General Relativistic Case Research Articles

Gravitational lensing from clusters of galaxies to test disformal couplings theories

In this study, we investigate the potential existence of a non-minimal coupling between dark matter and gravity using a compilation of galaxy clusters. We focus on the disformal scenario of a non-minimal model with an associated coupling length L. Within the Newtonian approximation, this model introduces a modification to the Poisson equation, characterized by a term proportional to L2∇2ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2 \ abla ^2 \\rho $$\\end{document}, where ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} represents the density of the DM field. We have tested the model by examining strong and weak gravitational lensing data available for a selection of 19 high-mass galaxy clusters observed by the CLASH survey. We have employed a Markov Chain Monte Carlo code to explore the parameter space, and two different statistical approaches to analyse our results: a standard marginalisation and a profile distribution method. Notably, the profile distribution analysis helps out to bypass some volume-effects in the posterior distribution, and reveals lower Navarro–Frenk–White concentrations and masses in the non-minimal coupling model compared to general relativity case. We also found a nearly perfect correlation between the coupling constant L and the standard Navarro–Frenk–White scale parameter rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_s$$\\end{document}, hinting at a compelling link between these two lengths.

Closed time-like curves in [formula omitted] modified gravity theory

In this manuscript, we investigate solutions that allow closed time-like curves (CTCs) in general relativity (GR) within the framework of a modified gravity theory. We consider here an alternative theory recently proposed in gravity theories known as f(R,A)=(R+αA) gravity or Ricci-inverse (RI) gravity, α is the coupling constant. This theory incorporates modifications into the Einstein-Hilbert action through a coupling with an anti-curvature scalar derived from the anti-curvature tensor. We investigate a family of Petrov type-N solutions that are non-vacuum solutions of the field equations, characterized by a negative cosmological constant. The matter-energy content is Vaidya radiation, and its energy density may either remain constant or vary with axial distance. One distinctive feature of the considered solutions is the formation of CTCs, which violate the causality condition. Another observation is that the determinant of the Ricci tensor, Rμν, differs from zero, confirming the existence of an anti-curvature tensor, Aμν, the inverse of the Ricci tensor, defined as Aμν=Rμν−1, and hence, the anti-curvature scalar A=gμνAμν. We demonstrate that the family of cosmological models serves as valid solutions within the framework of Ricci-inverse gravity model, with Vaidya radiation as the matter-energy content whose energy density is modified by the coupling parameter. Thus, our results affirm that the Ricci-inverse gravity theory allows for the existence of CTCs, similar to the case in general relativity.

Dynamical system analysis of scalar field cosmology in coincident f(Q) gravity

In this article, we investigate scalar field cosmology in the coincident f(Q) gravity formalism. We calculate the motion equations of f(Q) gravity under the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a scalar field. We consider a non-linear f(Q) model, particularly f(Q) = − Q + α Q n , which is nothing but a polynomial correction to the Symmetric Teleparallel Equivalent to General Relativity (STEGR) case. Further, we assumed two well-known specific forms of the potential function, specifically the exponential from V(ϕ) = V 0 e −β ϕ and the power-law form V(ϕ) = V 0 ϕ −k . We employ some phase-space variables and transform the cosmological field equations into an autonomous system. We calculate the critical points of the corresponding autonomous systems and examine their stability behaviors. We discuss the physical significance corresponding to the exponential case for parameter values n = 2 and n = − 1 with β = 1, and n = − 1 with β=3 . Moreover, we discuss the same corresponding to the power-law case for the parameter value n = − 2 and k = 0.16. We also analyze the behavior of corresponding cosmological parameters such as scalar field and dark energy density, deceleration, and the effective equation of state parameter. Corresponding to the exponential case, we find that the results obtained for the parameter constraints in Case III is better among all three cases, and that represents the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era via matter-dominated epoch. Further, in the power-law case, we find that all trajectories exhibit identical behavior, representing the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era. Lastly, we conclude that the exponential case shows better evolution as compared to the power-law case.

