Field Equations Of Gravity Research Articles

Scalar Field Source Teleparallel Robertson–Walker F(T) Gravity Solutions

This paper investigates the teleparallel Robertson–Walker (TRW) F(T) gravity solutions for a scalar field source. We use the TRW F(T) gravity field equations (FEs) for each k-parameter value case added by a scalar field to find new teleparallel F(T) solutions. For k=0, we find an easy-to-compute F(T) solution formula applicable for any scalar field source. Then, we obtain, for k=−1 and +1 situations, some new analytical F(T) solutions, only for specific n-parameter values and well-determined scalar field cases. We can find by those computations a large number of analytical teleparallel F(T) solutions independent of any scalar potential V(ϕ) expression. The V(ϕ) independence makes the FE solving and computations easier. The new solutions will be relevant for future cosmological applications in dark matter, dark energy (DE) quintessence, phantom energy and quintom models of physical processes.

Closed causal curves in f(ℛ,𝒜,AμνAμν) gravity

In this paper, we investigate a [Formula: see text] solution of Einstein field equations, an extension of [Formula: see text] Misner space in the context of Ricci-inverse ([Formula: see text])-gravity theory. For that, we consider two different class, namely, Class-II model which is defined by the function [Formula: see text] and Class-III model defined by the function [Formula: see text]. Here, [Formula: see text] is the anti-curvature tensor with [Formula: see text] as its scalar, and [Formula: see text] is the Ricci scalar. Using this [Formula: see text] metric as background, the modified field equations for Ricci-inverse gravity were derived and obtain the results. These derived field equations are then solvable by choosing the pure radiation field as the energy-momentum tensor, including a cosmological constant as does in the general relativity. This implies that the chosen [Formula: see text] space-time is a valid solution in this novel gravity theory, and thereby violate the causality condition, analogous to general relativity.

Field equation of thermodynamic gravity and galactic rotational curves

The rotational velocity curve (RC) of galaxy NGC 3198 is modelled in various theoretical frameworks: Thermodynamic Gravity (TG) is compared to Dark Matter (DM) and Modified Newtonian Dynamics (MOND). The nonlinear gravitational field equation of TG is solved using the baryonic mass density as the source of the gravitational field. In this paper, first, a dissipation motivated numerical method is verified with the help of exact solutions. Then, the obtained optimal velocity curve is compared to DC14 model DM and MOND EFE (Modified Newtonian Dynamics-External Field Effect aspect) parametrisations for the RC of the galaxy.

Impact of particle creation in Rastall gravity

In this paper, we investigate the Friedmann–Lemaitre–Robertson–Walker cosmological models within the framework of Rastall gravity incorporating particle creation. The modified field equations for Rastall gravity are derived and exact solutions are obtained under various assumptions of the scale factor. The qualitative behavior of our solutions depends on the Rastall coupling parameter [Formula: see text]. Following Akarsu et al. [Ö. Akarsu et al., Rastall gravity extension of the standard [Formula: see text] CDM model: Theoretical features and observational constraints, Eur. Phys. J. C 80 (2020) 1050], we have restricted the Rastall coupling parameter [Formula: see text] to the range [Formula: see text] at 68% CL from CMB+BAO data. Further, we have discussed the distinct physical behavior of the derived models in detail.

FLRW cosmology in Weyl type f(Q) gravity and observational constraints

Inspired by various works in a Weyl type f(Q) gravity to reduce some serious problems in General Relativity Theory (GR), we develop a model of the universe in a Weyl type f(Q) gravity which shows the transition from a decelerating state to an accelerating state of the universe at present when we consider a particular functional form of the f(Q) gravity as f(Q)=(H02)(α1+α2log(H0−2Q)). We numerically solve Weyl type f(Q) gravity field equations and obtain the numerical solutions to the Hubble parameter, deceleration parameter, distance modulus, and the apparent magnitudes of stellar objects using Ia Supernovae. Also, we obtain numerical solutions for the Weyl vector w, non-metricity scalar Q, and the Lagrangian multiplier λ appearing in the action of f(Q) gravity. We compare our model with the error bar plots of the observed Hubble dataset of 77 points, SNIa datasets of 580 points, and 1048 supernova Pantheon datasets of the apparent magnitudes, and the statistical analysis using Baryon Acoustic Oscillations (BAO). It is found that our results fit well with the observed values. The model envisages a unique feature: although the universe is filled with perfect fluid as dust whose pressure is zero, the Weyl vector dominance f(Q) creates acceleration.

