Rastall Theory Research Articles

Combined Rastall and rainbow theories of gravity with applications to neutron stars

The possibility of modifications on general relativity is investigated. We propose an alternative theory of gravity constructed with the combination of Rastall and Rainbow theories. The hydrostatic equilibrium equations are obtained in order to test the new theory in neutron stars, whose mass-radius diagrams are obtained using modern equations of state of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff equations. We conclude that substantial modifications are obtained even for very small alterations on the two free parameters, making the reproduction of astrophysical observations an easy task.

Neutral regular black hole solution in generalized Rastall gravity * * Supported by the National Natural Science Foundation of China (NNSFC) (11805166), as well as Brazilian funding agencies Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

We investigate the static, spherically symmetric regular black hole solutions in the generalized Rastall gravity. In particular, the prescription of Rastall gravity implies that the present approach does not necessarily involve nonlinear electrodynamics. Subsequently, the resulting regular black hole solutions can be electrically and magnetically neutral. The general properties of the regular black hole solutions are explored. Moreover, specific solutions are derived and discussed, particularly regarding the parameter related to the degree of violation of the energy-momentum conservation in the Rastall theory.

Higher dimensional power-Maxwell charged black holes in Einstein and Rastall gravity

The black hole solutions in higher-dimensional spacetimes with the presence of the power-Maxwell field, surrounded by quintessence, are investigated for Einstein as well as Rastall gravity. The obtained solutions accommodate for spherical, planar and hyperbolic symmetries with the presence of the cosmological constant. Besides, we show that several known black hole solutions in literature such as those for linear Maxwell theory and BTZ black hole can be obtained as special cases. The implications of Rastall's theory related to the present study and the thermodynamics of the black hole solutions are discussed.

4-Index theory of gravity and its relation with the violation of the energy–momentum conservation law

Recently, a 4-index generalization of the Einstein theory has been proposed by Moulin [F. Moulin, Eur. Phys. J. C 77, 878 (2017)]. Using this method, we find the most general 2-index field equations derivable from the Einstein–Hilbert action. The application of Newtonian limit, the role of gravitational coupling constant and the effects of the properties of ordinary energy–momentum tensor in obtaining a 4-index gravity theory have been studied. We also address the results of building Weyl free 4-index gravity theory. Our study displays that both the Einstein and Rastall theories can be obtained as the subclasses of a 4-index gravity theory which shows the power of 4-index method in unifying various gravitational theories. It is also obtained that the violation of the energy–momentum conservation law may be allowed in 4-index gravity theory, and moreover, the contraction of 4-index theory generally admits a non-minimal coupling between geometry and matter field in the Rastall way. This study also shows that, unlike the Einstein case, the gravitational coupling constant of 4-index Rastall theory generally differs from that of the ordinary 2-index Rastall theory.

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.

Impact of the Rastall parameter on perfect fluid spheres

We examine the effects of the Rastall parameter on the behaviour of spherically symmetric static distributions of perfect fluid matter. It was claimed by Visser [Physics Letters B, 782, 83, (2018)] that the Rastall proposition is completely equivalent to the Einstein theory. While many authors have raised contrary arguments, our intention is to analyse the properties of Rastall gravity through variation of the Rastall parameter in the context of perfect fluids spheres that may be used to model neutron stars or cold fluid planets. This analysis also serves to counter the claim that Rastall gravity is equivalent to the standard Einstein theory. It turns out that the condition of pressure isotropy is exactly the same as for Einstein gravity and hence that any known solution of the Einstein equations may be used to study the effects of the Rastall dynamical quantities. Moreover, by choosing the well studied Tolman metrics, we discover that in the majority of cases there is substantial deviation from the Einstein case when the Rastall parameter vanishes and in cases where the Einstein model displays defective behaviour, certain Rastall models obey the well known elementary requirements for physical plausibility. These empirical findings do not support the idea that Rastall theory is equivalent to Einstein theory as several deviations in physical behaviour are displayed as counter-examples.

