General Relativistic Counterpart Research Articles

Exploring perturbative constraints in higher-order curvature gravity theories

Abstract In the realm of general relativity (GR) and extended theories of gravity, obtaining solutions for scenarios of physical interest is a highly intricate challenge. By employing the formalism of mathematical perturbation theory within the GR framework, we demonstrate that, for a significant class of vacuum f ( R , R μ ν R μ ν ) theories, the corresponding solutions do not yield additional effects beyond those predicted by GR’s perturbation theory. However, models characterized by terms of the form f ( R , R μ ν R μ ν , R μ ν σ δ R μ ν σ δ ) exhibit distinctive contributions not present in GR. We assert that fundamental limitations exist, explaining why solutions of certain f ( R , R μ ν R μ ν ) models can deviate from their GR counterparts, indicating non-connected solutions or non-analytic behavior. Conversely, in the models f ( R , R μ ν R μ ν , R μ ν σ δ R μ ν σ δ ) , the solutions seamlessly connect with those of GR. This distinction highlights the nuanced interplay between higher-order curvature terms and their impact on gravitational dynamics, offering new insights into the landscape of modified gravity theories.

Anisotropic quark stars in gravity* *Takol Tangphati was Supported by Walailak University under the New Researcher Development scheme (WU67268). A. Pradhan expresses gratitude to the IUCCA in Pune, India, for offering facilities under associateship programs. In addition, İzzet Sakallı thanks TÜBİTAK, ANKOS, and SCOAP3 for their contributions. Takol Tangphati and İzzet Sakallı also appreciate COST Actions CA21106 and CA22113 for

We investigated the impact of gravity on the internal structure of compact stars, expecting this theory to manifest prominently in the high-density cores of such stars. We considered the algebraic function , where α represents the matter-geometry coupling constant. We specifically chose the matter Lagrangian density to explore compact stars with anisotropic pressure. To this end, we employed the MIT bag model as an equation of state. Subsequently, we numerically solved the hydrostatic equilibrium equations to obtain mass-radius relations for quark stars (QSs), examining static stability criteria, adiabatic index, and speed of sound. Finally, we used recent astrophysical data to constrain the coupling parameter α, which may lead to either larger or smaller masses for QSs, compared to their counterparts in general relativity.

Neutron stars in f(R,T) theory: slow rotation approximation

In this paper, we study the slowly rotating neutron stars in f(R, T) gravity based on Hartle-Thorne formalism. We first consider the simplest matter-geometry coupled modified gravity, namely f(R, T) = R + 2χ T. We compute the mass, radius, moment of inertia, change in radius, and binding energy due to rotation, eccentricity, quadrupole moment, and the tidal love number. The quantities, which are of the second order in angular velocity, like change in radius and binding energy due to rotation, eccentricity, and quadrupole moment, deviate more from their corresponding general relativistic counterparts in lighter neutron stars than heavier ones. Whereas the moment of inertia, which is of the first order in angular velocity, in f(R, T) = R + 2χ T modified gravity, barely diverges from the general relativistic one. The Equation of state-independent I-Love-Q relation retains in this f(R, T) modified gravity, and it coincides with the general relativistic ones within less than one percent even for the maximum allowed coupling parameters. We also study the slowly rotating neutron star in f(R, T) = R + αR 2 + 2χT up to first order their angular velocity. We calculate the mass, radius, and moment of inertia of neutron stars in this modified gravity. The results show that the impact of the matter-geometric coupling parameter is greater on lighter neutron stars in both of these modified gravity models.

Influence of pressure anisotropy on mass-radius relation and stability of millisecond pulsars in f(Q) gravity

