ultra-massive oxygen-neon white dwarf cooling tracks with masses of M⋆ > 1.29 M⊙ which fully take into account the effects of general relativity on their structural and evolutionary properties. Methods. We computed the full evolution sequences of 1.29, 1.31, 1.33, 1.35, and 1.369 M⊙ white dwarfs with the La Plata stellar evolution code, LPCODE. For this work, the standard equations of stellar structure and evolution have been modified to include the effects of general relativity. Specifically, the fully general relativistic partial differential equations governing the evolution of a spherically symmetric star are solved in a way so that they resemble the standard Newtonian equations of stellar structure. For comparison purposes, the same sequences have been computed for the Newtonian case. Results. According to our calculations, the evolutionary properties of the most massive white dwarfs are strongly modified by general relativity effects. In particular, the resulting stellar radius is markedly smaller in the general relativistic case, being up to 25% smaller than predicted by the Newtonian treatment for the more massive ones. We find that oxygen-neon white dwarfs more massive than 1.369 M⊙ become gravitationally unstable with respect to general relativity effects. When core chemical distribution due to phase separation on crystallization is considered, such instability occurs at somewhat lower stellar masses, ≳1.36 M⊙. In addition, cooling times for the most massive white dwarf sequences are about a factor of two smaller than in the Newtonian case at advanced stages of evolution. Finally, a sample of white dwarfs have been identified as ideal candidates to test these general relativistic effects. Conclusions. We conclude that the general relativity effects should be taken into account for an accurate assessment of the structural and evolutionary properties of the most massive white dwarfs. These new ultra-massive white dwarf models constitute a considerable improvement over those computed in the framework of the standard Newtonian theory of stellar interiors.

Effect of Dark Matter Distribution on Scalaron Gravity near the Galactic Center Black Hole and Its Prospects

In this paper, we report the effect of exponential and power-law dark matter density profiles near the Galactic Center black hole on the relative scalaron field amplitude , ψ 0/ϕ (ϕ being Newtonian potential and ψ 0 being the scalaron field amplitude), of f(R) gravity theory. Constraints on the density profiles derived earlier on the basis of orbital motion of the S-2 star are used in conjunction with scalarons having a mass range 10−22–10−16 eV to investigate the dependency of screening or unscreening of modified gravity on the dark matter density through the condition that the rate of pericenter shift due to dark matter is equal to that due to scalaron gravity + general relativistic effects. The semimajor axes are chosen as a = 45 au, 100 au, and 1000 au. It is found that scalarons get screened for extremely low and extremely high mass. This is found to be independent of the black hole spin in the range (χ = 0.1–0.9). For wider orbits scalarons of almost all the masses tend to remain unscreened for the dark matter profiles. It has been found that low dark matter density has a natural tendency to unscreen the scalaron gravity with extremely small coupling strength. We remap screened gravity in the available observational constraints on the scale of modified gravity near the black hole. Astrophysical prospects are presented.

Gravitational radiation from inspiralling compact objects: Spin effects to the fourth post-Newtonian order

The linear- and quadratic-in-spin contributions to the binding potential and gravitational-wave flux from binary systems are derived to next-to-next-to-leading order in the Post-Newtonian (PN) expansion of general relativity, including finite-size and tail effects. The calculation is carried out through the worldline effective field theory framework. We find agreement in the overlap with the available PN literature and test-body limit. As a direct application, we complete the knowledge of spin effects in the evolution of the orbital phase for aligned-spin circular orbits to fourth PN order. We estimate the impact of the new results in the number of accumulated gravitational-wave cycles. We find they will play an important role in providing reliable physical interpretation of gravitational-wave signals from spinning binaries with future detectors such as LISA and the Einstein Telescope.

Atom interferometers and a small-scale test of general relativity

Since the first appearance of general relativity in 1916, various experiments have been conducted to test the theory. Due to the weakness of the interactions involved, all of the documented tests were carried out in a gravitational field generated by objects of an astronomical scale. We propose an idea for an experiment that could detect purely general-relativistic effects in a lab-generated gravitational field. It is shown that a set of dense rapidly-revolving cylinders produce a frame-dragging effect substantial enough to be two orders of magnitude away from the observable range of the next generation of atomic interferometers. The metric tensor due to a uniform rotating axisymmetric body in the weak-field limit is calculated and the phase shift formula for the interferometer is derived. This article is meant to demonstrate feasibility of the concept and stimulate further research into the field of low-scale experiments in general relativity. It is by no means a fully developed experiment proposal.