Black brane solution in Rastall AdS massive gravity and viscosity bound

In this paper, we introduced the black brane solution in Rastall theory and in the context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. Our result shows that the KSS bound violates this theory.

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 in Rastall gravity with entropy corrections

We explore the thermodynamic analysis at the apparent horizon in the framework of Rastall theory of gravity. We take different entropies such as the Bakenstein, logarithmic corrected, power law corrected, and the Renyi entropies. We investigate the first law and generalized second law of thermodynamics analytically for these entropies which hold under certain conditions. Furthermore, the behavior of the total entropy in each case is analyzed. As a result, it is implied that the generalized second law of thermodynamics is satisfied. We also check whether the thermodynamic equilibrium condition for these entropies is met at the present horizon.

Isotropic compact stars model in Rastall theory admitting conformal motion

We study a new solution for an isotropic compact star model admitting conformal motion in the background of Rastall theory. The conformal Killing vector (\(\mathit{CKV}\)) and the equation of state (EoS) \(p=\omega \rho \), where \(\omega \) satisfying \(0<\omega <1\) is the \(\mathit{EoS}\) parameter for normal matter distribution, are the main ingredients of our methodology. Several physical aspects of the model has been explored analytically to observe the behavior of compact stars such as \(\mathit{TOV}\) equation, energy conditions, Buchdahl condition, stability analysis, compactness and surface redshift. Graphical analysis of the physical parameters have also been presented to support our analytical investigation. We observed that all the physical requirements are fulfilled and the presented model is quite acceptable.

Cosmological consequences in the framework of generalized Rastall theory of gravity

The paper deals with generalized Rastall theory of gravity and its cosmological consequences in the background of homogeneous and isotropic flat FLRW model with perfect fluid as the matter context. The model shows a non singular era (emergent scenario) at the early phase of expansion for a particular choice of the Rastall parameter. Also the model finds to be equivalent to the particle creation mechanism in Einstein gravity in the framework of non-equilibrium thermodynamics. Universal thermodynamics is briefly presented and it is found that the entropy function in Rastall theory is the usual Bekenstein entropy and there is no correction to it. Finally, a complete cosmic history starting from inflation to late time acceleration is presented for suitable choices of the Rastall parameter.

Rotating black hole in Rastall theory

Rotating black hole solutions in theories of modified gravity are important as they offer an arena to test these theories through astrophysical observation. The non-rotating black hole can be hardly tested since the black hole spin is very important in any astrophysical process. We present rotating counterpart of a recently obtained spherically symmetric exact black hole solution surrounded by perfect fluid in the context of Rastall theory, viz, rotating Rastall black hole that generalize the Kerr–Newman black hole solution. In turn, we analyze the specific cases of the Kerr–Newman black holes surrounded by matter like dust and quintessence fields. Interestingly, for a set of parameters and a chosen surrounding field, there exists a critical rotation parameter (a=a_{E}), which corresponds to an extremal black hole with degenerate horizons, while for a<a_{E}, it describes a non-extremal black hole with Cauchy and event horizons, and no black hole for a>a_{E} with value a_E is also influenced by these parameters. We also discuss the thermodynamical quantities associated with rotating Rastall black hole, and analyze the particle motion with the behavior of effective potential.

Tunneling Glashow-Weinberg-Salam Model Particles from Black Hole Solutions in Rastall Theory

Using the semiclassical WKB approximation and Hamilton-Jacobi method, we solve an equation of motion for the Glashow-Weinberg-Salam model, which is important for understanding the unified gauge-theory of weak and electromagnetic interactions. We calculate the tunneling rate of the massive charged W-bosons in a background of electromagnetic field to investigate the Hawking temperature of black holes surrounded by perfect fluid in Rastall theory. Then, we study the quantum gravity effects on the generalized Proca equation with generalized uncertainty principle (GUP) on this background. We show that quantum gravity effects leave the remnants on the Hawking temperature and the Hawking radiation becomes nonthermal.

