Rastall Theory Of Gravity Research Articles

Possible dark energy stars in Rastall gravity

Observational evidence revealed that in the composition of the Universe, the dark energy is in heap proportion which is mainly responsible for the accelerated expansion of the Universe. The astrophysicists hypothesized that every astrophysical object is likely interact with the dark energy Sakti and Sulaksono [Phys. Rev. D 103 (2021) 084042]. Therefore, researchers are intended to study the astrophysical objects with dark energy interaction. In this paper, we proposed a dark energy stars (composed of with dark matter and ordinary matter) model in the Rastall theory of gravity. The Rastall field equations are obtained in the Tolman–Kuchowicz-type metric. To solve the field equations, the arbitrary constants involved in the field equations (due to Tolman–Kuchowicz ansatz) are obtained by matching the interior geometry with the exterior Schwarzschild geometry. The obtained solution is tested physically by computing some analytical results and plotting graphs of different physical parameters like pressure, density for ordinary matter, density for dark matter, mass function, compactness and surface redshift. Stability of the model is also analyzed by different tests like velocity of sound, adiabatic index and TOV equations. The influence of the Rastall parameter on the model has been studied by plotting graphs and computing numerical values of model’s physical parameters for different values of the Rastall parameter. We infer that our propounded model fulfills all the necessary requirements for a physically plausible model.

A study of Yukawa–Casimir wormholes in some Rastall frameworks via conformal killing vectors approach

Present work explores the possibility of obtaining analytical wormhole solutions in Rastall theory of gravity and its modified torsion based version where the conformal killing vectors are introduced. To achieve this target, we assume spherically symmetric wormhole metric with anisotropic background matter and find the analytical solutions by taking Casimir as well as Yukawa corrected energy densities into account. The formulated solutions are then examined graphically for checking the essential properties of wormhole configuration and also, the impact of Rastall parameter, in this respect, is explored. It is found that primary wormhole properties hold in all cases while the obtained wormhole solutions in torsion based Rastall theory do not fulfill asymptotic flatness criteria for some certain choices of Rastall parameter. Further, behavior of null energy constraint is explored and the volume integral quantifier is computed for each case. We also discuss the equilibrium of proposed wormhole configurations by checking the behavior of four different forces using generalized Tolman–Oppenheimer–Volkoff equation in Rastall background (as the equilibrium condition gets modified) and conclude that these forces refer to the stability of the system in all cases, especially when one moves away from the wormhole throat.

Warm inflation driven by complex quintessence field within rastall gravity

This manuscript is devoted to examining the role of the “complex quintessence field” (CQF) in driving warm inflation (WI) within the Rastall theory of gravity (RTG). Recently, the accelerating cosmic expansion has been described by CQF, which is linked to several other cosmic scenarios. In this approach, we construct the corresponding dynamical equations for inflation using the flat Friedmann–Robertson–Walker (FRW) spacetime. We begin with a fundamental approach of selecting intermediate, logamediate, and power-law models to study how inflation is realized from these models. For each model, we find analytic solutions of the scalar field and corresponding effective potential necessary to produce inflation under slow-roll (SR) conditions. These solutions allow us to develop inflationary observable in the strong dissipative regime, including the SR parameters, e-folding number, scalar/tensor power spectra, scalar spectral index (ns) and its running (αs) and finally tensor to scalar ratio (r). We checked the impact of additional theory parameter λ on the evolutionary trajectories in ns−r and ns−αs planes for the underlying inflationary models. For all three models, it is concluded that CQF-inspired inflation in RTG provides interesting and feasible results which fully satisfy the Planck constraints.

Comprehensive study of cylindrical Levi-Civita and cosmic string solutions in Rastall theory of gravity

In this manuscript, the main aim is to investigate the cylindrically symmetric solutions in a well known Rastall theory of gravity. For this purpose, we consider the cylindrically symmetric space–time to discuss the cylindrical solutions in some realistic regions. First, we investigate four distinct cases of exact solutions using the field equations of Rastall theory of gravity. Furthermore, we set some suitable values of the Rastall coupling constant (λ) for the investigation of well-known Levi-Civita and cosmic string solutions. The Energy conditions are also investigated for all different cases and observed that null energy conditions are violated, which is the indication of the existence of cylindrical wormholes.

The phase transition of Rastall AdS black hole with cloud of strings and quintessence

In this paper, we introduce the black hole solution in Rastall theory of gravity in the presence of quintessence and the cloud of strings. Our investigations show that this model meets only second-order phase transition in four dimensions. While both the first- and second-order phase transitions are seen in five dimensions. Therefore, according to the AdS/CFT duality, the confinement–deconfinement phase transition only occurs in five dimensions for this model.

