Theory Of Gravity Research Articles

Complexity factor for a static self-gravitating sphere in Rastall–Rainbow gravity

We generalized Herrera’s definition of complexity factor for static spherically symmetric fluid distributions to Rastall–Rainbow theory of gravity. For this purpose, an energy-dependent equation of motion is employed in accordance with the principle of gravity’s rainbow. It is found that the complexity factor appears in the orthogonal splitting of the Riemann curvature tensor, and measures the deviation of the value of the active gravitational mass from the simplest system under the combined corrections of Rastall and rainbow. In the low-energy limit, all the results we have obtained reduce to the counterparts of general relativity when the non-conserved parameter is taken to be one. We also demonstrate how to build an anisotropic or isotropic star model using complexity approach. In particular, the vanishing complexity factor condition in Rastall–Rainbow gravity is exactly the same as that derived in general relativity. This fact may imply a deeper geometric foundation for the complexity factor.

Astrophysical Tests of General Relativity

At the initial stage of its development, general relativity (GR) was verified and confirmed in a weak gravitational field limit. However, with the development of astronomical observation technologies, GR predictions in a strong gravitational field began to be discussed and confirmed, such as the profile of the X-ray iron \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K\\alpha $$\\end{document} line (in the case if the emission region is very close to the event horizon), the trajectories of stars near black holes and the shapes and sizes of shadows of supermassive black holes in M87* and Sgr A*. In 2005 it was predicted that a shadow formed near a supermassive black hole at the Galactic Center could be reconstructed from observations of ground based global VLBI system or ground—space interferometer acting in mm or sub-mm bands. In 2022 this prediction was confirmed since the Event Horizon Telescope (EHT) collaboration reported about a shadow reconstructions for Sgr A*. In 2019 the EHT collaboration presented the first image reconstruction around the shadow for the supermassive black hole in M87. In 2021 the EHT collaboration constrained parameters (“charges”) of spherical symmetrical metrics of black holes from an allowed interval for shadow radius. In 2022 the EHT collaboration constrained charges of metrics for the supermassive black hole at the Galactic Center. Earlier, we obtained analytical expressions for the shadow radius as a function of charge (including a tidal one) in the case of Reissner–Nordström metric. Based on results of the shadow size evaluation for M87* done by the EHT collaboration we constrained a tidal charge. We discussed opportunities to use shadows to test alternative theories of gravity and alternative models for galactic centers.

A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the Möbius representation

We establish the mathematical fundamentals for a unified description of curvature, torsion, and non-metricity 2-forms in the way extending the so-called Möbius representation of the affine group, which is the method to convert the semi-direct product into the ordinary matrix product, to revive the fertility of gauge theories of gravity. First of all, we illustrate the basic concepts for constructing the metric-affine geometry. Then the curvature and torsion 2-forms are described in a unified manner by using the Cartan connection of the Möbius representation of the affine group. In this unified-description, the curvature and torsion are derived by Cartan’s structure equation with respect to a common connection 1-form. After that, extending the Möbius representation, the dilation and shear 2-forms, or equivalently, the non-metricity 2-form, are introduced in the same unified manner. Based on the unified-description established in this paper, introducing a new group parametrization and applying the Inönü–Wigner group contraction to the full theory, the relationships among symmetries, geometric quantities, and geometries are investigated with respect to the three gauge groups: the metric-affine group and its extension, and an extension of the (anti)-de Sitter group in which the non-metricity exists. Finally, possible applications to theories of gravity are briefly discussed.

Constraints on metric-Palatini gravity from QPO data

AbstractIn this work, we study metric-Palatini gravity extended by the antisymmetric part of the affine curvature. This gravity theory leads to general relativity plus a geometric Proca field. Using our previous construction of its static spherically-symmetric AdS solution (Eur Phys J. C 83(4):318, 2023), we perform a detailed analysis in this work using the observational quasiperiodic oscillations (QPOs) data. To this end, we use the latest data from stellar-mass black hole GRO J1655-40, intermediate-mass black hole in M82-X1, and the super-massive black hole in SgA* (our Milky Way) and perform a Monte-Carlo-Markov-Chain (MCMC) analysis to determine or bound the model parameters. Our results shed light on the allowed ranges of the Proca mass and other parameters. The results imply that our solutions can cover all three astrophysical black holes. Our analysis can also be extended to more general metric-affine gravity theories.