In this study we explore the astrophysical implications of pressure anisotropy on the physical characteristics of millisecond pulsars within the framework of f(Q) gravity, in particular f(Q) = - α Q - β,where α and β are constants. Starting off with the field equations for anisotropic matter configurations, we adopt the physically salient Durgapal-Fuloria ansatz together with a well-motivated anisotropic factor for the interior matter distribution. This leads to a nonlinear second order differential equation which is integrated to give the complete gravitational and thermodynamical properties of the stellar object. The resulting model is subjected to rigorous tests to ensure that it qualifies as a physically viable compact object within the f(Q)-gravity framework. We study in detail the impact of anisotropy on the mass, radius and stability of the star. Our analyses indicate that our models are well-behaved, singularity-free and can account for the existence of a wide range of observed pulsars with masses ranging from 2.08 to 2.67 M ⊙, with the upper value being in the so-called mass gap regime observed in gravitational events such as GW190814. A comparison of the so-called Symmetric Teleparallel Equivalent to GR (STEGR) models with classical General Relativity (GR) models reveal that the anisotropy parameter and the sign of β impact on the predicted radii of pulsars. In particular, STEGR models have larger radii than their GR counterparts.

Semi-symmetric metric gravity: From the Friedmann–Schouten geometry with torsion to dynamical dark energy models

In this paper, we develop a geometric generalization of General Relativity based on the semi-symmetric metric connection introduced by Friedmann and Schouten in 1924. Although the mathematical properties of this connection, which allows for torsion, have been extensively studied, its physical implications remain underexplored. We provide a detailed exposition of the differential geometric aspects of semi-symmetric connections and formulate the corresponding field equations induced by the specific form of torsion we are investigating. We consider the cosmological applications of the theory by deriving the generalized Friedmann equations in a flat, homogeneous and isotropic geometry. The Friedmann equations also include some supplementary terms as compared to their general relativistic counterparts, which can be interpreted as a geometric type dark energy. To evaluate the proposed theory, we consider three cosmological models — the first with constant effective density and pressure, the second with the dark energy satisfying a linear equation of state, and a third one with a polytropic equation of state. We also compare the predictions of the semi-symmetric metric gravitational theory with the observational data for the Hubble function, and with the predictions of the ΛCDM model. Our findings indicate that the semi-symmetric metric cosmological models give a good description of the observational data, and for certain values of the model parameters, they can reproduce almost exactly the predictions of the ΛCDM paradigm. Consequently, Friedmann’s initially proposed geometry emerges as a credible alternative to standard general relativity, in which dark energy has a purely geometric origin.

Moment of inertia and compactness of quark stars within the context of f(R, T, L m ) gravity

Within the metric formalism of f(R, T, L m ) gravity theories, we investigate the hydrostatic equilibrium structure of compact stars taking into account both isotropic and anisotropic pressure. For this purpose, we focus on the f(R, T, L m ) = R + α TL m model, where α is a free parameter. We derive the modified TOV equations and the relativistic moment of inertia in the slowly rotating approximation. Using an equation of state (EoS) for color-superconducting quark stars, we examine the effects of the α TL m term on the different macroscopic properties of these stars. Our results reveal that the decrease of the parameter α leads to a noticeable increase in the maximum-mass values. For negative α with sufficiently small ∣α∣, we obtain a qualitative behavior similar to the general relativistic (GR) context, namely, it is possible to obtain a critical stellar configuration such that the mass reaches its maximum. However, for sufficiently large values of ∣α∣ keeping negative α, the critical point cannot be found on the mass-radius diagram. We also find that the inclusion of anisotropic pressure can provide masses and radii quite consistent with the current observational measurements, which opens an outstanding window onto the physics of anisotropic quark stars. By comparing the I − C relations of isotropic quark stars in modified gravity, we show that such a correlation remains almost unchanged as the parameter α varies from GR counterpart. On the other hand, given a fixed α, the I − C relation is insensitive to variations of the anisotropy parameter β to O(4%) .

Universal features of 2→N scattering in QCD and gravity from shockwave collisions

A remarkable double-copy relation of Einstein gravity to QCD in Regge asymptotics is Γμν=12CμCν−12NμNν, where Γμν is the gravitational Lipatov vertex in the 2→3 graviton scattering amplitude, Cμ its Yang-Mills counterpart, and Nμ the QED bremsstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing the 2→N scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2D effective field theory framework describing trans-Planckian 2→N graviton scattering. We construct a quantitative correspondence between a semiclassical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to RS,L, RS,H≪b, where RS,L, RS,H are the respective emergent Schwarzchild radii generated in shockwave collisions and b is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in the close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute 2→N amplitudes that incorporates graviton Reggeization and coherent graviton multiple scattering. Published by the American Physical Society 2024