Optical properties of an axially symmetric black hole in the Rastall gravity

This work is devoted to the study of the optical properties of the charged-rotating-NUT-Kiselev (CRNK) black hole in the Rastall theory of gravity. By investigating the motion of photons in the CRNK black hole spacetime in the Rastall gravity, we show that the deflection angle of photons due to the gravitational lensing is mostly influenced by the NUT charge, parameter of the equation of state for the quintessence and the quintessential intensity. We observe that the effects of the rest of the spacetime parameters are negligible on the deflection angle. We present the shape of the shadow cast by the CRNK black hole in the Rastall gravity for various values of the spacetime parameters. We demonstrate that spin parameter a of the black hole changes the position and size of the shadow of the black hole very little, while changing the values of the rest of the spacetime parameters can alter the shape and the size of the observed shadow of the black hole significantly. We observe that the radius of the black hole shadow and the deflection angle of photon are bigger for the CRNK black hole in the Rastall gravity, as compared with the case of the Kerr black hole. Lastly, we show how the spacetime parameters can change the observables $$R_s$$ and $$\delta _s$$ , being the average radius of the shadow and the distortion parameter that measures the deviation of the shape of the shadow from a perfect circle with radius $$R_s$$ , respectively. Our results show that in most scenarios, for bigger values of $$R_s$$ , we get smaller values of the parameter $$\delta _s$$ .

Study of warm inflation using irreversible thermodynamical description within Rastall gravity

This manuscript aims to study warm inflation via “irreversible thermodynamics of open systems” with matter creation/decay within Rastall theory of gravity. Interacting scalar field and radiation are assumed to be the components of cosmological fluid in spatially flat FRW universe model. Considering early universe as an open system, and implementing the thermodynamics along with the dynamical equations in Rastall gravity on the interacting cosmological fluid leads to modify the standard formalism of warm inflationary model, including the creation(decay) pressure, which is considered as part of the energy–momentum tensor explicitly. The analysis is done using constant as well as Higgs potential. Under slow-roll approximation and introducing some dimensionless variables, numerical solutions of the thermodynamical equations (scale factor, number of scalar field particles, energy densities of scalar field and radiation and temperature) are obtained and represented graphically. For appropriate set of initial conditions, these results depict the phase transition from acceleration to deceleration phase. Using obtained solutions, we calculate inflationary observable like “slow-roll parameters, number of e-folds, scalar/tensor power spectra, scalar/tensor spectral indices and tensor-to-scalar ratio”. By constraining the free model parameters, the theoretical predictions of the under lying model are compared with the Planck-2018 data.

Complexity factor for anisotropic self-gravitating sphere in Rastall gravity

This paper investigates the new definition of complexity factor for the case of irrotational spherical relativistic structure in the Rastall theory of gravity (RTG). To do so, we assumed static spherically symmetric metric with anisotropic self-gravitating fluid. We studied Rastall field equations, generalized nonconservation equation, mass function and physical impacts of Rastall parameter [Formula: see text] on various material variables by employing certain observational data of compact objects like PSR J1614-2230, 4U1608-52, SAX J 1808.4-3658, 4U1820-30 and Vela X-1. We obtained structure scalars through orthogonal decomposition of the curvature tensor and then utilize these scalars to find the complexity factor of the self-gravitating spherical structure. We examined that the vanishing complexity factor condition is an effective energy density inhomogeneity and an effective anisotropy of pressure which must cancel each other, employed the condition [Formula: see text]. Moreover, we also depicted the solutions of interior formation of spherical stellar object regarding to this vanishing complexity condition. Finally, it is found that the complexity of the system enhances due to the presence of nonminimal to curvature matter couple parameter [Formula: see text]. It is very fascinating to report here that these outcomes could be recovered back to former solutions about complexity factor in General Relativity (GR) by imposing [Formula: see text].

Rapidly rotating compact stars in Rastall’s gravity

In this work we study rapidly rotating stars by considering the Rastall theory of gravity. We obtain and solve the equations by numerical methods for two usual parametrization of polytropic stars. Then the mass–radius relations, moments of inertia and other results of interest are obtained and compared with the ones for non-rotating stars.

Study of gravastars in Rastall gravity

Gravastars have been considered as a feasible alternative to black holes in the past couple of decades.Stable models of gravastar have been studied in many of the alternative gravity theories besides standard GeneralRelativity (GR). The Rastall theory of gravity is a popular alternative to GR, specially in the cosmological andastrophysical context. Here, we propose a stellar model under the Rastall gravity following Mazur-Mottola's [1,2]conjecture. The gravastar consists of three regions, viz., (I) Interior region, (II) Intermediate shell region,and (III) Exterior region. The pressure within the interior core region is assumed with a constant negativematter-energy density which provides a repulsive force over the entire thin shell region. The shell is assumed tobe made up of fluid of ultrarelativistic plasma which follows the Zel'dovich's conjecture of stiff fluid [3,4].It is also assumed that the pressure is proportional to the matter-energy density according to Zel'dovich's conjecture,which cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum which isdescribed by the Schwarzschild-de Sitter solution. Under all these specifications we obtain a set of exact andsingularity-free solutions of the gravastar model presenting several physically valid features within the frameworkof Rastall gravity. The physical properties of the shell region namely, the energy density, proper length, totalenergy and entropy are explored. The stability of the gravastar model is investigated using the surface redshiftagainst the shell thickness and maximizing the entropy of the shell within the framework of Rastall gravity.