Galactic dynamics in general relativity: the role of gravitomagnetism

It is a well-known fact that, in the absence of dark matter, the observation of the rotation curves of galaxies cannot be explained in terms of Newtonian gravity. Rotation curves become flat in the outer regions, in contrast to what is expected according to Keplerian motion. Far from the galactic center, the gravitational field is supposed to be weak enough so we expect to be able to use Newtonian gravity; however, even in the weak-field approximation, there are general relativistic effects without a Newtonian counterpart, such as the gravitomagnetic effects originating from mass currents. Using the gravitoelectromagnetic approach to the solution of Einstein equations in the weak-field and slow-motion approximation, we discuss some simple arguments that suggest the surprising result that gravitomagnetic effects may have a relevant role in better understanding the impact of dark matter on galactic dynamics. In addition, treating matter as a fluid of dust, we study the influence of post-Newtonian effects on the fluid vorticity.

Production of hot Jupiter candidates from high-eccentricity mechanisms for different initial planetary mass configurations

ABSTRACT Hot Jupiters (HJs) are giant planets with orbital periods of the order of a few days with semimajor axis within ∼0.1 au. Several theories have been invoked in order to explain the origin of this type of planets, one of them being the high-eccentricity migration. This migration can occur through different high-eccentricity mechanisms. Our investigation focused on six different kinds of high-eccentricity mechanisms, namely, direct dispersion, coplanar, Kozai–Lidov, secular chaos, E1 and E2 mechanisms. We investigated the efficiency of these mechanisms for the production of HJ candidates in multiplanet systems initially tightly-packed in the semimajor axis, considering a large set of numerical simulations of the exact equations of motion in the context of the N-body problem. In particular, we analyzed the sensitivity of our results to the initial number of planets, the initial semimajor axis of the innermost planetary orbit, the initial configuration of planetary masses, and to the inclusion of general relativity (GR) effects. We found that the E1 mechanism is the most efficient in producing HJ candidates both in simulations with and without the contribution of GR, followed by the Kozai–Lidov and E2 mechanisms. Our results also revealed that, except for the initial equal planetary mass configuration, the E1 mechanism was notably efficient in the other initial planetary mass configurations considered in this work. Finally, we investigated the production of HJ candidates with prograde, retrograde, and alternating orbits. According to our statistical analysis, the Kozai–Lidov mechanism has the highest probability of significantly exciting the orbital inclinations of the HJ candidates.

Frame-Dragging in Extrasolar Circumbinary Planetary Systems

Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital motion of a relatively distant planet with Lense-Thirring-type precessional effects which, under certain circumstances, may amount to a significant fraction of the static, gravitoelectric ones, analogous to the well known Einstein perihelion precession of Mercury, depending only on the masses of the system’s bodies. Instead, when the gravitomagnetic field is due solely to the spin of each of the central star(s), the Lense-Thirring shifts are several orders of magnitude smaller than the gravitoelectric ones. In view of the growing interest in the scientific community about the detection of general relativistic effects in exoplanets, the perspectives of finding new scenarios for testing such a further manifestation of general relativity might be deemed worth of further investigations.

First minutes of a binary-driven hypernova

We simulate the first minutes of the evolution of a binary-driven hypernova (BdHN) event, with a special focus on the associated accretion processes of supernova (SN) ejecta onto the newborn neutron star ($\nu$NS) and the NS companion. We calculate the rotational evolution of the $\nu$NS and the NS under the torques exerted by the accreted matter and the magnetic field. We take into account general relativistic effects and use realistic hypercritical accretion rates obtained from three-dimensional smoothed-particle-hydrodynamics (SPH) numerical simulations of the BdHN for a variety of orbital periods. We show that the rotation power of the $\nu$NS has a unique double-peak structure while that of the NS has a single peak. These peaks are of comparable intensity and can occur very close in time or even simultaneously depending on the orbital period and the initial angular momentum of the stars. We outline the consequences of the above features in the early emission and their consequent observation in long gamma-ray bursts (GRBs).