Spectral method for metric perturbations of black holes: Kerr background case in general relativity

Spectral method for metric perturbations of black holes: Kerr background case in general relativity

Cosmological Aspects of the Theory of Equations of the Vlasov–Einstein Type and Their Consequences

The authors propose a general scheme of derivation from the general relativistic Einstein-Hilbert action for a system of gravitationally interacting charged particles, Hamilton’s dynamics equations and field equations. In accordance with the proposed methodology, new forms of equations of Vlasov type are obtained in the general relativistic case, nonrelativistic and weakly relativistic limits. Expressions are established for the resulting corrections in the equation Poisson, which can contribute to the action of dark matter and dark energy. An effective approach to synchronizing the proper times of different particles of a many-particle system is proposed based on invariance of the form of action. Authors derived (using hydrodynamic substitution) and solved the Euler-type equations leading to the cosmological Friedmann and Milne-McCrea models.

Stars and junction conditions in Einstein–Gauss–Bonnet gravity

The junction conditions for a higher dimensional spherically symmetric charged and anisotropic static star are derived in Einstein–Gauss–Bonnet (EGB) gravity with nonvanishing cosmological constant. It is shown that for a timelike boundary hypersurface of zero thickness, the generalised matching conditions across this surface in EGB gravity are satisfied. A sufficient condition is that the Israel-Darmois conditions are valid. Therefore it is possible to generate a complete stellar model in EGB gravity. The interior matches to the exterior higher dimensional charged Boulware–Deser spacetime with cosmological constant. The barotropic radial pressure has to vanish at the boundary of the star which is also the case in general relativity.

Extreme gravitational interactions in the problem of three black holes in general relativity

We study the three-body problem going from Newtonian mechanics to general relativity. In the classical case, we model the interactions in a typical chaotic configuration, identifying extreme gravitational interactions (EGIs), namely transients in which the system manifests complex, highly-energetic dynamics. We then concentrate on the main part of the work, by selecting these EGIs as initial data for the general relativistic case, and performing a campaign of numerical relativity simulations. To provide a comprehensive menu of cases, we investigate different global configurations. By comparing with the more ‘quiet’ two-body inspiral, we observe strong nonlinear emission of gravitational waves. The multi-body signals have been inspected by employing both Fourier and wavelet analyses, showing net differences among the global configurations. The wavelet analysis reveals the reminiscence of the EGIs in the three black holes problem. Such a survey of simulations might be a guide for future observations.

Thin accretion disc luminosity and its image around rotating black holes in perfect fluid dark matter

ABSTRACTMotivated by the fact that the universe is dominated by dark matter and dark energy, we consider rotating black holes surrounded by perfect fluid dark matter and study the accretion process in thin disc around such black holes. Here, we are interested in how the presence of dark matter affects the properties of the electromagnetic radiation emitted from a thin accretion disc. For this purpose, we use the Novikov–Thorne model and obtain the electromagnetic spectrum of an accretion disc around a rotating black hole in perfect fluid dark matter and compare with the general relativistic case. The results indicate that for small values of dark matter parameter we considered here, the size of the innermost stable circular orbits would decrease and thus the electromagnetic spectrum of the accretion disc increases. Therefore, discs in the presence of perfect fluid dark matter are hotter and more luminous than in general relativity. Finally, we construct thin accretion disc images around these black holes using the numerical ray-tracing technique. We show that the inclination angle has a remarkable effect on the images, whereas the effect of dark matter parameter is small.

