General Relativity Field Research Articles

Simulating the Universe from the cosmological horizon to halo scales

Ultra-large scales close to the cosmological horizon will be probed by the upcoming observational campaigns. They hold the promise to constrain single-field inflation as well as general relativity, but in order to include them in the forthcoming analyses, their modelling has to be robust. In particular, general relativistic effects may be mistaken for primordial signals, and no consensus has emerged either from analytical modelling nor from the numerical route, obstructed by the large dynamical range to be simulated. In this work, we present a numerical technique to overcome the latter limitation: we compute the general relativistic displacement field with the N-body relativistic code gevolution and combine it with the accurate Newtonian simulation Gadget-4. This combination leads to an effective simulation reproducing the desired behaviour at the level of the matter power spectrum and bispectrum. We then measure, for the first time in a simulation, the relativistic scale-dependent bias in Poisson gauge; at redshift z = 0, we find b 1 GR = -8.1 ± 2.8. Our results at the field level are only valid in the Poisson gauge and need to be complemented with a relativistic ray tracing algorithm to compute the number count observable.

The dressing field method for diffeomorphisms: a relational framework

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M) -invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic ‘extended bracket’ for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Frölicher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M) -theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent ( diff(M) ) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M) -invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the ‘dressed’ (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.

When the Anomalistic, Draconitic and Sidereal Orbital Periods Do Not Coincide: The Impact of Post-Keplerian Perturbing Accelerations

In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such degeneracy is removed when post-Keplerian perturbing acceleration enters the equations of motion, yielding generally different corrections to the Keplerian period for the three aforementioned characteristic orbital timescales. They are analytically worked out in the case of the accelerations induced by the general relativistic post-Newtonian gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of the central body. The resulting expressions hold for completely general orbital configurations and spatial orientations of the spin axis of the primary. Astronomical systems characterized by extremely accurate measurements of orbital periods like transiting exoplanets and binary pulsars may offer potentially viable scenarios for measuring such post-Keplerian features of motion, at least in principle. As an example, the sidereal period of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as small as ≃10−5s, while its predicted post-Newtonian gravitoelectric correction amounts to 0.07s; however, the accuracy with which the Keplerian period can be calculated is just 572 s. For double pulsar PSR J0737–3039, the largest relativistic correction to the anomalistic period amounts to a few tenths of a second, given a measurement error of such a characteristic orbital timescale as small as ≃10−6s. On the other hand, the Keplerian term can be currently calculated just to a ≃9 s accuracy. In principle, measuring at least two of the three characteristic orbital periods for the same system independently would cancel out their common Keplerian component, provided that their difference is taken into account.

Hubble tension and gravitational self-interaction

One of the most important problems vexing the ΛCDM cosmological model is the Hubble tension. It arises from the fact that measurements of the present value of the Hubble parameter performed with low-redshift quantities, e.g. the Type IA supernova, tend to yield larger values than measurements from quantities originating at high-redshift, e.g. fits of cosmic microwave background radiation. It is becoming likely that the discrepancy, currently standing at 5σ, is not due to systematic errors in the measurements. Here we explore whether the self-interaction of gravitational fields in General Relativity, which are traditionally neglected when studying the evolution of the Universe, can contribute to explaining the tension. We find that with field self-interaction accounted for, both low- and high-redshift data are simultaneously well-fitted, thereby showing that gravitational self-interaction yield consistent H 0 values when inferred from SnIA and cosmic microwave background observations. Crucially, this is achieved without introducing additional parameters.

Reissner-Nordström black holes surrounded by perfect fluid dark matter: Testing the viability of weak gravity conjecture and weak cosmic censorship conjecture simultaneously

