Eddington-inspired Born-Infeld Gravity Research Articles

Polytropic spherical astrocosmic fluid stability in the EiBI gravity with strong collective correlative effects

We herein present a dynamical analysis of the Jeans (gravitational) instability in a viscoelastic polytropic astrocloud within the Eddington-inspired Born-Infeld (EiBI) gravity framework in spherical geometry. The zeroth-order material density curvature corrections to the effective self-gravitational potential are properly incorporated. The applied spherical normal mode analysis yields a unique form of monic cubic dispersion relation with multiparametric coefficients dependent on the diverse equilibrium astrofluidic conditions without invoking any kind of traditional quasi-classic approximation. It is seen that the positive EiBI gravity parameter (χ>0) acts as a stabilizing agent and a negative EiBI gravity parameter (χ<0) acts as a destabilizing agent against the inward non-local self-gravity action. Additionally, we find that larger astroclouds are more prone to gravitational collapse, irrespective of the χ-polarity, and vice-versa. It is further investigated that the cloud temperature plays a stabilizing role at larger wavenumbers and destabilizing at smaller wavenumbers for χ>0. However, for χ<0, the fluid temperature consistently exhibits a destabilizing effect. The viscoelastic relaxation time stabilizes the astrofluid against the self-gravity irrespective of the χ-polarity. The fluid density acts as a stabilizer for χ>0, destabilizer for χ<0, and so forth. This study could be potentially applicable in the EiBI-modified gravitational theory in exploring gravity-driven large-scale astrocosmic phenomena towards structure formation mechanism via the canonical Jeans condensation in diverse astrocosmic conditions.

Gravitational lensing in a spacetime with cosmic string within the Eddington-inspired Born–Infeld gravity

This study explores the deflection angle of photon rays or light-like geodesics within the framework of Eddington-inspired Born–Infeld (EiBI) gravity background space-time, taking into account the influence of cosmic strings. The primary focus lies in deriving the effective potential of the system applicable to both null and time-like geodesics, as well as determining the angle of deflection for light-like geodesics. Our analysis shows that the presence of cosmic strings induces modifications in these physical quantities, leading to shifts in their respective values.

On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole

We consider Klein–Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born–Infeld gravity (EiBI-gravity) and in a Wu–Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some conditionally exact, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We report the effects of the Eddington parameter κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}, GM-parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, WYMM strength σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}, KG-oscillators’ frequency Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document}, and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number nr≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_r\\ge 0$$\\end{document} and include energy levels clustering at κ>>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa>>1$$\\end{document} (i.e., extreme EiBI-gravity), and at |σ|>>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\sigma |>>1$$\\end{document} (i.e., extreme WYMM strength).

Behavior of spin-0 scalar particles in Eddington-inspired Born–Infeld gravity global monopole with harmonic oscillator potential

In this paper, we investigate the behavior of a scalar bosonic field within the backdrop of Eddington-inspired Born–Infeld gravity with a global monopole configuration. Additionally, we consider the presence of both scalar and vector potentials. To introduce the scalar potential, we perform a transformation on the mass term, replacing [Formula: see text] with [Formula: see text]. For the vector potential, we apply a minimal coupling scheme, transforming [Formula: see text] within the relativistic Klein–Gordon equation. We opt for a harmonic oscillator scenario where the scalar and vector potentials are equal, i.e. [Formula: see text]. Through this setup, we analytically solve the wave equation using the confluent Heun equation form. Subsequently, we delve into the quantum system in the absence of any potential, determining the permissible values for bound-state relativistic energy levels and the scalar field’s wave function. Our analysis reveals that the energy levels and wave function are influenced by various parameters present in the eigenvalue expression.

