Gravitational Action Research Articles

The energy–momentum complex in non-local gravity

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator [Formula: see text] are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

Structural properties of anisotropic stars in modified teleparallel gravity: a brief study via an embedding approach

In this paper, we attempt to construct the anisotropic solution for compact stellar configurations using the observed mass and radius of compact stars from the literature under the influence of Rastall Teleparallel gravity. To investigate the crucial elements of spherically symmetric metric space, we employed the embedding class one spacetime paradigm with Karmarkar’s condition. The field equations have been computed under the gravitational action of Rastall Teleparallel gravity. However, the unknown constants were evaluated via junction conditions using the Schwarzschild metric as the outer geometry. The compact stars analysis’s crucial physical and mathematical requirements are all admitted and shared by the model, which is physically viable and supports the emergence of novel realistic stellar configurations in Rastall Teleparallel gravity. We fix the parameters of our model to compare with three compact stars (LMC X-4, Cen X-3, and EXO 1785-248) and find that it can be regular, robust, and stable.

Computation of irreversible seismic displacements of rock wedges: an application to dam abutment safety assessment

The paper discusses a method to assess the seismic performance of rock wedges in contact with arch-dam abutments based on the Newmark displacement approach, conveniently modified to include all possible three-dimensional failure mechanisms and forces transmitted by the structure. Under rigid-block and no-rotations assumptions, the method allows to consider the three components of the seismic input, the progressive detachment of the block from the supporting discontinuity planes, the possible recover of the contact, and the temporary complete detachment of the block from the rock mass. In addition to gravitational and seismic inertial actions, static and dynamic forces exerted at the dam-wedge contact, including those related to the inertial interaction with the reservoir, are included in the analyses.A case study is presented, referred to the seismic verification of the Ridracoli arch-gravity dam (Italy), founded on a marly-arenaceous formation. In particular, the right abutment is thoroughly investigated against wedge sliding involving bedding planes of particularly poor resistance. The results in terms of maximum wedge displacements are compared with the corresponding factor of safety obtained with a limit equilibrium approach, indicating that even a wedge resulting unstable with limit equilibrium analyses shows relatively small displacements at the end of the seismic excitement.

Cosmological distances scale. Part 15: cosmically jerk and the dipole of gravitational heterogeneity

The central question of the cosmic shock in the series of articles “Cosmological Distance Scale” is considered: do the data for parametric identification of the Friedman-Robertson-Walker model in the form of a dependence of the photometric distance on the redshift of type Ia supernovae used in the work of the High-Z SN Search Team and Supernovae Cosmology Project allow us to consider the acceleration of the expansion of the Universe as the most plausible hypothesis on the criterion of the minimum error of inadequacy. The previously discovered discrepancies (changes in the structure and parameters of the systematic component of the model) and rank inversions of photometric distances of supernovae SN Ia for the systematic component of this model are analyzed. It is shown that the cause of these metric violations is the isotropy of the Friedman-Robertson-Walker model. In the anisotropic model of the cosmological distance scale, the disjunctions and rank inversions are associated with the orientation of the gravitational dipoles of the heterogeneity of the large-scale structure of the Universe. These dipoles represent diametrically opposite pairs of “super cluster galaxies – giant void” on the celestial sphere. Due to the size of only the super-void in the constellation Eridanus, comparable to the size of the observable part of the Universe, a colossal imbalance of the gravitational action of a massive super cluster of galaxies is created. This leads to disturbances in the form of disorders and rank inversions in isotropic Friedman-Robertson-Walker type models.

Slowly rotating and accelerating α′ -corrected black holes in four and higher dimensions

We consider the low-energy effective action of string theory at order $\alpha '$, including $R^2$-corrections to the Einstein-Hilbert gravitational action and non-trivial dilaton coupling. By means of a convenient field redefinition, we manage to express the theory in a frame that enables us to solve its field equations analytically and perturbatively in $\alpha ' $ for a static spherically symmetric ansatz in an arbitrary number of dimensions. The set of solutions we obtain is compatible with asymptotically flat geometries exhibiting a regular event horizon at which the dilaton is well-behaved. For the 4-dimensional case, we also derive the stationary black hole configuration at first order in $\alpha '$ and in the slowly rotating approximation. This yields string theory modifications to the Kerr geometry, including terms of the form $a$, $a^2$, $\alpha '$ and $a\alpha '$. In addition, we obtain the first $\alpha'$ correction to the C-metrics, which accommodates accelerating black holes. We work in the string frame and discuss the connection to the Einstein frame, for which rotating black holes have already been obtained in the literature.