A possible violation of the weak gravity conjecture (WGC) by cosmic censorship is one of the major challenges in the field of general relativity. The cosmic censorship is a fundamental principle that ensures the consistency of the theory of gravity. According to this principle, a charged black hole in four dimensions cannot violate the weak cosmic censorship conjecture (WCCC) under normal conditions. However, in this paper, we explore the possibility of reconciling the WGC and the WCCC by considering Reissner-Nordström (R-N) black holes embedded in perfect fluid dark matter (PFDM) in asymptotically flat spacetimes. These two conjectures are seemingly unrelated, but a recent proposal suggested that they are connected surprisingly. In particular, We argue a promising class of valid counterexamples to the WCCC in the four-dimensional Einstein-Maxwell theory, considering a charged black hole when WGC is present. We demonstrate that by imposing certain constraints on the parameters of the metric, the WGC and the WCCC can be compatible. Furthermore, we investigate the properties of the charged black hole in the presence of PFDM for Q>M and present some intriguing figures to test the validity of the WGC and the WCCC simultaneously. When PFDM is absent (γ=0), the RN black hole either has two event horizons if Q2/M2≤1 or none if Q2/M2>1. The second scenario results in a naked singularity, which contradicts the WCCC. But when PFDM is present (γ≠0), the RN black hole has event horizons with regard to Q and M. This implies that the singularity is always covered, and the WGC and the WCCC are fulfilled. Furthermore, we demonstrate that there is a critical value of γ, called γext, that makes the RN black hole extremal when γ=γext. In this situation, the black hole has an event horizon, and the WGC and the WCCC are still fulfilled. We infer that PFDM can make the WGC and the WCCC compatible with the RN black hole and that the WGC and the WCCC agree with each other when PFDM is present.

Causal Structure in Spin Foams

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry.

The geometrization of Maxwell's equations and the emergence of gravity and antimatter

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density and the four-velocity that describe its motion geometric definitions. Introducing mass using a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

Fermi-normal coordinates for the Newtonian approximation of gravity

In this work, we compute the metric corresponding to a static and spherically symmetric mass distribution in the general relativistic weak field approximation to quadratic order in Fermi-normal coordinates surrounding a radial geodesic. To construct a geodesic and a convenient tetrad transported along it, we first introduce a general metric, use the Cartan formalism of differential forms, and then specialize the space-time by considering the nearly Newtonian metric. This procedure simplifies the calculations significantly, and the expression for the radial geodesic admits a simple form. We conclude that in quadratic order, the effects of a Schwarzschild gravitational field measured locally by a freely falling observer equals the measured by an observer in similar conditions in the presence of a Newtonian approximation of gravitation.

Emerging electric or magnetic parts of Weyl tensor

In this paper, we study the PNDP-manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the Weyl tensor are the dimensions of the PNDP-manifold and the interaction that emerges as “virtual” point-like manifolds and as a manifold with positive/ negative dimensions results in the generation of the purely electric or purely magnetic parts of the Weyl tensor. The PNDP metric for the electric or magnetic parts of the Weyl tensor is also derived. The generalized Lorentz transformations on the PNDP manifold are introduced. These can give rise to novel forms of gauge theories if we consider local Lorentz transformations. Also we briefly show that principal fiber bundles with PNDP manifolds as base manifolds can be constructed.

Unimodular gravity traversable wormholes

Wormholes are outstanding solutions of Einstein’s General Relativity. They were worked out in the late 1980s by Morris and Thorne, who have figured out a recipe that wormholes must obey in order to be traversable, that is, safely crossed by travelers. A remarkable feature is that General Relativity Theory wormholes must be filled by exotic matter, which Morris and Thorne define as matter satisfying $$-p_r>\rho$$ , in which $$p_r$$ is the radial pressure and $$\rho$$ is the energy density of the wormhole. In the present article, we introduce, for the first time in the literature, traversable wormhole solutions of Einstein’s Unimodular Gravity Theory. Unimodular Gravity was proposed by Einstein himself as the theory for which the field equations are the traceless portion of General Relativity field equations. Later, Weinberg has shown that this approach elegantly yields the solution of the infamous cosmological constant problem. The wormhole solutions here presented satisfy the metric conditions of “traversability” and remarkably evade the exotic matter condition, so we can affirm that Unimodular Gravity wormholes can be filled by ordinary matter.

Simulation of Closed Timelike Curves in a Darwinian Approach to Quantum Mechanics

Closed timelike curves (CTCs) are non-intuitive theoretical solutions of general relativity field equations. The main paradox associated with the physical existence of CTCs, the so-called grandfather paradox, can be satisfactorily solved by a quantum model named Deutsch-CTC. An outstanding theoretical result that has been demonstrated in the Deutsch-CTC model is the computational equivalence of a classical and a quantum computer in the presence of a CTC. In this article, in order to explore the possible implications for the foundations of quantum mechanics of that equivalence, a fundamental particle is modelled as a classical-like system supplemented with an information space in which a randomizer and a classical Turing machine are stored. The particle could then generate quantum behavior in real time in case it was controlled by a classical algorithm coding the rules of quantum mechanics and, in addition, a logical circuit simulating a CTC was present on its information space. The conditions that, through the action of evolution under natural selection, might produce a population of such particles with both elements on their information spaces from initial sheer random behavior are analyzed.

Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar-tensor gravity

We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.

Magnetic-field Induced Deformation in Hybrid Stars

The effects of strong magnetic fields on the deconfinement phase transition expected to take place in the interior of massive neutron stars are studied in detail for the first time. For hadronic matter, the very general density-dependent relativistic mean field model is employed, while the simple, but effective vector-enhanced bag model is used to study quark matter. Magnetic-field effects are incorporated into the matter equation of state and in the general-relativity solutions, which also satisfy Maxwell’s equations. We find that for large values of magnetic dipole moment, the maximum mass, canonical mass radius, and dimensionless tidal deformability obtained for stars using spherically symmetric Tolman–Oppenheimer–Volkoff (TOV) equations and axisymmetric solutions attained through the LORENE library differ considerably. The deviations depend on the stiffness of the equation of state and on the star mass being analyzed. This points to the fact that, unlike what was assumed previously in the literature, magnetic field thresholds for the approximation of isotropic stars and the acceptable use of TOV equations depend on the matter composition and interactions.

ϕ-modes of neutron stars in a massless scalar–tensor theory

Scalar–tensor theories allow for a rich spectrum of quasinormal modes of neutron stars. The presence of the scalar field allows for polar monopole and dipole radiation, as well as for additional higher multipole modes led by the scalar field. Herein, we present one family of the modes which are dominated by the scalar fields, the scalar-led ϕ-modes computed numerically with a shooting method, for the lowest multipoles, that is, l = 0, 1, and 2 for a massless scalar–tensor theory of the Brans–Dicke type, motivated by the R2 theory, and compare with those of a minimally coupled scalar field in general relativity. We consider a set of six realistic equations of state and extract universal relations for the modes.

Conformally Schwarzschild cosmological black holes

We thoroughly investigate conformally Schwarzschild spacetimes in different coordinate systems to seek for physically reasonable models of a cosmological black hole. We assume that a conformal factor depends only on the time coordinate and that the spacetime is asymptotically flat Friedmann–Lemaître–Robertson–Walker Universe filled by a perfect fluid obeying a linear equation state p = wρ with w > −1/3. In this class of spacetimes, the McClure–Dyer spacetime, constructed in terms of the isotropic coordinates, and the Thakurta spacetime, constructed in terms of the standard Schwarzschild coordinates, are identical and do not describe a cosmological black hole. In contrast, the Sultana–Dyer and Culetu classes of spacetimes, constructed in terms of the Kerr–Schild and Painlevé–Gullstrand coordinates, respectively, describe a cosmological black hole. In the Sultana–Dyer case, the corresponding matter field in general relativity can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous null fluid, which is valid everywhere in the spacetime unlike Sultana and Dyer’s interpretation. In the Culetu case, the matter field can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous anisotropic fluid. However, in both cases, the total energy–momentum tensor violates all the standard energy conditions at a finite value of the radial coordinate in late times. As a consequence, the Sultana–Dyer and Culetu black holes for −1/3 < w ⩽ 1 cannot describe the evolution of a primordial black hole after its horizon entry.

Black bounces, wormholes, and partly phantom scalar fields

Simpson and Visser recently proposed a phenomenological way to avoid some kinds of space-time singularities by replacing a parameter whose zero value corresponds to a singularity (say, $r$) with the manifestly nonzero expression $r(u) = \sqrt{u^2 + b^2}$, where $u$ is a new coordinate, and $b =$ \const $>0$. This trick, generically leading to a regular minimum of $r$ beyond a black hole horizon (called a "black bounce"), may hopefully mimic some expected results of quantum gravity, and was previously applied to regularize the Schwarzschild, Reissner-Nordstr\"om, Kerr and some other metrics. In this paper it is applied to regularize the Fisher solution with a massless canonical scalar field in general relativity (resulting in a traversable wormhole) and a family of static, spherically symmetric dilatonic black holes (resulting in regular black holes and wormholes). These new regular metrics represent exact solutions of general relativity with a sum of stress-energy tensors of a scalar field with a nonzero self-interaction potential and a magnetic field in the framework of nonlinear electrodynamics with a Lagrangian function $L(F)$, $F = F_{\mu\nu} F^{\mu\nu}$. A novel feature in the present study is that the scalar fields involved have "trapped ghost" properties, that is, are phantom in a strong-field region and canonical outside it, with a smooth transition between the regions. It is also shown that any static, spherically symmetric metric can be obtained as an exact solution to the Einstein equations with the stress-energy tensor of the above field combination.