Dynamics of pulsational mode in the EiBI gravity fabric

We systematically theorise a model formalism to investigate the linear pulsational mode dynamics excitable in self-gravitating dust molecular clouds (DMCs) in the framework of the Eddington-inspired Born-Infeld (EiBI) gravity. The adopted spherical DMC consists of thermalized lighter (non-inertial) electrons and ions, both treated analogously as the Boltzmann species, whereas the partially ionised heavier (inertial) dust grains as the constitutive neutral and charged dust fluids. The model closure comes from the coupling gravito-electrostatic Poisson equations governing the resultant potential distributions sourced in the material and charge density fields. Application of spherical normal mode (Fourier-based) analysis transforms the model DMC into a quartic linear dispersion relation with diverse atypical multi-parametric dispersion coefficients. A numerical platform is constructed for an illustrative dispersion analysis. It shows that the positive EiBI parameter, dust charge number, and cloud size act as stabilizing agents against the inward non-local self-gravity. In contrast, a negative EiBI parameter, dust mass, and equilibrium dust population density play destabilizing roles. The modal propagatory and oscillatory features are portrayed graphically and interpreted elaborately. The reliability of our calculation scheme is validated in light of the closely related results previously reported in the literature. The analyses presented here could be relevant in the context of understanding astrophysical structure formation dynamics through the self-gravitational canonical condensation processes in diverse real astronomic environs.

Towards precise constraints in modified gravity: bounds on alternative coupling gravity using white dwarf mass-radius measurements

Tests have to be performed to rule out proposals for gravity modification. We propose a new idea for constraining alternative theories of gravity using temperature-dependent white dwarf (WD) mass-radius (MR) observational data. We have shown that several alternatives to general relativity (GR), which modified GR only within matter, might be reduced to the well-known Poisson equation similar to that of Eddington-inspired Born Infeld (EiBI) and Minimal Exponential Measure (MEMe) gravity. Retaining EiBI notation, we constrain the value of the coupling constant, kappa , using a high-precision model-independent measurement of WD MR observations. We have demonstrated that the WD model should include detailed physics to achieve good precision. The model should include their temperature and evolutionary aspects, which may be computationally expensive. To overcome this issue, we construct a semi-analytical surrogate model based on Mestel’s model, calibrated with tabulated, detailed realistic models, to correct the zero-temperature radius. We have shown that the best-fit value of kappa depends on the WD model, with the ’thick’ envelope models more consistent in describing data. The tightest bound obtained from the most precise MR measurement, QS Vir, with -0.19lesssim kappa lesssim 0.22 in 10^3 m^5kg^{-1} s^{-2} for 2sigma (sim 95%) credibility. Overall, we assert that the recent precise WD MR measurements, combined with our current understanding of WD structure, are insufficient to see the deviation from the one predicted by GR. Both more precise observation data and detailed WD modelling are required to rule out gravity modification.

Jeans instability analysis of viscoelastic astrofluids in Eddington-Inspired-Born–Infeld(EiBI) gravity

The Jeans instabilities in viscoelastic astrofluids are investigated in the context of Eddington-Inspired-Born–Infeld(EiBI) gravity based on hydrodynamics theory. The results show that the positive EiBI gravity parameter and effective generalized fluid viscosity act as stabilizing agents. Conversely, the negative EiBI parameter and viscoelastic relaxation time act as destabilizing factors. The results of present work may help probing the effects of EiBI theory in viscoelastic dense media.

Pre-main sequence evolution of low-mass stars in Eddington-inspired Born–Infeld gravity

We study three aspects of the early-evolutionary phases in low-mass stars within Eddington-inspired Born–Infeld (EiBI) gravity, a viable extension of General Relativity. These aspects are concerned with the Hayashi tracks (i.e. the effective temperature-luminosity relation); the minimum mass required to belong to the main sequence; and the maximum mass allowed for a fully convective star within the main sequence. Using analytical models accounting for the most relevant physics of these processes, we find in all cases a dependence of these quantities not only on the theory’s parameter, but also on the star’s central density, a feature previously found in Palatini f(R) gravity. Using this, we investigate the evolution of these quantities with the (sign of the) EiBI parameter, finding a shift in the Hayashi tracks in opposite directions in the positive/negative branches of it, and an increase (decrease) for positive (negative) parameter in the two masses above. We use these results to elaborate on the chances to seek for traces of new physics in low-mass stars within this theory, and the limitations and difficulties faced by this approach.