Tidal Deformability of Neutron Stars in Scalar-tensor Theories of Gravity

Gravitational waves from compact binary coalescences are valuable for testing theories of gravity in the strong field regime. By measuring neutron star tidal deformability using gravitational waves from binary neutron stars, stringent constraints were placed on the equation of state of matter at extreme densities. Tidal Love numbers in alternative theories of gravity may differ significantly from their general relativistic counterparts. Understanding exactly how the tidal Love numbers change will enable scientists to untangle physics beyond general relativity from the uncertainty in the equation of state measurement. In this work, we explicitly calculate the fully relativistic l ≥ 2 tidal Love numbers for neutron stars in scalar-tensor theories of gravitation. We use several realistic equations of state to explore how the mass, radius, and tidal deformability relations differ from those of general relativity. We find that tidal Love numbers and tidal deformabilities can differ significantly from those in general relativity in certain regimes. The electric tidal deformability can differ by ∼200%, and the magnetic tidal deformability differs by ∼300%. These deviations occur at large compactnesses (C = M/r ≳ 0.2) and vary slightly depending on the equation of state. This difference suggests that using the tidal Love numbers from general relativity could lead to significant errors in tests of general relativity using the gravitational waves from binary neutron star and neutron star black hole mergers.

Shadows and photon rings of regular black holes and geonic horizonless compact objects

Abstract The optical appearance of a body compact enough to feature an unstable bound orbit, when surrounded by an accretion disk, is expected to be dominated by a luminous ring of radiation enclosing a central brightness depression typically known as the shadow. Despite observational limitations, the rough details of this picture have been now confirmed by the results of the Event Horizon Telescope (EHT) Collaboration on the imaging of the M87 and Milky Way supermassive central objects. However, the precise characterization of both features—ring and shadow—depends on the interaction between the background geometry and the accretion disk, thus being a fertile playground to test our theories on the nature of compact objects and the gravitational field itself in the strong-field regime. In this work we use both features in order to test a continuous family of solutions interpolating between regular black holes and horizonless compact objects, which arise within the Eddington-inspired Born–Infeld theory of gravity, a viable extension of Einstein’s general relativity (GR). To this end we consider seven distinctive classes of such configurations (five black holes and two traversable wormholes) and study their optical appearances under illumination by a geometrically and optically thin accretion disk, emitting monochromatically with three analytic intensity profiles previously suggested in the literature. We build such images and consider the sub-ring structure created by light rays crossing the disk more than once and existing on top of the main ring of radiation. We discuss in detail the modifications as compared to their GR counterparts, the Lyapunov exponents of unstable nearly-bound orbits, as well as the differences between black hole and traversable wormholes for the three intensity profiles. In addition we use the claim by the EHT Collaboration on the radius of the bright ring acting (under proper calibrations) as a proxy for the radius of the shadow itself to explore the parameter space of our solutions compatible with such a result.

Revisiting Vainshtein screening for fast N-body simulations

We revisit a method to incorporate the Vainshtein screening mechanism in N-body simulations proposed by R. Scoccimarro in [1]. We further extend this method to cover a subset of Horndeski theories that evade the bound on the speed of gravitational waves set by the binary neutron star merger GW170817. The procedure consists of the computation of an effective gravitational coupling that is time and scale dependent, G eff (k,z), where the scale dependence will incorporate the screening of the fifth-force. This is a fast procedure that when contrasted to the alternative of solving the full equation of motion for the scalar field inside N-body codes, reduces considerably the computational time and complexity required to run simulations. To test the validity of this approach in the non-linear regime, we have implemented it in a COmoving Lagrangian Approximation (COLA) N-body code, and ran simulations for two gravity models that have full N-body simulation outputs available in the literature, nDGP and Cubic Galileon. We validate the combination of the COLA method with this implementation of the Vainshtein mechanism with full N-body simulations for predicting the boost function: the ratio between the modified gravity non-linear matter power spectrum and its General Relativity counterpart. This quantity is of great importance for building emulators in beyond-ΛCDM models, and we find that the method described in this work has an agreement of below 2% for scales down to k ≈ 3h/Mpc with respect to full N-body simulations.