Lensing effects in galactic retarded gravity: Why “Dark Matter” is the same for both gravitational lensing and rotation curves

Galaxies are huge physical systems having a generic size of tens of thousands of parsecs. Thus, any modification at the center of the galaxy will affect the outskirts only tens of millennia afterwards. Those retardation considerations seem to be neglected in present day analysis used to estimated rotational velocities of matter in the rim of the galaxy and its surrounding gas. The significant differences between the velocities predicted by Newtonian action at a distance theory and observations are usually dealt with by either assuming an unobservable type of matter usually referred to as “dark matter” or by modifying the laws of gravity (MOND as a typical example). Here we demonstrate that considering general relativistic effects one can explain the apparent excess matter leading to gravitational lensing in both galaxies and galaxy clusters. We also explain why the amount of “dark matter” must be the same for both rotational curves and gravitational lensing.

A Deep and Wide Twilight Survey for Asteroids Interior to Earth and Venus

We are conducting a survey using twilight time on the Dark Energy Camera with the Blanco 4 m telescope in Chile to look for objects interior to Earth’s and Venus’ orbits. To date we have discovered two rare Atira/Apohele asteroids, 2021 LJ4 and 2021 PH27, which have orbits completely interior to Earth’s orbit. We also discovered one new Apollo-type Near Earth Object (NEO) that crosses Earth’s orbit, 2022 AP7. Two of the discoveries have diameters ≳1 km. 2022 AP7 is likely the largest Potentially Hazardous Asteroid (PHA) discovered in about eight years. To date we have covered 624 square degrees of sky near to and interior to the orbit of Venus. The average images go to 21.3 mag in the r band, with the best images near 22nd mag. Our new discovery 2021 PH27 has the smallest semimajor axis known for an asteroid, 0.4617 au, and the largest general relativistic effects (53 arcsec/century) known for any body in the solar system. The survey has detected ∼15% of all known Atira NEOs. We put strong constraints on any stable population of Venus co-orbital resonance objects existing, as well as the Atira and Vatira asteroid classes. These interior asteroid populations are important to complete the census of asteroids near Earth, including some of the most likely Earth impactors that cannot easily be discovered in other surveys. Comparing the actual population of asteroids found interior to Earth and Venus with those predicted to exist by extrapolating from the known population exterior to Earth is important to better understand the origin, composition, and structure of the NEO population.

Thermal Radiation from Compact Objects in Curved Space-Time

We highlight here the fact that the distantly observed luminosity of a spherically symmetric compact star radiating thermal radiation isotropically is higher by a factor of (1+zb)2 compared to the corresponding flat space-time case, where zb is the surface gravitational redshift of the compact star. In particular, we emphasize that if the thermal radiation is indeed emitted isotropically along the respective normal directions at each point, this factor of increment (1+zb)2 remains unchanged even if the compact object would lie within its photon sphere. Since a canonical neutron star has zb≈0.1, the actual X-ray luminosity from the neutron star surface could be ∼20% higher than what would be interpreted by ignoring the general relativistic effects described here. For a static compact object, supported by only isotropic pressure, compactness is limited by the Buchdahl limit zb<2.0. However, for compact objects supported by anisotropic pressure, zb could be even higher (zb<5.211). In addition, in principle, there could be ultra-compact objects having zb≫1. Accordingly, the general relativistic effects described here might be quite important for studies of thermal radiation from some ultra-compact objects.

Overcoming 1 part in 10^9 of earth angular rotation rate measurement with the G Wettzell data

The absolute measurement of the Earth angular rotation rate with ground-based instruments becomes challenging if the 1 part in 10^9 of precision has to be obtained. This threshold is important for fundamental physics and for geodesy, to investigate effects of General Relativity and Lorentz violation in the gravity sector and to provide the fast variation of the Earth rotation rate. High sensitivity Ring Laser Gyroscopes (RLG) are currently the only promising technique to achieve this task in the near future, but their precision has been so far limited by systematics related to the laser operation. In this paper we analyze two different sets of observations, each of them three days long. They were obtained from the G ring laser at the Geodetic Observatory Wettzell. The applied method has been developed for the GINGERINO ring laser in order to identify and extract the laser systematics. For the available data sets the residuals show mostly white noise behavior and the Allan deviation drops below 1 part in 10^9 after an integration time of about 10^4 s.