Motion of spinning particles around electrically charged black hole in Eddington-inspired Born–Infeld gravity

A test particle possessing spin angular momentum moves along a non-geodesic path due to an additional spin-curvature force. We study the spinning test particle moving in the vicinity of the electrically charged black hole formation in Eddington-inspired Born–Infeld (EiBI) gravity. Through the numerical analysis of its effective potential and orbits, it is found that the orbital eccentricity reduces as the deviation parameter kappa increases. By comparing the orbits for the observed stars around Sagittarius A*, we conclude that the observed orbits with too large radii can not give a stringent constraint with acceptable magnitude. To dig out the potential observation effects of the relations between the orbits and parameter kappa , we mainly focus on the orbits in the vicinity of black hole in this paper. The parameters of inner most stable circular orbit (ISCO) decrease monotonously with kappa when the spin angular momentum is small, however they change non-monotonously with kappa when the spin is large enough. Moreover, the spin dependences of ISCO parameters have similar behavior to that of Reissner–Nordström (RN) black hole. We analyze the causality of the circular orbits by using the superluminal constraint condition as well. As a result, two new parameter regions may emerge in case of large kappa , where the particle has two stable circular orbits with one subluminal and the other superluminal.

An infinite class of exact rotating black hole metrics of modified gravity

We build an infinite class of exact axisymmetric solutions of a metric-affine gravity theory, namely, Eddington-inspired Born-Infeld gravity, coupled to an anisotropic fluid as a matter source. The solution-generating method employed is not unique of this theory but can be extended to other Ricci-Based Gravity theories (RBGs), a class of theories built out of contractions of the Ricci tensor with the metric. This method exploits a correspondence between the space of solutions of General Relativity and that of RBGs, and is independent of the symmetries of the problem. For the particular case in which the fluid is identified with non-linear electromagnetic fields we explicitly derive the corresponding axisymmetric solutions. Finally, we use this result to work out the counterpart of the Kerr-Newman black hole when Maxwell electrodynamics is set on the metric-affine side. Our results open up an exciting new avenue for testing new gravitational phenomenology in the fields of gravitational waves and shadows out of rotating black holes.

Kundt wave geometries in Eddington-inspired Born-Infeld gravity: New solutions and memory effects

We explore memory effects for novel Kundt wave spacetimes in the recently proposed Eddington-inspired Born-Infeld (EiBI) theory of gravity. First, we construct new, exact Kundt wave geometries in this theory for two different matter sources--(i) generic matter designed to satisfy the field equations as well as energy conditions, and (ii) electromagnetic field. For both sources we find that the EiBI theory parameter $\kappa$ couples only with the nonradiative part of the physical metric solution. Thereafter, we solve the geodesic and the geodesic deviation equations, in the above spacetimes with the aim of arriving at memory effects. This analysis is carried out numerically and reveals unique memory features depending on the type of matter source present and the signature of the spacetime scalar curvature. The role of $\kappa$ in influencing the memory effect, for a given background spacetime, is also noted. Thus, apart from providing novel radiative solutions in EiBI gravity, we also show how different matter configurations are responsible for distinct memory characteristics.

Gravitational lensing for stationary axisymmetric black holes in Eddington-inspired Born-Infeld gravity