On the stability of electrovacuum space-times in scalar–tensor gravity

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Algebras and Hilbert spaces from gravitational path integrals. Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT

Recent works by Chandrasekaran, Penington, and Witten have shown in various special contexts that the quantum-corrected Ryu-Takayanagi (RT) entropy (or its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization) can be understood as computing an entropy on an algebra of bulk observables. These arguments do not rely on the existence of a local holographic dual field theory. We show that analogous-but-stronger results hold in any UV-completion of asymptotically anti-de Sitter quantum gravity with a Euclidean path integral satisfying a simple and (largely) familiar set of axioms. We consider a quantum context in which a standard Lorentz-signature classical bulk limit would have Cauchy slices with asymptotic boundaries BL ⊔ BR where both BL and BR are compact manifolds without boundary. Our main result is then that (the UV-completion of) the quantum gravity path integral defines type I von Neumann algebras ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document} of observables acting respectively at BL, BR such that ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document} are commutants. The path integral also defines entropies on ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document}. Positivity of the Hilbert space inner product then turns out to require the entropy of any projection operator to be quantized in the form ln N for some N ∈ ℤ+ (unless it is infinite). As a result, our entropies can be written in terms of standard density matrices and standard Hilbert space traces. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT-formula with quantum corrections. Our work thus provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, it is plausible that they hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

Inconsistency of modified gravity in cosmology

We show that there is a fundamental flaw in the application of modified gravity theories in cosmology, taking f(R) gravity as a paradigmatic example. This theory contains a scalar degree of freedom that couples to the matter stress-energy tensor but not to gravitational energy. However, when applied to cosmology this theory is unable to distinguish between gravitational and non-gravitational energy. Hence the cosmological version of the theory does not coincide with its own macroscopic average, and we show that this leads to order-one discrepancies. We argue that the same inconsistency is common to many other modified gravity theories with extra degrees of freedom. Our results put into question whether these theories can make sense as the cosmological average of a fundamental theory, hence challenging their physical significance.

A chiral limit for Chern-Simons-matter theories

Large N quasi-fermionic Chern-Simons-matter theories have an approximate higher-spin symmetry that strongly constrains their correlation functions. In particular, the 3-point functions for generic spins are combinations of 3 structures (with specific dependence on the positions and helicities), and the coupling-dependence of the coefficient of each structure is uniquely determined. In the past few years, several relations between different structures were found. In this paper we show that all the relations between the structures follow from (or, conversely, they imply) a specific form written by Skvortsov for the vertices of the dual higher-spin gravity theory on four-dimensional anti-de Sitter space, when written in spinor-helicity variables. The dual bulk theory has a specific limit where it simplifies and becomes a “chiral higher-spin gravity theory”, and we discuss what can be said about this limit in the dual Chern-Simons-matter theories, where it involves an analytic continuation to complex couplings.

Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy

We consider the dimensional reduction to two dimensions of certain gravitational theories in D ≥ 4 dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl-Lewis-Papapetrou coordinates. In contrast with previous proposals, we find that the gauge group of the Yang-Mills single copy carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, the Kaluza-Klein rotating attractor solution, the Einstein-Rosen wave solution and the self-dual Kleinian Taub-NUT solution.