Exact cylindrically symmetric solutions in Rastall theory of gravity

In this paper, we explore some exact cylindrically symmetric solutions in the context of Rastall theory of gravity. For this purpose, we consider the general form of a metric in the cylindrical Weyl coordinates. The modified field equations are developed in the presence of charge. In particular, we try to recover the well-known Levi–Civita’s static cylindrically symmetric solution in the framework of Rastall gravity. The graphical behavior of energy density and pressure component is presented along with the discussion of energy conditions. Finally, the solutions in the context of general relativity are discussed. It is concluded that Levi–Civita’s static cylindrically symmetric charged solutions do exist in Rastall theory of gravity.

Models of non-static and inhomogeneous gravitating source in Rastall gravity

In this paper, we have explored the non-static anisotropic gravitational collapse and expansion solutions in Rastall theory of gravity. The field equations have been formulated for the non-static and inhomogeneous gravitating source. The Misner–Sharp mass function, auxiliary solution and trapped condition have been used to obtained a trapped surface. The auxiliary solutions have been used to obtain the expansion and collapse solutions; these solutions depend on [Formula: see text] and parameter [Formula: see text] (which appears due to parametric form of metric components); also the range of parameter [Formula: see text] has been examined. The expansion scalar [Formula: see text] depends on parameter [Formula: see text], in the case of expansion [Formula: see text] for [Formula: see text], while for collapse [Formula: see text] with [Formula: see text]. Also, the dynamics of the gravitating spherical source has been discussed graphically with the effects of Rastall parameter [Formula: see text]. For the physically reasonable fluid, the validity of energy conditions has been discussed for expansion and collapse solutions with the various values of [Formula: see text].

Confronting the warm vector inflation in Rastall theory of gravity with Planck 2018 data

Abstract The main focus of this manuscript is to explore the effectiveness of Rastall theory of gravity in describing very early epoch of the universe, called cosmic inflation. In this framework, we develop the basic inflationary dynamical equations for flat FRW metric. To find out the exact solutions of inflaton field and corresponding potentials, we start with a basic technique of choosing a known solution of the scale factor, i.e., intermediate and logamediate forms and then extracted the effective potential necessary to support the inflation under slow-roll condition. Via these solutions, we calculate the inflationary observable such as the slow-roll parameters, e-folding number, scalar/tensor power spectra, scalar spectral index and tensor–scalar ratio in both strong and weak dissipative regimes. The recent Planck 2018 data sets bounds for scalar power spectrum, scalar spectral index, n s = 0 . 966 and tensor–scalar ratio, R 0 . 16 . We have plotted graphical trajectories of R − n s by constraining the model parameters, which show that Planck bounds are fully satisfied by Rastall theory of gravity. Hence, this modified gravity theory has ability to describe the early as well as the late-time cosmic eras elegantly.

Non-commutative wormholes exhibiting conformal motion in Rastall gravity

In the present paper, we explore the existence of wormhole solutions using conformal symmetries in Rastall theory of gravity. For this purpose, we take spherical symmetric model filled with matter distribution as anisotropic fluid. For the sake of simplifications, we consider the energy density profiles of Gaussian and Lorentzian distributions of non-commutative geometry. Using both these distributions, we obtain analytic wormhole solutions in terms of some special math functions like gamma, exponential and hypergeometric functions. For graphical illustrations, we take some appropriate choices of the free parameters along with different values of Rastall parameter. It is seen that in both cases, the obtained wormhole solutions satisfy the basic criteria of wormhole existence. Further, we describe the possible constraints for the positivity of active gravitational mass in both distributions. We also explore the stability of obtained wormholes solutions by utilizing the modified equilibrium condition in terms of four different forces in Rastall theory. It is concluded that the constructed solutions are stable and physically viable.

Kerr–Newman–NUT–Kiselev black holes in Rastall theory of gravity and Kerr/CFT correspondence

We present a new twisted rotating black hole solution by performing Demiański–Newman–Janis algorithm to the electrically and dyonically charged black hole with quintessence in Rastall theory of gravity. Using our black hole solution, we argue that Rastall gravity is not equivalent with Einstein gravity. For further explanation, the black hole properties such as the horizon and ergosphere are studied for which there are some different properties for those theories. Some thermodynamic properties of the black hole solution are also discussed. At the end, considering the Kerr/CFT correspondence is valid for our black hole solution, the central charge from the CFT of this extremal solution is derived.