A panorama of viable F(R) gravity dark energy models

In this work, we shall study the late-time dynamics of several F(R) gravity models. By appropriately expressing the field equations in terms of the redshift and of a statefinder function, we shall solve numerically the field equations using appropriate physical motivated initial conditions. We consider models which, by construction, are described by a nearly [Formula: see text]-model at early epochs and we fine tune the parameters to achieve viability and compatibility with the latest Planck constraints at late times. Such models provide a unified description of inflation and dark energy era and notably a common feature of all the models is the presence of dark energy oscillations. Furthermore, we show that, in contrast to general relativistic fluids and scalar field descriptions, a large spectrum of different dark energy physics is generated by simple F(R) gravity models, varying from phantom, to nearly de Sitter and to quintessential dark energy eras.

The nozzle shock in tidal disruption events

ABSTRACT Tidal disruption events (TDEs) occur when a star gets torn apart by the strong tidal forces of a supermassive black hole, which results in the formation of a debris stream that partly falls back towards the compact object. This gas moves along inclined orbital planes that intersect near pericentre, resulting in a so-called ‘nozzle shock’. We perform the first dedicated study of this interaction, making use of a two-dimensional simulation that follows the transverse gas evolution inside a given section of stream. This numerical approach circumvents the lack of resolution encountered near pericentre passage in global three-dimensional simulations using particle-based methods. As it moves inward, we find that the gas motion is purely ballistic, which near pericentre causes strong vertical compression that squeezes the stream into a thin sheet. Dissipation takes place at the resulting nozzle shock, inducing a rise in pressure that causes the collapsing gas to bounce back, although without imparting significant net expansion. As it recedes to larger distances, this matter continues to expand while remaining thin despite the influence of pressure forces. This gas evolution specifies the strength of the subsequent self-crossing shock, which we find to be more affected by black hole spin than previously estimated. We also evaluate the impact of general relativistic effects, viscous dissipation, magnetic fields, and radiative processes on the nozzle shock. This study represents an important step forward in the theoretical understanding of TDEs, bridging the gap between our robust knowledge of the fallback rate and the more complex following stages, during which most of the emission occurs.

Research on the cooperative network of relativity and quantum cosmology researchers

The collaboration networks are classified and studied by analysing various properties of the collaboration data of contributing scholars, and the modules with high information flow are identified for identifying the collaboration patterns of authors in science and technology disciplines. The basic model of the collaboration network is described in terms of statistical parameters such as network degree distribution, clustering coefficients, efficiency and average network path length, and then more efficient core communities of the original network are visualized and analysed after k-core decomposition and modularly identified.The present study shows that authors contributing to the field of general relativity and quantum cosmology tend to cooperate with the same fraction of the population, which results in information transfer efficiency in and between core communities being much greater than the overall network efficiency. In addition, there are also individual authors who prefer to do their research independently.

Accretion onto a quintessence contaminated rotating black hole: violating the lower limit for eta over s

Viscous accretion flow around a rotating supermassive black hole sitting in a quintessence tub is studied in this article. To introduce such a dark energy contaminated black hole’s gravitational force, a new pseudo-Newtonian potential is used. This pseudo-Newtonian force can be calculated if we know the distance from the black hole’s center, spin of the black hole and equation of state of the quintessence inside which the black hole is considered to lie. This force helps us to avoid complicated nonlinearity of general relativistic field equations. Transonic, viscous, continuous and Keplerian flow is assumed to take place. Fluid speed, sonic speed profile and specific angular momentum to Keplerian angular momentum ratio are found out for different values of spin parameter and quintessence parameter. Density variation is built and tallied with observations. Shear viscosity to entropy density ratio is constructed for our model and a comparison with theoretical lower limit is done.