Reassessing the problem of time of quantum gravity

In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for which the problem can be solved, while I argue in this paper that there are good reasons for doubting about these resolutions when the theory is not deparametrizable, which is the case of general relativity. I introduce an example of a non-deparametrizable model, a double harmonic oscillator system expressed by its Jacobi action, and argue that the problem of time for this model is not solvable, in the sense that its canonical quantization doesn’t lead to the quantum theory of two harmonic oscillators and the standard resolutions of the problem of time don’t work for this case. I argue that as general relativity is strongly analogous to this model, one should take seriously the view that the canonical quantization of general relativity doesn’t lead to a meaningful quantum theory. Finally, I comment that this has an impact on the foundations of different approaches to quantum gravity.

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.

A comparative study of new generic wormhole models with stability analysis via thin-shell

This analysis is devoted to exploring the interesting aspects of wormhole geometry. The energy conditions are checked for two different new generic shape functions, which satisfy the required wormhole properties. The presence of exotic matter is confirmed due to the violation of the energy conditions in the background of f(R, T) gravity as well as in the general relativity case. The traversable wormholes respecting the null energy conditions can be realized in both considered frameworks. A thin-shell around a wormhole geometry with two different generic shape functions is obtained by using the cut and paste approach taking Schwarzschild spacetime as an exterior manifold. The stability of thin-shell is explored with linearized perturbation along the equilibrium shell radius. Stable regions and the position of the expected event horizon depend on the choice of physical parameters. It is concluded that the number of expected event horizons increases for the second shape function.

Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The second order in rotation

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals.

Linear perturbations of Einstein-Gauss-Bonnet black holes

We study linear perturbations about non rotating black hole solutions in scalar-tensor theories, more specifically Horndeski theories. We consider two particular theories that admit known hairy black hole solutions. The first one, Einstein-scalar-Gauss-Bonnet theory, contains a Gauss-Bonnet term coupled to a scalar field, and its black hole solution is given as a perturbative expansion in a small parameter that measures the deviation from general relativity. The second one, known as 4-dimensional-Einstein-Gauss-Bonnet theory, can be seen as a compactification of higher-dimensional Lovelock theories and admits an exact black hole solution. We study both axial and polar perturbations about these solutions and write their equations of motion as a first-order (radial) system of differential equations, which enables us to study the asymptotic behaviours of the perturbations at infinity and at the horizon following an algorithm we developed recently. For the axial perturbations, we also obtain effective Schrödinger-like equations with explicit expressions for the potentials and the propagation speeds. We see that while the Einstein-scalar-Gauss-Bonnet solution has well-behaved perturbations, the solution of the 4-dimensional-Einstein-Gauss-Bonnet theory exhibits unusual asymptotic behaviour of its perturbations near its horizon and at infinity, which makes the definition of ingoing and outgoing modes impossible. This indicates that the dynamics of these perturbations strongly differs from the general relativity case and seems pathological.

Black hole perturbations in higher-order scalar–tensor theories: initial value problem and dynamical stability

We propose a physically sensible formulation of initial value problem for black hole perturbations in higher-order scalar–tensor theories. As a first application, we study monopole perturbations around stealth Schwarzschild solutions in a shift- and reflection-symmetric subclass of degenerate higher-order scalar–tensor (DHOST) theories. In particular, we investigate the time evolution of the monopole perturbations by solving a two-dimensional wave equation and analyze the Vishveshwara’s classical scattering experiment, i.e., the time evolution of a Gaussian wave packet. As a result, we confirm that stealth Schwarzschild solutions in the DHOST theory are dynamically stable against the monopole perturbations with the wavelength comparable or shorter than the size of the black hole horizon. We also find that the damped oscillations at the late time do not show up unlike the ringdown phase in the standard case of general relativity. Moreover, we investigate the characteristic curves of the monopole perturbations as well as a static spherically symmetric solution with monopole hair.

The Heuristic Power of Theory Classification, the Case of General Relativity

The Heuristic Power of Theory Classification, the Case of General Relativity

Constraining scalar-tensor theories using neutron star mass and radius measurements

We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter $\beta$ for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is considerably less effective in constraining the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more commonly to test alternative theories in general.