Recent years have witnessed a surge of interest of the lensing of the black holes arising from general as well as other modified theories of gravity due to the experimental data available from the Event Horizon Telescope (EHT) results. The EHT may open a new door indicating the possible existence of the rotating black hole solutions in modified theories of gravity in the strong field regime. With this motivation, we investigate in the present paper the equatorial lensing $(\ensuremath{\theta}=\ensuremath{\pi}/2)$ by a recently obtained exact rotating black holes solution in Eddington-inspired Born-Infeld (EiBI) theory in both the strong- and weak-field limits. Such black holes are the modification of Kerr-Newman black holes in general relativity, characterized by their mass $M$, the charge $Q$, and the rotation parameter $a$. and an additional term $\ensuremath{\epsilon}$ accounting for the correction to the Kerr-Newman solutions. We show numerically the variations of the impact parameter ${u}_{m}$, the light deflection coefficients $p$ and $q$, and the total azimuthal bending angle ${\ensuremath{\alpha}}_{D}$ and find a close dependence of these quantities on the charge parameter ${r}_{q}$, the correction term $\ensuremath{\epsilon}$, and the spin $a$. We also calculate the angular position ${\ensuremath{\theta}}_{\ensuremath{\infty}}$, the angular separation $s$, and the magnification of the relativistic images. In addition, we also discuss the weak lensing of the black holes in Eddington-inspired Born-Infeld (EiBI) theory using the Gauss-Bonnet theorem. We calculate the weak lensing parameter and find its variation with different values of the parameters ${r}_{q}$ and $\ensuremath{\epsilon}$.

A Stellar Constraint on Eddington-inspired Born–Infeld Gravity from Cataclysmic Variable Binaries

Abstract Eddington-inspired Born–Infeld gravity is an important modification of Einstein’s general relativity, which can give rise to nonsingular cosmologies at the classical level, and avoid the end-stage singularity in a gravitational collapse process. In the Newtonian limit, this theory gives rise to a modified Poisson’s equation, as a consequence of which stellar observables acquire model dependent corrections, compared to the ones computed in the low energy limit of general relativity. This can in turn be used to establish astrophysical constraints on the theory. Here, we obtain such a constraint using observational data from cataclysmic variable binaries. In particular, we consider the tidal disruption limit of the secondary star by a white dwarf primary. The Roche lobe filling condition of this secondary star is used to compute stellar observables in the modified gravity theory in a numerical scheme. These are then contrasted with the values obtained by using available data on these objects, via a Monte Carlo error progression method. This way, we are able to constrain the theory within the 5σ confidence level.

Charged BTZ-type solutions in Eddington-inspired Born-Infeld gravity

We construct an axially symmetric solution of Eddington-inspired Born-Infeld gravity coupled to an electromagnetic field in 2+1 dimensions including a (negative) cosmological constant term. This is achieved by using a recently developed mapping procedure that allows to generate solutions in certain families of metric-affine gravity theories starting from a known seed solution of General Relativity, which in the present case corresponds to the electrically charged Banados-Teitelboim-Zanelli (BTZ) solution. We discuss the main features of the new configurations, including the modifications to the ergospheres and horizons, the emergence of wormhole structures, and the consequences for the regularity (or not) of these space-times via geodesic completeness.

2.6  M⊙ compact object and neutron stars in Eddington-inspired Born-Infeld theory of gravity

In the context of whether a massive compact object recently observed in the GW190814 event is a neutron star (NS) or not, we have studied the role of the parameters $\kappa$ and $\Lambda_c$ of the Eddington-inspired Born-Infeld (EiBI) gravity theory on the NS mass-radius relation, moment of inertia, and tidal deformability. The results are compared to recent observation constraints extracted from the analysis of NS observation data. The NS core equation of state (EoS) is calculated using the relativistic mean-field model with the G3 parameter set. In the hyperon sector, the SU(3) and hyperon potential depths are used to determine the hyperon coupling constants. For the inner and outer crusts, we use the crust EoS from Miyatsu et al. (2013). We also maintain the sound speed to not exceed $c$/$\sqrt{3}$ at high densities. We have found that, in general, the NS mass significantly depends on the value of $\kappa$, and the radius $R$ is sensitive to the value of $\Lambda_c$. Moreover, as $\Lambda_c$ is equal to zero or less than the accepted bound of the cosmological constant, the NS within the EiBI theory is compatible with observation constraints, including $2.0 M_\odot$ mass, canonical radius $R_{1.4 M_{\odot}}$, moment of inertia, and tidal deformation. Our investigation also reveals that the $2.6 M_\odot$ mass compact object and current observational constraint of canonical radius $R_{1.4 M_{\odot}}$ can simultaneously be satisfied only when the $\Lambda_c$ value is unphysically too large and negative. Therefore, within the spesific EoS employed in this work, we conclude that the secondary object with $2.6 M_\odot$ observed in the GW190814 event is not likely a static (or a slow-rotating) NS within the EiBI gravity theory.