Properties of dynamical black hole entropy

We study the first law for non-stationary perturbations of a stationary black hole whose event horizon is a Killing horizon, that relates the first-order change in the mass and angular momentum to the change in the entropy of an arbitrary horizon cross-section. Recently, Hollands, Wald and Zhang [1] have shown that the dynamical black hole entropy that satisfies this first law, for general relativity, is Sdyn = (1 − v∂v)SBH, where v is the affine parameter of the null horizon generators and SBH is the Bekenstein-Hawking entropy, and for general diffeomorphism covariant theories of gravity Sdyn = (1 − v∂v)SWall, where SWall is the Wall entropy. They obtained the first law by applying the Noether charge method to non-stationary perturbations and arbitrary cross-sections. In this formalism, the dynamical black hole entropy is defined as an “improved” Noether charge, which is unambiguous to first order in the perturbation. In the present article we provide a pedagogical derivation of the physical process version of the non-stationary first law for general relativity by integrating the linearised Raychaudhuri equation between two arbitrary horizon cross-sections. Moreover, we generalise the derivation of the first law in [1] to non-minimally coupled matter fields that are smooth on the horizon, using boost weight arguments rather than Killing field arguments, and we relax some of the gauge conditions on the perturbations by allowing for non-zero variations of the horizon Killing field and surface gravity. Finally, for f(Riemann) theories of gravity we show explicitly using Gaussian null coordinates that the improved Noether charge is Sdyn = (1 − v∂v)SWall, which is a non-trivial check of [1].

Amplitudes, supersymmetric black hole scattering at OG5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({G}^5\\right) $$\\end{document}, and loop integration

We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 8 supergravity at the fifth post-Minkowskian order and to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present the solution to the differential equations for all master integrals necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

Action at a distance: From Newton’s gravity to quantum theory

Abstract Isaac Newton’s theory of gravity seems to postulate action at a distance. Two distant massive bodies act on one another gravitationally instantaneously without a causal mechanism to mediate the action. This paper will argue that a strategy found in the Principia that allows Newton’s theory to be explanatory without providing a causal explanation can be extended to the quantum case. However, while causal action at a distance can be avoided, the explanatory cost of avoiding any form of nonlocality is higher in the quantum case than in the case of Newton’s theory of universal gravitation.

Parametric resonance of gravitational waves in general scalar-tensor theories

Gravitational waves offer a potent mean to test the underlying theory of gravity. In general theories of gravity, such as scalar-tensor theories, one expects modifications in the friction term and the sound speed in the gravitational wave equation. In that case, rapid oscillations in such coefficients, e.g. due to an oscillating scalar field, may lead to narrow parametric resonances in the gravitational wave strain. We perform a general analysis of such possibility within DHOST theories. We use disformal transformations to find the theory space with larger resonances, within an effective field theory approach. We then apply our formalism to a non-minimally coupled ultra-light dark matter scalar field, assuming the presence of a primordial gravitational wave background, e.g., from inflation. We find that the resonant peaks in the spectral density may be detectable by forthcoming detectors such as LISA, Taiji, Einstein Telescope and Cosmic Explorer.

Comparing inflationary models in extended Metric-Affine theories of gravity

We study slow-roll inflation as a common feature in Metric-affine Theories of Gravity. In particular, we take into account extended metric, teleparallel and symmetric-teleparallel theories of gravity, based on different geometric invariants, discussing analogies and differences. The analysis for each model is performed in two approaches. First, we focus on the potential-slow-roll approach by studying the reconstructed potentials for different forms of the extended models related to the considered gravitational theory in the Einstein frame. Secondly, we investigate the Hubble-slow-roll approach for some conventional inflationary potentials related to the specific extended model in the Jordan frame. We compare all results with cosmic microwave background anisotropy observations coming from Planck 2018 and BICEP2/Keck array satellites in order to find the observational constraints on the parameters space of the models as well as their prediction from the spectral parameters. Eventually, we attempt to present a qualitative comparison between three classes of considered modified gravities using the obtained inflationary results. The aim is to select, in principle, cosmological signatures capable of discriminating among concurrent models in view to point out the representation of gravity, according with geometric invariants, which better addresses the early universe dynamics.

Time-machines construct in f(ℛ, 𝒜, Aμν Aμν ) and f(ℛ) modified gravity theories

In this paper, our objective is to explore a time-machine space-time formulated in general relativity, as introduced by Li (Phys. Rev. D 59, 084016 (1999)), within the context of modified gravity theories. We consider Ricci-inverse gravity of all Classes of models, i.e., (i) Class-I: f(ℛ, 𝒜) = (ℛ + κℛ2 + β 𝒜), (ii) Class-II: f(ℛ, Aμν Aμν ) = (ℛ + κℛ2 + γ Aμν Aμν ) model, and (iii) Class-III: f(ℛ, 𝒜, Aμν Aμν ) = (ℛ + κℛ2 + β𝒜 + δ𝒜2 + γ Aμν Aμν ) model, where Aμν is the anti-curvature tensor, the reciprocal of the Ricci tensor, Rμν , 𝒜 = gμν Aμν is its scalar, and β, κ, γ, δ are the coupling constants. Moreover, we consider f(ℛ) modified gravity theory and investigate the same time-machine space-time. In fact, we show that Li time-machine space-time serve as valid solutions both in Ricci-inverse and f(ℛ) modified gravity theories. Thus, both theory allows the formation of closed time-like curves analogue to general relativity, thereby representing a possible time-machine model in these gravity theories theoretically.