Density Perturbation and Cosmological Evolution in the Presence of Magnetic Field in f R Gravity Models

In this paper, we have investigated the density perturbations and cosmological evolution in the FLRW universe in the presence of a cosmic magnetic field, which may be assumed to mimic primordial magnetic fields. Such magnetic fields have sufficient strength to influence galaxy formation and cluster dynamics, thereby leaving an imprint on the CMB anisotropies. We have considered the FLRW universe as a representative of the isotropic cosmological model in the 1 + 3 covariant formalism for f R gravity. The propagation equations have been determined and analyzed, where we have assumed that the magnetic field is aligned uniformly along the x -direction, resulting in a diagonal shear tensor. Subsequently, the density perturbation evolution equations have been studied, and the results have been interpreted. We have also indicated how these results change in the general relativistic case and briefly mentioned the expected change in higher-order gravity theories.

Charged radiation collapse in Einstein–Gauss–Bonnet gravity

We generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an extended, weak and initially naked central conical singularity. With the presence of an electromagnetic field, collapse terminates with the emergence of a branch singularity separating the physical spacetime from the complex region. We show that this marked difference in singularity formation is only prevalent in five dimensions. We extend our analysis to higher dimensions and show that for all dimensions Nge 5, charged collapse ceases with the above mentioned branch singularity. This is significantly different than the uncharged scenario where a strong curvature singularity forms post collapse for all Nge 6 and a weak conical singularity forms when N=5. A comparison with charged radiation collapse in general relativity is also given.

Amplification of Primordial Gravitational Waves by a Geometrically Driven non‐canonical Reheating Era

AbstractIn order to describe inflation in general relativity, scalar fields must inevitably be used, with all the setbacks of that description. On the other hand, gravity and other modified gravity theories seem to provide a unified description of early and late‐time dynamics without resorting to scalar or phantom theories. The question is, can modified gravity affect directly the mysterious radiation domination era? Addressing this question is the focus in this work, and we shall consider the case for which in the early stages of the radiation domination era, namely during the reheating era, the background equation of state parameter is different from . As we show, in the context of gravity, an abnormal reheating era can affect the primordial gravitational wave energy spectrum today. Since future interferometers will exactly probe this era, which consists of subhorizon modes that reentered the horizon during the early stages of the radiation domination era, the focus in this work is how a short abnormal reheating era that deviates from the standard perfect fluid pattern with , and generated by higher order curvature terms, can affect the primordial gravitational wave energy spectrum. Using a WKB approach, we calculate the effect of an gravity generated abnormal reheating era, and as we show the primordial gravitational wave spectrum is significantly amplified, a result which is in contrast to the general relativistic case, where the effect is minor.

Is backreaction in cosmology a relativistic effect? On the need for an extension of Newton’s theory to non-Euclidean topologies

Cosmological backreaction corresponds to the effect of inhomogeneities of structure on the global expansion of the Universe. The main question surrounding this phenomenon is whether or not it is important enough to lead to measurable effects on the scale factor evolution, eventually explaining its acceleration or the Hubble tension. One of the most important results on this subject is the Buchert-Ehlers theorem [T. Buchert and J. Ehlers, Astron. Astrophys. 320, 1 (1997)] stating that backreaction is exactly zero when calculated using Newton's theory of gravitation, which may not be the case in general relativity. It is generally said that this result implies that backreaction is a purely relativistic effect. We will show that this is not necessarily the case, in the sense that this implication does not apply to a universe which is still well-described by Newton's theory on small scales but has a non-Euclidean topology. The theorem should therefore be generalized to account for such a scenario. In a heuristic calculation where we construct a theory which is locally Newtonian but defined on a non-Euclidean topology, we show that the backreaction is nonzero, meaning that it might be nonrelativistic depending on the topological class of our Universe. However, that construction is not unique and remains to be justified from a nonrelativistic limit of general relativity.