Euclidean Action of Electrically Charged Black Holes in the Eddington-inspired Born-Infeld Gravity

We investigate the Euclidean action of electrically charged black hole in the Eddington-inspired Born-Infeld (EiBI) gravity utilizing a semiclassical approach. The Euclidean action is computed in the canonical ensemble. We found that by imposing an appropriate set of boundary terms, the expression of the black hole’s entropy could be found. The obtained form of the entropy is also found to be consistent with previous results.

Jeans instability in Eddington-inspired Born-Infeld (EiBI) gravity: a quantum approach

This paper addresses the process of Jeans gravitational instability in the framework of Eddington-inspired Born-Infeld (EiBI) theory, by accounting for quantum effects. In the Newtonian limit, the model reduces to a generalized Schrödinger-Poisson model, which is treated in two different ways: from a quantum hydrodynamic approach and from a quantum kinetic approach, based on the Wigner (quasi-)distribution. We show that, depending on the sign of κ, EiBI gravity leads to more or less stable structures: For , EiBI gravity produces a pressure-like term that acts, together with quantum pressure, against gravity, leading to more stable structures, while for the effect goes in the opposite direction. Our approach reproduces correctly the classical hydrodynamic and kinetic results in the proper limits, which is made more transparent by introducing a nonlinear Schrödinger equation accounting for the degree of quantumness. Our results may open up a novel route for probing EiBI gravity in dense astrophysical media, where quantum effects are no longer negligible.

Geodesic study of spherically symmetric black holes in Palatini-type gravity

This paper probes the geodesic structure of spherically symmetric charged black holes using modified theory of gravity. We explore the geodesic structures of different black holes in the background of Palatini [Formula: see text] theory as well as Eddington-inspired Born–Infeld gravity. We have examined the stability of orbits with the analysis of effective potential. The impacts of modified gravity on particle dynamics specially the circular orbits, the deflection angle and trajectory followed by lightlike as well as for timelike particles are scrutinized. We find that the orbits are more stable for the large values of charge and Born–Infeld parameter.

Generating rotating spacetime in Ricci-based gravity: naked singularity as a black hole mimicker

Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin of the compact object. Compared to the spacetime prior to the mapping, we find that the high-energy modifications at the Born-Infeld scale are able to suppress but not remove the curvature divergence of the original naked null singularity. Depending on the sign of the Born-Infeld coupling constant, these modifications may even give rise to an additional timelike singularity exterior to the null one. In spite of that, both of the naked singularities before and after the mapping are capable of casting shadows, and as a consequence of the mapping relation, their shadows turn out to be identical as seen by a distant observer on the equatorial plane.Even though the scalar field induces a peculiar oblateness to the appearance of the shadow with its left and right endpoints held fixed, the closedness condition for the shadow contour sets a small upper bound on the absolute value of the scalar charge, which leads to observational features of the shadow closely resembling those of a Kerr black hole.

Strong gravitational lensing in a spacetime with topological charge within the Eddington-inspired Born-Infeld gravity

In this work we calculate the angular deflection of light in the strong field limit in two spacetimes which were previously studied within the Eddington-inspired Born-Infeld gravity, namely, a black hole and a wormhole, both with topological charge. We show that the presence of the parameters characterizing Eddington-inspired Born-Infeld gravity and the topological charge promote significant changes in the angular deflection of light with respect to that one obtained in Schwarzschild spacetime. Using the expression for angular deflection in the strong field limit, we calculate the position and magnification of the respective relativistic images.