Cost of holographic path integrals

We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in T\overline{T}TT¯ deformed holographic CFTs. In Nielsen’s geometric formulation cost is the length of a not-necessarily-geodesic path in a metric space of operators. Our cost proposals differ from holographic state complexity proposals in that (1) the boundary dual is cost, a quantity that can be 'optimised' to state complexity, (2) the set of proposals is large: all functions on all bulk subregions of any co-dimension which satisfy the physical properties of cost, and (3) the proposals are by construction UV-finite. The optimal path integral that prepares a given state is that with minimal cost, and cost proposals which reduce to the CV and CV2.0 complexity conjectures when the path integral is optimised are found, while bounded cost proposals based on gravitational action are not found. Related to our analysis of gravitational action-based proposals, we study bulk hypersurfaces with a constant intrinsic curvature of a specific value and give a Lorentzian version of the Gauss-Bonnet theorem valid in the presence of conical singularities.

Stability of non-degenerate Ricci-type Palatini theories

We study the stability of theories where the gravitational action has arbitrary algebraic dependence on the three first traces of the Riemann tensor: the Ricci tensor, the co-Ricci tensor, and the homothetic curvature tensor. We collectively call them Ricci-type tensors. We allow arbitrary coupling to matter. We consider the case when the connection is unconstrained, and the cases when either torsion or non-metricity is assumed to vanish. We find which combinations of Ricci-type tensors lead to new degrees of freedom around Minkowski and FLRW space, and when there are ghosts. None of the theories with new degrees of freedom are healthy, except the previously known case when torsion is zero and the action depends only on the Ricci tensor. We find that projective invariance is not a sufficient condition for a theory to be ghost-free.

Born–Infeld-f(R) gravity with de Sitter solutions

In this study, we consider Born–Infeld-[Formula: see text] gravity in which the [Formula: see text] term enters directly into the square root in the Palatini formulation. We briefly analyzed this model for an explicit [Formula: see text] function which includes positive and negative powers of the curvature scalar. We also show that both the ordinary Born–Infeld-[Formula: see text] and this modification reduce to the same gravitational action form under the conformal approach. Then, we consider the existence of a maximally symmetric vacuum solution for the gravitational field equations and find the de Sitter solution for this modified model.

Kiselev and Schwarzschild–de Sitter black holes in higher derivative theories of gravitation

We consider the influence of the higher-order correction to the gravitational action inspired by the Goroff-Sagnotti term upon the Kiselev black hole with $\stackrel{\texttildelow{}}{\ensuremath{\omega}}=\ensuremath{-}2/3$ and contrast the thus obtained results with the analogous results obtained for the Schwarzschild--de Sitter black hole. Expressing the perturbed solution in terms of the exact radius of the event horizon and the radius of the cosmological horizon of the unperturbed black hole we calculate corrections to the line element, to the cosmological horizon, and to the surface gravity. It is shown that although in both cases the lukewarm configuration does not exist classically (the equality of the surface gravities is possible only for the merged horizons), the sixth-order term removes the degeneracy of the classical solution and simultaneously shifts the degenerate horizon to a new place in the space of parameters. The lukewarm configuration is characterized by the value of the parameters that classically characterize the extremal solution. It is shown that the Karlhede scalar still may serve as the detector of the event and the cosmological horizon. Finally, we study the complex frequencies of the low-lying fundamental modes of the quasinormal oscillations and argue that they are the best candidates (at least theoretically) to distinguish between different black hole configurations.

Dark matter as a Weyl geometric effect

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type geometry, and its associated conformally invariant Weyl geometric quadratic gravity. As a first step in our investigations we write down the simplest possible conformally invariant gravitational action, constructed in Weyl geometry, and containing the Weyl scalar, and the strength of the Weyl vector only. By introducing an auxiliary scalar field, the theoretical model can be reformulated in the Riemann geometry as scalar-vector-tensor theory, containing a scalar field, and the Weyl vector, respectively. The field equations of the theory are derived in the metric formalism, in the absence of matter. A specific static, spherically symmetric model, in which the Weyl vector has only a radial component, is considered. In this case, an exact analytic solution of the gravitational field equations can be obtained. The behavior of the galactic rotation curves is also considered in detail, and it is shown that an effective geometric mass term, with an associated density profile, can also be introduced. Three particular cases, corresponding to some specific functional forms of the Weyl vector, are also investigated. A comparison of the model with a selected sample of galactic rotation curves is also performed when an explicit breaking of conformal invariance is introduced, which allows the fix of the numerical values of the free parameters of the model. Our results show that Weyl geometric models can be considered as a viable theoretical alternative to the dark matter paradigm.