Modified [formula omitted] gravity models and their cosmological consequences

In this work, we consider three different f(Q) models, such as power-law, exponential, and logarithmic, to study which model better mimics ΛCDM evolution theoretically. Henceforth, we determine solutions to the f(Q) gravity field equations in the isotropic and homogeneous universe. Since all the models contain two model parameters, we reduce the degrees of freedom using the first Friedman equation at the present time. Further, we check the behavior of cosmological parameters using the obtained solution to the field equations and compare it with the ΛCDM model. As a result, the power-law model shows a good match with ΛCDM model for λ=−1 and λ=−2, while the exponential model behaves well for the range 5≤β<11, and the logarithmic model matches for 3.8<γ<4.4.

New non-conserved gravity theory and alleviate current acceleration epoch without dark energy field

Recently, a new modified theory of gravity was proposed in which Rastall's idea Tμ;νν=α,μ is reexamined. Although Rastall's idea shows potential for exploring field equations of gravity at high levels of energy, there are concerns about Rastall's proposal α=γR. In Ref. [1], it is suggested to find the viable form for α by reevaluating the first law of thermodynamics in a relativistic system. In this context, Israel and his colleagues have proposed a covariant equation linking the flux of the energy-momentum tensor and the 4-vector of entropy of the system, respecting the Gibbs-Duhem relation in flat spacetime [2,3]. Extending this idea to curved spacetime provides the theoretical form of α that supports Rastall's idea Tμ;νν=α,μ. However, this modified theory of gravity, known as ‘non-conserved gravity’, cannot present dark energy in FRW spacetime for the comoving observer without the cosmological constant. Through this study and considering the application of this gravity theory in cosmology, it was demonstrated that the model can explain the current acceleration epoch in the absence of extra fluid as dark energy. Therefore, the non-conserved theory of gravity attributes the matter field as the source of current accelerated expansion. This model also aligns with matter structure formations and thus does not conflict with observations in the past (high redshift) Universe.

Gravitationally decoupled charged anisotropic solutions in Rastall gravity

This paper develops the stellar interior geometry for charged anisotropic spherical matter distribution by developing an exact solution of the field equations of Rastall gravity using the notion of gravitational decoupling. The main purpose of this investigation is the extension of the well-known isotropic model within the context of charged isotropic Rastall gravity solutions. The second aim of this work is to apply gravitational decoupling via a minimal geometric deformation scheme in Rastall gravity. Finally, the third one is to derive an anisotropic version of the charged isotropic model previously obtained by applying gravitational decoupling technology. We construct the field equations which are divided into two sets by employing the geometric deformation in radial metric function. The first set corresponds to the seed (charged isotropic) source, while the other one relates the deformation function with an extra source. We choose a known isotropic solution for spherical matter configuration including electromagnetic effects and extend it to an anisotropic model by finding the solution of the field equations associated with a new source. We construct two anisotropic models by adopting some physical constraints on the additional source. To evaluate the unknown constants, we use the matching of interior and exterior spacetimes. We investigate the physical feasibility of the constructed charged anisotropic solutions by the graphical analysis of the metric functions, density, pressure, anisotropy parameter, energy conditions, stability criterion, mass function, compactness, and redshift parameters. For the considered choice of parameters, it is concluded that the developed solutions are physically acceptable as all the physical aspects are well-behaved.

Classical and quantum gravity from the axioms of relativistic quantum mechanics

It is common practice to describe elementary particles by irreducible unitary representations of the Poincaré group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincaré group. Representations of the Poincaré group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.

Bianchi type cosmological models in f(T) tele-parallel gravity

Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of motions defines an affine symmetry group. Here, we assume there exists a three-dimensional group of affine symmetries acting simply transitively on a spatial hypersurface and that this group of symmetry actions defines our affine frame symmetry group. We determine the general form of the co-frame and spin connection for each spatially homogeneous Bianchi type. We then construct the corresponding field equations for f(T) tele-parallel gravity. We show that if the symmetry group is of Bianchi type A (I, II, VI 0, VII 0, VIII or IX) then there exists a co-frame/spin connection pair that is consistent with the antisymmetric part of the field equations of f(T) tele-parallel gravity. For those geometries having a Bianchi type B symmetry group (IV, V, VIh , VIIh ), we find that in general these geometries are inconsistent with the antisymmetric part of the f(T) tele-parallel gravity field equations unless the theory reduces to an analog of General Relativity with a cosmological constant.