Perturbations of Spinning Black Holes beyond General Relativity: Modified Teukolsky Equation

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars $\Psi_0$ and $\Psi_4$. We first focus on non-Ricci-flat, Petrov type D black hole backgrounds in modified gravity, and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type D, black hole backgrounds in GR by generalizing Chandrasekhar's approach, and derive the decoupled modified Teukolsky equation. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity.

Shadow revisiting and weak gravitational lensing with Chern-Simons modification

Dynamical Chern-Simons (dCS) gravity has been attracting plenty of attentions due to the fact that it is a parity-violating modified theory of gravity that corresponds to a well-posed effective field theory in weak coupling approximation. In particular, a rotating black hole in dCS gravity is in contrast to the general relativistic counterparts. In this paper, we revisit the shadow of analytical rotating black hole spacetime in dCS modified gravity, based on which we study the shadow observables, discuss the constraint on the model parameters from the Event Horizon Telescope (EHT) observations, and analyze the real part of quasi-normal modes (QNMs) in the eikonal limit. In addition, we explore the deflection angle in weak gravitational field limit with the use of Gauss-Bonnet theorem. We find that the shadow related physics and the weak gravitational lensing effect are significantly influenced by the CS coupling, which could provide theoretical predictions for a future test of the dCS theory with EHT observations.

Compact stellar structures in Weyl geometric gravity

We consider the structure and physical properties of specific classes of neutron, quark, and Bose-Einstein condensate stars in the conformally invariant Weyl geometric gravity theory. The basic theory is derived from the simplest conformally invariant action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To keep the theory conformally invariant the trace condition is imposed on the matter energy-momentum tensor. The field equations are derived by varying the action with respect to the metric tensor, Weyl vector field and scalar field. By adopting a static spherically symmetric interior geometry, we obtain the field equations, describing the structure and properties of stellar objects in Weyl geometric gravity. The solutions of the field equations are obtained numerically, for different equations of state of the neutron and quark matter. More specifically, constant density stellar models, and models described by the stiff fluid, radiation fluid, quark bag model, and Bose-Einstein condensate equations of state are explicitly constructed numerically in both general relativity and Weyl geometric gravity, thus allowing an in depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, Weyl geometric gravity stars are more massive than their general relativistic counterparts. As a possible astrophysical application of the obtained results we suggest that the recently observed neutron stars, with masses in the range of $2{M}_{\ensuremath{\bigodot}}$ and $3{M}_{\ensuremath{\bigodot}}$, respectively, could be in fact conformally invariant Weyl geometric neutron or quark stars.

Observational signatures of Schwarzschild-MOG black holes in scalar–tensor–vector gravity: images of the accretion disk

The present paper contains the investigations with respect to the optical appearance, redshift distribution, and observed energy flux of the thin accretion disk described by the Novikov-Thorne model in modified gravity (MOG) proposed by Moffat. The results show that the gravity coupling parameter alpha plays an indispensable role in the size of direct and secondary images of the accretion disk, while the image profile is mainly affected by the observational angles. In addition, an increase of the parameter alpha leads to that of the redshift factor, but a decrease in the radiation energy flux of the accretion disk. These results are due to the enhancement of the parameter alpha that strengthens the black hole’s gravitational effects. By comparing the accretion disk images of the Schwarzschild-MOG black hole, the Schwarzschild black hole, and the Reissner–Nordström black hole, we point out that the Schwarzschild-MOG black hole exhibits the largest inner shadow and the lowest luminosity. This finding provides a potential way to distinguish Schwarzschild-MOG black holes from their counterparts in General Relativity.

Dressed black holes in the new tensor–vector–scalar theory

As incarnations of gravity in its prime, black holes are arguably the best target for us to demystify gravity. Keeping in mind the prominent role black holes play in gravitational wave astronomy, it becomes a must for a theory to possess black hole solutions with only measurable departures from their general relativity counterparts. In this paper, we present black holes in a tensor-vector-scalar representation of relativistic modified Newtonian dynamics. We find that the theory allows Schwarzschild and nearly-Schwarzschild black holes as solutions, while the nontrivial scalar and vector fields generally diverge at the event horizon. Whether this is a physical pathology or not poses a challenge for these solutions, and by extension, the model. However, even if it is, this pathology could be overcome when the black hole hair vanishes.