Late-time constraints on modified Gauss-Bonnet cosmology

In this paper, we consider a gravitational action containing a combination of the Ricci scalar, R, and the topological Gauss-Bonnet term, G. Specifically, we study the cosmological features of a particular class of modified gravity theories selected by symmetry considerations, namely the $$f(R,G)= R^n G^{1-n}$$ model. In the context of a spatially flat, homogeneous and isotropic background, we show that the currently observed acceleration of the Universe can be addressed through geometry, hence avoiding de facto the shortcomings of the cosmological constant. We thus present a strategy to numerically solve the Friedmann equations in presence of pressureless matter and obtain the redshift behavior of the Hubble expansion rate. Then, to check the viability of the model, we place constraints on the free parameters of the theory by means of a Bayesian Monte Carlo method applied to late-time cosmic observations. Our results show that the f(R, G) model is capable of mimicking the low-redshift behavior of the standard $$\Lambda $$ CDM model. Finally, we investigate the energy conditions and show that, under suitable choices for the values of the cosmographic parameters, they are all violated when considering the mean value of n obtained from our analysis, as occurs in the case of a dark fluid.

Conservation of boundary term for gravitational action

In this paper, we intend to establish a rigorous mathematical relation between the Gibbons–Hawking–York (GHY) boundary term and the conserved symmetric current which arises due to Noether’s second theorem. The GHY term is necessary to ensure that the equations of motion in general relativity are well-posed, and it is a key ingredient in the thermodynamics of black holes and the derivation of the Bekenstein–Hawking entropy. Noether’s second theorem on the other hand relates the symmetries of the action to conserved quantities of the system. In this paper, we prove that the connection between the GHY term and Noether’s second theorem can be established by considering a diffeomorphism that preserves the boundary condition of the surface integral. Additionally, we also derive the associated conserved current and charge.

Non-singular bouncing model in energy momentum squared gravity

This work is concerned to study the bouncing nature of the Universe for an isotropic configuration of fluid and Friedmann-Lemaître-Robertson-Walker metric scheme. This work is carried out under the novel gravitation by assuming a specific model i.e. = with α and λ are constants, serving as free parameters. The terms and served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in the gravitational action respectively, and is proportional to . A specific functional form of the Hubble parameter is taken to provide the evolution of cosmographic parameters. A well known equation of state parameter, is used to represent the dynamical behavior of energy density, matter pressure and energy conditions. A detailed graphical analysis is also provided to review the bounce. Furthermore, all free parameters are set in a way, to make the supposed Hubble parameter act as the bouncing solution and ensure the viability of energy conditions. Conclusively, all necessary conditions for a bouncing model are checked.

Revisiting Fractional Cosmology

Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting theory is compared against observational data. In this context, dynamical systems can be used along with an analysis the phase spaces for different values of the fractional order of the derivative and their different matter contents. The equilibrium points are classified, providing a range for the order of the fractional derivative in order to investigate whether the cosmological history can be reconstructed and a late-time accelerating power-law solution obtained for the scale factor. In this paper, we discuss the physical interpretation of the corresponding cosmological solutions with particular emphasis on the influence of the fractional order of the derivative in a theory of gravity that includes a scalar field minimally coupled to gravity. The presented results improve and extend those obtained previously, further demonstrating that fractional calculus can play a relevant role in cosmology.