Existence of realistic stellar objects in Rastall gravity with linear equation of state

In this paper, we have discussed the anisotropic matter configuration to explore the existence of realistic stellar objects in non-conservative theory named as Rastall theory of gravity. We have assumed a static spherically symmetric metric with linear equation of state (EoS) to formulate the dynamical equations. The Durgapal and Banerji transformation is employed to investigate the gravitational behavior of compact objects. In this regard, a particular gravitational potential is selected to solve the system of dynamical equations numerically. We compared change in behavior of physical quantities like energy density, anisotropy parameter, and radial and tangential pressures by plotting three particular cases. With the help of physical analysis, it can be seen that the solutions of compact spheres hold physical acceptability criteria and depict stability.

Strange stars with MIT bag model in the Rastall theory of gravity

The aim of this paper is to study the charged anisotropic strange stars in the Rastall framework. Basic formulation of field equations in this framework is presented in the presence of charged anisotropic source. To obtain the solutions of the Rastall field equations in spherically symmetric Karori and Barua (KB) type space-time, we have considered a linear equation of state of strange matter, using the MIT bag model. The constraints on the Rastall dimensionless parameter [Formula: see text] are also discussed to obtain the physically reasonable solution. We explore some physical features of the presented model like energy conditions, stability and hydrostatic equilibrium, which are necessary to check the physical viability of the model. We also sought for the influence of the Rastall dimensionless parameter on the behavior of the physical features of obtained solution. We plot the graphs of matter variables for different chosen values of the parameter [Formula: see text] to inspect more details of analytical investigations and predict the numerical values of these variables exhibited in the tabular form. For this analysis, we choose four different arbitrary models of strange stars with compactness [Formula: see text] 0.25, 0.30, 0.35 and 0.40. We observed that all the necessary physical conditions are satisfied and the presented model is quite reasonable to study the strange stars.

Models of anisotropic compact stars in the Rastall theory of gravity

In the present work, we have studied the anisotropic compact stars in the regime of Rastall theory using Karori and Barua $(\mathit{KB})$ type metric. For this investigation, we have considered three different known compact stars with anisotropic configuration namely, 4U 1820-30, Her X-1 and SAX J 1808.4-3658(SSI) with radii 10 km, 7.7 km and 7.07 km respectively. Formulation of field equations in this modified theory have also been presented. The unknown constants in KB metric have been obtained by using the matching of interior solution with the exterior vacuum solution. We investigate the various physical aspects of the presented model such as variation of energy density, energy conditions, hydrostatic equilibrium, stability, compactness and surface redshift. Graphical analysis of the variables involved in the obtained solution is also presented to observe their behavior more clearly. We also demonstrate the numerical values of some physical parameters in the tabular form by using the observational values of mass and radius. We also compute the numerical values of $\frac{2M}{R}$ using the presented model to check the Buchdahl limit for our system. The detailed analysis of matter variables revealed the regularity and stability of our proposed model.

A new model of quintessence compact stars in the Rastall theory of gravity

In the present work, we study a new model of anisotropic compact stars in the regime of Rastall theory. To solve the Rastall field equations we have used the Karori and Barua (KB) ansatz along with the quintessence dark energy characterized by a parameter $\omega_{q}$ with $-1<\omega_{q}<-\frac{1}{3}$. We present a comparative study to demonstrate the physical acceptance of our proposed model. We compare the numerical values of physical parameters obtained from our model with those of general relativity ($GR$) model given by Bhar \cite{1} and observe that our model is more compatible (for some chosen values of Rastall dimensionless parameter $\gamma=\kappa\lambda$) with observational data than $GR$ model. For this analysis we have consider four different compact stars, $SAX J1808-3658 (SSI)$, $4U 1820-30$, $Vela X-12$ and $PSR J1416-2230$ with radii $7.07km$, $10km$, $9.99km$ and $10.3km$, respectively. In this investigation we also present some physical aspects of the proposed model necessary to check the validity of the model and inferred that our model is acceptable physically and geometrically.

Thermodynamics of black holes in Rastall gravity

A promising theory in modifying general relativity (GR) by violating the ordinary energy–momentum conservation law in curved spacetime is the Rastall theory of gravity. In this theory, geometry and matter fields are coupled to each other in a nonminimal way. Here, we study thermodynamic properties of some black hole (BH) solutions in this framework, and compare our results with those of GR. We demonstrate how the presence of these matter sources amplifies the effects caused by the Rastall parameter in thermodynamic quantities. Our investigation also shows that BHs with radius smaller than a certain amount ([Formula: see text]) have negative heat capacity in the Rastall framework. In fact, it is a lower bound for the possible values of horizon radius satisfied by the stable BHs.