APPLICATION OF KEPLER'S LAWS IN PHYSICS

Kepler’s laws of planetary motion provide fundamental insights into the mechanics of celestial bodies. These laws are crucial in understanding orbital mechanics, which play a significant role in modern astrophysics, satellite engineering, and space exploration. This paper presents a comprehensive exploration of the application of Kepler's laws in physics, emphasizing their relevance to both historical and contemporary scientific advancements. The study evaluates the laws' contributions to Newtonian mechanics and modern applications in satellite technology and gravitational theory.

Impact of charge on the stability of pulsar SAX J1748.9-2021 in modified symmetric teleparallel gravity

In this paper, we explore the effect of charge on the stability of pulsar star SAX J1748.9-2021 in f(Q) gravity, where Q represents non-metricity. For this purpose, we apply the Krori-Barua metric ansatz with anisotropic fluid and use a linear f(Q) model f(Q)=ζQ, where ζ is a non-zero constant. We derive exact relativistic solutions of the corresponding field equations. Furthermore, we study its geometric and physical properties through astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. We examine features like anisotropic pressure, the mass–radius relationship, redshift, the Zeldovich condition, energy and causality conditions, the adiabatic index, the Tolman–Oppenheimer–Volkoff equation, the equation of state parameter and compactness. Our findings align with the observational data which indicate that the pulsar SAX J1748.9-2021 is viable and stable under this modified theory of gravity.

Thermodynamics analysis of non-interacting Barrow holographic dark energy in Brans-Dicke theory

In the present paper, we study Barrow holographic dark energy in Brans-Dicke theory of gravity for flat Frieddman-Lemaitre-Robertson-Walker metric. We have assumed power law form of Brans-Dicke scalar field in terms of scale factor . The thermodynamics analysis of the model is discussed. It is observed that the model satify generalized second law of thermodynamics for all values of the parameter in past, present as well as in the future universe.

On the Equivalence of Gravitational Waves Formulations in Teleparallel Gravity and General Relativity

Abstract Gravitational waves have become a vital way to test our current understanding of gravity. In this work, we explore the formulations of gravitational waves in two distinct theories of gravity: the Teleparallel Equivalent of General Relativity (TEGR), a subclass of Teleparallel Gravity (TG), and General Relativity (GR). By linearizing the gravitational field equations in each theory, we demonstrate that the formulations of gravitational waves in TEGR and GR are equivalent. This equivalence suggests that the teleparallel formalism can effectively describe gravitational waves, providing a novel perspective on the topic and potentially broadening the scope of gravitational wave research.

Growth of cosmic perturbations in the modified [formula omitted] gravity

We explore the generalized f(R,T) modified theory of gravity, where the gravitational Lagrangian is a function of Ricci scalar R and the trace of the energy–momentum tensor T. We derive modified field equations to the linear order of perturbations in the context of f(R,T) model. We then investigate the growth of perturbations in the context of f(R,T) modified gravity. Primary numerical investigations based on matter power spectra diagrams indicate a structure growth suppression in f(R,T) gravity, which exhibits consistency with local measurements. Also, we notice that matter-geometry interaction in f(R,T) model would results in the specific feature named as ”matter acoustic oscillations” appeared in matter power spectra diagrams. Moreover, we put constraints on the cosmological parameters of f(R,T) model, utilizing current observations, chiefly cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results based on MCMC calculations imply that f(R,T) is a qualified theory of modified gravity in reconciling Planck CMB data with local probes of large scale structures, by reporting lower values for the structure growth parameter σ8 compared to the standard model of cosmology.