The case of HD 106906 debris disc: a binary’s revenge

ABSTRACTDebris disc architecture presents [exo-]planetary scientists with precious clues for processes of planet formation and evolution, including constraints on planetary mass perturbers. This is particularly true of the disc in HD 106906, which in early HST, then follow up polarimetric observations, presented asymmetries and needle-like features that have been attributed to perturbations by a massive, and unusually distant external planetary companion. Here, we revisit the long-term secular dynamical evolution of the HD 106906 disc allowing for the combined gravitational action of the planetary companion and the inner stellar binary which holds the system together. We argue that the binary is strong enough to impose a dynamical break at the disc’s location, resulting in distinctive observational signatures which we render via simulated surface density maps and vertical structure profiles. Within uncertainties on the planet’s orbit, we show that the disc can go from being fully dominated by the inner binary to significantly so, and is hardly ever outside its reach. The extent of binary dominance impacts the disc’s mean eccentricity, a metric which we map as a function of the planet’s semimajor axis and orbital eccentricity, with and without radiation pressure. We can thus constrain the planet’s orbit to ease the tension between evident axisymmetry in the millimeter, and apparent asymmetry in scattered light. We discuss phase space structure, then inclination distribution, arguing for the relevance of our results to a variety of hierarchical systems, as we set the stage for generalizations that allow for disc self-gravity and collisional evolution.

Polarized primordial gravitational waves in spatial covariant gravities

The spatial covariant gravities provide a natural way to including odd-order spatial derivative terms into the gravitational action, which breaks the parity symmetry at gravitational sector. A lot of parity-violating scalar-tensor theories can be mapped to the spatial covariant framework by imposing the unitary gauge. This provides us with a general framework for exploring the parity-violating effects in primordial gravitational waves (PGWs). The main purpose of this paper is to investigate the polarization of PGWs in the spatial covariant gravities and their possible observational effects. To this end, we first construct the approximate analytical solution to the mode function of the PGWs during the slow-roll inflation by using the uniform asymptotic approximation. With the approximate solution, we calculate explicitly the power spectrum and the corresponding circular polarization of the PGWs analytically. It is shown that the new contributions to power spectrum from spatial covariant gravities contain two parts, one from the parity-preserving terms and the other from the parity-violating terms. While the parity-preserving terms can only affect the overall amplitudes of PGWs, the parity-violating terms induce nonzero circular polarization of PGWs, i.e., the left-hand and right-hand polarization modes of GWs have different amplitudes. The observational implications of this nonzero circular polarization is also briefly discussed.

Late time cosmology in f(R,{{mathcal {G}}}) gravity with exponential interactions

Cosmological models with f(R) modified gravity are significant to investigate the present and late-time behavior of the Universe. The dynamics of the Universe is studied in the framework of f(R)= R + gamma R^2- lambda left( frac{R}{3m_s^2} right) ^{delta } gravity (gamma , lambda , delta are arbitrary constants) with a coupled Gauss–Bonnet (GB) term in the gravitational action and estimate the constraints on the model parameters as well as the late time behavior of the Universe. In this case, the coupled Gauss–Bonnet term is coupled with a free scalar field in the presence of interacting fluid. In addition, we investigate the same for a different form of gravity f(R)=R, where the coupled GB term is coupled with a scalar field in a self-interacting potential.

Modified Brans–Dicke cosmology with minimum length uncertainty

We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann--Lema\^{\i}tre--Robertson--Walker metric. We investigate the dynamics and the cosmological evolution for the dynamical variables of the theory and we compare the results with the unmodified Brans-Dicke theory. It follows that in consideration because of the additional degrees of freedom in the energy-momentum tensor the dynamical variables describe various aspects of the cosmological history. This is one of the first studies on the effects of GUP in a Machian gravitational theory.

The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

A convenient gauge for virial identities in axial symmetry

Virial identities are a useful mathematical tool in General Relativity. Not only have they been used as a numerical accuracy tool, but they have also played a significant role in establishing no-go and no-hair theorems while giving some physical insight into the considered system from an energy balance perspective. While the calculation of these identities tends to be a straightforward application of Derrick's scaling argument [1], the complexity of the resulting identity is system dependent. In particular, the contribution of the Einstein-Hilbert action, due to the presence of second order derivatives of the metric functions, becomes increasingly complex for generic metrics. Additionally, the Gibbons-Hawking-York term needs to be taken into account [2]. Thankfully, since the gravitational action only depends on the metric, it is expected that a “convenient” gauge that trivializes the gravitational action contribution exists. While in spherical symmetry such a gauge is known (the m−σ parametrization), such has not been found for axial symmetry. In this letter, we propose a “convenient” gauge for axial symmetry and use it to compute an identity for Kerr black holes with scalar hair.