Neutron stars in degenerate higher-order scalar-tensor theories

We study neutron star configurations in a simple shift-symmetric subfamily of degenerate higher-order scalar-tensor (DHOST) theories, whose deviations from General Relativity (GR) are characterized by a single parameter. We compute the radial profiles of neutron stars in these theories of modified gravity, using several realistic equations of state for the neutron star matter. We find neutron stars with masses and radii significantly larger than their GR counterparts. We then consider slowly-rotating solutions and determine the relation between the dimensionless moment of inertia and the compactness, relation that has the property to be almost insensitive to the equation of state.

Cosmic censorship and charged radiation in second order Lovelock gravity

The conditions for naked singularity formation are considered for a radiating metric of Boulware–Deser type within an electromagnetic field in second order Lovelock (or Einstein–Gauss–Bonnet) gravity. The spacetime metric remains real only up to certain maximum charge contribution. This differs from general relativity. Beyond a certain maximal charge, there exists no real and physical spacetime since the metric becomes complex. We establish that, under certain parameters and for specific values of the mass function and charge contribution, this branch singularity is indeed a naked singularity. This is in contrast to the neutral case where the spacetime metric is always real for a positive mass function, and further, a weak, initially naked singularity always occurs before it becomes covered by an event horizon for all future time. We highlight that both neutral and charged collapse under gravity in Einstein–Gauss–Bonnet gravity differ significantly to their general relativistic counterparts.

Regular black holes without mass inflation instability

Generic models of regular black holes have separate outer and inner horizons, both with nonzero surface gravity. It has been shown that a nonzero inner horizon surface gravity results in exponential instability at the inner horizon controlled by this parameter. This phenomenon takes the name of “mass inflation instability”, and its presence has put in question the physical viability of regular black holes as alternatives to their (singular) general relativity counterparts. In this paper, we show that it is possible to make the inner horizon surface gravity vanish, while maintaining the separation between horizons, and a non-zero outer horizon surface gravity. We construct specific geometries satisfying these requirements, and analyze their behavior under different kinds of perturbations, showing that the exponential growth characteristic of mass inflation instability is not present for these geometries. These “inner-extremal” regular black holes are thereby better behaved than singular black holes and generic regular black holes, thus providing a well-motivated alternative of interest for fundamental and phenomenological studies.

Fingerprints of modified gravity on galaxies in voids

ABSTRACT We search for detectable signatures of f(R) gravity and its chameleon screening mechanism in the baryonic and dark matter (DM) properties of simulated void galaxies. The enhancement of the gravitational acceleration can have a meaningful impact on the scaling relations as well as on the halo morphology. The galaxy rotational velocity field (calculated with the velocity of the gas disc and the acceleration fields) deviates from the typical values of the Tully–Fisher Relation in General Relativity (GR). For a given stellar mass, f(R) gravity tends to produce greater maximum velocities. On the other hand, the mass in haloes in f(R) gravity is more concentrated than their counterparts in GR. This trend changes when the concentration is calculated with the dynamical density profile, which takes into account the unscreened outer regions of the halo. Stellar discs interact with the overall potential well in the central regions, modifying the morphology of the screening regions and reshaping them. We find a trend for galaxies with a more dominant stellar disc to deviate further from round screening regions. We find that small haloes are less triaxial and more round in f(R) than their GR counterparts. The difference between halo morphology becomes smaller in f(R) haloes whose inner regions are screened. These results suggest possible observables that could unveil modified gravity effects on galaxies in voids in future cosmological tests of gravity.

Anisotropic quark stars in f(R) = R 1+ϵ gravity

Within the metric formalism of f(R) theories of gravity, where R is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the f(R) = R 1+ϵ model and we examine small deviations from general relativity for |ϵ| ≪ 1. A suitable definition of mass function is explicitly formulated from the field equations and the value of the Ricci scalar at the center of each star is chosen such that it satisfies the asymptotic flatness requirement. We find that both the mass and the radius of a compact star are larger with respect to the general relativistic counterpart. Furthermore, we remark that the substantial changes due to anisotropy occur mainly in the high-central-density region.