Implications of the Conformal Constraint on Sound Speed on the Radius of PSR J0952–0607 within Rastall Gravity

It has been shown that the nonminimal coupling between geometry and matter can provide models for massive compact stars that are consistent with the conformal bound on the sound speed, , where the core density approaches a few times the nuclear saturation density. We impose the conformal upper bound on the sound speed on Rastall’s field equations of gravity, with Krori–Barua potentials in the presence of an anisotropic fluid as a matter source, to estimate the radius of the most massive pulsar ever observed, PSR J0952–0607. For its measured mass M = 2.35 ± 0.17 M ⊙, we obtain a radius R = 14.087 ± 1.0186 km as inferred by the model. We investigate a possible connection between Rastall gravity and the MIT bag model with an equation of state, , in the radial direction, with and a surface density ρ s slightly above the nuclear saturation density ρ nuc = 2.7 × 1014 g cm–3. The corresponding mass–radius diagram is in agreement with our estimated value of the radius and with astrophysical observations of other pulsars at 68% confidence level.

Evaporation and information puzzle for 2D nonsingular asymptotically flat black holes

We investigate the thermodynamics and the classical and semiclassical dynamics of two-dimensional (2D), asymptotically flat, nonsingular dilatonic black holes. They are characterized by a de Sitter core, allowing for the smearing of the classical singularity, and by the presence of two horizons with a related extremal configuration. For concreteness, we focus on a 2D version of the Hayward black hole. We find a second order thermodynamic phase transition, separating large unstable black holes from stable configurations close to extremality. We first describe the black-hole evaporation process using a quasistatic approximation and we show that it ends in the extremal configuration in an infinite amount of time. We go beyond the quasistatic approximation by numerically integrating the field equations for 2D dilaton gravity coupled to N massless scalar fields, describing the radiation. We find that the inclusion of large backreaction effects (N ≫ 1) allows for an end-point extremal configuration after a finite evaporation time. Finally, we evaluate the entanglement entropy (EE) of the radiation in the quasistatic approximation and construct the relative Page curve. We find that the EE initially grows, reaches a maximum and then goes down towards zero, in agreement with previous results in the literature. Despite the breakdown of the semiclassical approximation prevents the description of the evaporation process near extremality, we have a clear indication that the end point of the evaporation is a regular, extremal state with vanishing EE of the radiation. This suggests that the nonunitary evolution, which commonly characterizes the evaporation of singular black holes, could be traced back to the presence of the singularity.

Comparison of basic equations of the Kaluza–Klein theory with the nonholonomic model of space–time of the sub-Lorentzian geometry

The field equations of gravity coupled to electromagnetism and equations of motion of a charged particle are part of the Kaluza–Klein theory where general relativity is extended to five dimensions. These equations can also be obtained if nonholonomic constrains are imposed on the 5-vector of particle’s velocity. Hence, further development of the general relativity theory can be sub-Riemannian (or sub-Lorentzian) geometry. Gauge transformations become a special case of coordinate transformations in both the Kaluza–Klein theory and the nonholonomic model. Sub-Riemannian geodesics are proved to be equations of motion of a charged particle. The Dirac operator can be extended for a 5-dimensional manifold as a first-order differential operator. Since the base manifold in physics contains the electromagnetic gauge group [Formula: see text], the eigenvalues of the charge operator are always an integer multiplied by the fundamental electric charge.

Nöther currents, black hole entropy universality and CFT duality in conformal Weyl gravity

In this paper, we study black hole entropy universality within the conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in conformal Weyl gravity via both the Nöther current method and Wald’s entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case, we couple the conformal Weyl gravity field equations to a near horizon (linear) [Formula: see text] gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However, despite non-universality, the respective black hole entropies are in congruence with Wald’s entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call [Formula: see text] and relating to the Weyl anomaly coefficient. The construction follows an [Formula: see text] correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work.

Impact of Rastall Gravity on Mass, Radius, and Sound Speed of the Pulsar PSR J0740+6620

Millisecond pulsars are perfect laboratories to test possible matter–geometry coupling and its physical implications in light of recent Neutron Star Interior Composition Explorer (NICER) observations. We apply Rastall field equations of gravity, where matter and geometry are nonminimally coupled, to Krori–Barua interior spacetime whereas the matter source is assumed to be anisotropic fluid. We show that all physical quantities inside the star can be expressed in terms of Rastall, ϵ, and compactness, C = 2GM/Rc 2, parameters. Using NICER and X-ray Multi-Mirror Newton X-ray-observational constraints on the mass and radius of the pulsar PSR J0740+6620, we determine the Rastall parameter to be at most ϵ = 0.041 in the positive range. The obtained solution provides a stable compact object; in addition the squared sound speed does not violate the conjectured sound speed unlike the general relativistic treatment. We note that no equations of state are assumed; the model however fits well with linear patterns with bag constants. In general, for ϵ > 0, the theory predicts a slightly larger-size star in comparison to general relativity for the same mass. This has been explained as an additional force, due to matter–geometry coupling, in the hydrodynamic equilibrium equation, which contributes to partially diminishing the gravitational force effect. Consequently, we calculate the maximal compactness as allowed by the strong energy condition to be C = 0.735, which is ∼2% higher than general relativity prediction. Moreover, for the surface density at saturation nuclear density ρ nuc = 2.7 × 1014 g cm−3, we estimate the maximum mass M = 4M ⊙ at radius R = 16 km.