Einstein static universe in the Rastall theory of gravity

We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy originating from conformally-invariant fields is stable. Using the fix point method and taking linear homogeneous perturbations, we find that the scale factor of Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the coupling parameter $\lambda$ between the energy-momentum tensor and the gradient of Ricci scalar. Thus, in the present model and in presence of vacuum energy, our universe can stay at the Einstein static state past-eternally, which means that the big bang singularity may be resolved successfully in the context of Einstein static universe in Rastall theory.

Anisotropic compact stars in non-conservative theory of gravity

We develop anisotropic compact stars in the scenario of non-conservative theory such as Rastall theory. We consider the Krori and Barua static spherically symmetric metrics and find their unknown constants by using the masses and radii of well-known compact stars. We investigate the anisotropic compact star through various physical quantities such as anisotropic behavior, regularity conditions, stability and surface redshift. It is found that the present compact stars are stable and are in the stellar equilibrium form.

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.

Traversable asymptotically flat wormholes in Rastall gravity

There are some gravitational theories in which the ordinary energy–momentum conservation law is not valid in the curved space–time. Rastall gravity is one of the known theories in this regard, which includes a non-minimal coupling between geometry and matter fields. Equipped with the basis of such theory, we study the properties of traversable wormholes with flat asymptotes. We investigate the possibility of exact solutions by a source with the baryonic matter state parameter. Our survey indicates that Rastall theory has considerable effects on the wormhole characteristics. In addition, we study various case studies and show that the weak energy condition may be met for some solutions. We also give a discussion regarding traversibility of such wormhole geometry with phantom sources.

The commutator algebra of covariant derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion

In this short review, we discuss the approach of the commutator algebra of covariant derivative to analyze the gravitational theories, starting from the standard Einstein's general theory of relativity (GTR) and focusing on the Rastall theory. After that, we discuss the important role of the torsion in this mathematical framework.In the appendix of the paper, we analyze the importance of the nascent gravitational wave (GW) astronomy as a tool to discriminate among the GTR and alternative theories of gravity.

Black hole solutions surrounded by perfect fluid in Rastall theory

In this work, we obtain uncharged∖charged Kiselev-like black holes as a new class of black hole solutions surrounded by perfect fluid in the context of Rastall theory. Then, we study the specific cases of the uncharged∖charged black holes surrounded by regular matter like dust and radiation, or exotic matter like quintessence, cosmological constant and phantom fields. By comparing the Kiselev-like black hole solutions in Rastall theory with the Kiselev black hole solutions in GR, we find an effective perfect fluid behavior for the black hole's surrounding field. It is shown that the corresponding effective perfect fluid has interesting characteristic features depending on the different ranges of the parameters in Rastall theory. For instance, Kiselev-like black holes surrounded by regular matter in Rastall theory may be considered as Kiselev black holes surrounded by exotic matter in GR, or Kiselev-like black holes surrounded by exotic matter in Rastall theory may be considered as Kiselev black holes surrounded by regular matter in GR.

A generalization to the Rastall theory and cosmic eras

A generalized version for the Rastall theory is proposed showing the agreement with the cosmic accelerating expansion. In this regard, a coupling between geometry and the pressureless matter fields is derived which may play the role of dark energy, responsible for the current accelerating expansion phase. Moreover, our study also shows that the radiation field may not be coupled to the geometry in a non-minimal way which represents that the ordinary energy-momentum conservation law is respected by the radiation source. It is also shown that the primary inflationary era may be justified by the ability of the geometry to couple to the energy-momentum source in an empty flat FRW universe. In fact, this ability is independent of the existence of the energy-momentum source and may compel the empty flat FRW universe to expand exponentially. Finally, we consider a flat FRW universe field by a spatially homogeneous scalar field evolving in potential mathcal {V}(phi ), and study the results of applying the slow-roll approximation to the system which may lead to an inflationary phase for the universe expansion.