Unified quantum gravity field equation describing the universe from the smallest to the cosmological scales

This paper introduces a new quantum gravity field equation that is derived from collision space‐time. It shows how changes in energy (collision-space) are linked to changes in matter (collision-time). This field equation can be written in several different forms. Gravity, at the deepest level, is linked to change in gravitational energy over the Planck time. In our view, this is linked to the collision between two indivisible particles, and this collision has a duration of the Planck time, not by assumption, but from calibration. We also show how an equation of the universe, which was recently derived from relativistic Newtonian theory, can also be derived directly from the unified quantum gravity field equation presented in this paper. This equation gives a new explanation for a cosmological redshift that does not seem to be related to expanding space or the big bang hypothesis. Also, the approximately 13.9 × 109 years of the Hubble time do not seem to be at all related to the age of the universe but to the aggregated collision time of the particles making up the mass in the observable universe.

Dark energy star in gravity's rainbow

The concept of dark energy can be a candidate for preventing the gravitational collapse of compact objects to singularities. According to the usefulness of gravity's rainbow in UV completion of general relativity (by providing a new description of spacetime), it can be an excellent option to study the behavior of compact objects near phase transition regions. In this work, we obtain a modified Tolman-Openheimer-Volkof (TOV) equation for anisotropic dark energy as a fluid by solving the field equations in gravity's rainbow. Next, to compare the results with general relativity, we use a generalized Tolman-Matese-Whitman mass function to determine the physical quantities such as energy density, radial pressure, transverse pressure, gravity profile, and anisotropy factor of the dark energy star. We evaluate the junction condition and investigate the dynamical stability of dark energy star thin shell in gravity's rainbow. We also study the energy conditions for the interior region of this star. We show that the coefficients of gravity's rainbow can significantly affect this non-singular compact object and modify the model near the phase transition region.

Wormhole solutions in Rastall teleparallel gravity

This paper is devoted to explore some interesting wormhole solutions for the Rastall teleparallel gravity. To complete this analysis, we consider the traceless energy–momentum tensor taken with the Casimir effect concept. Further, we develop two different relations between the pressure components. The anisotropic source of matter with the spherically symmetric space-time is taken to calculate the exact solution, as the shape function. The field equations for Rastall teleparallel gravity are calculated. All the energy conditions are presented for Rastall teleparallel gravity. The presence of exotic matter is confirmed via the violation of energy conditions. All the necessary properties for shape function in all cases are presented graphically. All the inquired results are concluded.

Black hole thermodynamics in (2+1)-dimensional scalar–tensor-Born–Infeld theory

The action of scalar–tensor (ST) gravity theory can be written in both of the Jordan and Einstein frames, which are related via conformal transformations. Here, by introducing a suitable conformal transformation (CT), the action of three-dimensional Einstein-dilaton-Born–Infeld (EdBI) gravity has been obtained from that of scalar–tensor-Born–Infeld (STBI) theory. Despite the field equations of ST gravity, the exact solutions of Einstein-dilaton (Ed) theory can be obtained, easily. The exact solutions of STBI theory have been obtained from those of EdBI gravity by applying the inverse CTs. As the result, two novel classes of ST black hole (BH) solutions have been introduced in the presence of Born–Infeld (BI) nonlinear electrodynamics. The BHs’ conserved and thermodynamic quantities have been calculated under the influence of nonlinear electrodynamics. Then, through a Smarr-type mass formula, it has been shown that these quantities satisfy the standard form of the thermodynamical first law, in both of the Jordan and Einstein frames. Thermal stability or phase transition of the BHs have been investigate by use of the canonical ensemble method and regarding the signature of specific heat (SH). The points of first- and second-order phase transitions, and the size of those BHs which remain locally stable have been determined.

Integrability of Three Dimensional Gravity Field Equations

We show that the tree dimensional Einstein vacuum feld equations with cosmological constant are integrable. Using the sl(2, R) valued soliton connections we obtain the metric of the spacetime in terms of the dynamical variables of the integrable nonlinear partial diferential equations.