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

2021 ◽  
Vol 18 (03) ◽  
pp. 2150042
Author(s):  
G. Abbas ◽  
M. Tahir ◽  
M. R. Shahzad
Keyword(s):  
Gravitational Collapse ◽  
Mass Function ◽  
Energy Conditions ◽  
Parametric Form ◽  
Field Equations ◽  
Expansion Formula ◽  
Spherical Source ◽  
Expansion Scalar ◽  
Theory Of Gravity ◽  
Trapped Surface

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].

Expansion and collapse of spherical source with cosmological constant

2019 ◽  
Vol 34 (05) ◽  
pp. 1950042
Author(s):  
G. Abbas ◽  
Shahid Qaisar ◽  
Hamood Ur Rehman ◽  
M. Younas
Keyword(s):  
Cosmological Constant ◽  
Mass Function ◽  
Parametric Form ◽  
De Sitter ◽  
Field Equations ◽  
Spherical Source ◽  
Expansion Scalar ◽  
Radial Heat ◽  
Metric Functions ◽  
Metric Function

In this research paper, we address the issues of expansion and gravitational collapse of anisotropic spherical source in the presence of cosmological constant. For this purpose, we have solved the Einstein field equations with gravitating source and cosmological constant. The absence of radial heat flux in the gravitating source provide the parametric form of two-metric functions in terms of a single-metric function. The expansion scalar and the mass function of the gravitating source is evaluated for the given metric. The trapping condition is applied to mass function which implies the existence of horizons, like the horizons of Schwarzschild de-Sitter black holes. The trapping condition provides the parametric form of the unknown metric function. The value of expansion scalar has been analyzed in detail to see its positivity and negativity, which correspond to expansion and collapse, respectively. So, the values of parameter [Formula: see text] for which expansion scalar is positive have been used to analyze the other physical variables including density, pressures and anisotropy. The same quantities have been evaluated for the values of [Formula: see text] that result in the negative values of expansion scalar leading to collapse. The effects of positive cosmological constant have been noted in both expansion and collapse solutions. Due to the presence of cosmological constant after collapse, there would occur inner and outer horizons or a unique horizon depending on the value of mass of the gravitating source.

Models of charged self-gravitating source in f(R,T) theory

2018 ◽  
Vol 27 (16) ◽  
pp. 1950005 ◽  
Author(s):  
M. Sharif ◽  
Aisha Siddiqa
Keyword(s):  
Momentum Tensor ◽  
Energy Conditions ◽  
Radial Coordinate ◽  
Physical Parameters ◽  
Field Equations ◽  
Expansion Formula ◽  
Anisotropic Parameter ◽  
Spherical Source ◽  
Model Parameter ◽  
Theory Formula

We discuss the anisotropic nonstatic charged spherical source describing the phenomena of collapse and expansion in the context of [Formula: see text] theory ([Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor). The Einstein–Maxwell field equations are formulated and an auxiliary solution is considered. We evaluate the corresponding expansion scalar [Formula: see text] and investigate the cases of collapse [Formula: see text] and expansion ([Formula: see text]). In both cases, we explore the influence of charge as well as model parameter on density, radial/tangential pressure, anisotropic parameter and mass through graphs. It is observed that the physical parameters vary with time for expansion while remain constant for collapse. However, the change with respect to the radial coordinate is the same for both cases. The model parameter has the same impact in both cases while charge affects only in the case of collapse. The energy conditions are satisfied for both solutions with particular values of the parameters.

scholarly journals Models of Anisotropic Self-Gravitating Source in Einstein-Gauss-Bonnet Gravity

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
G. Abbas ◽  
M. Tahir
Keyword(s):  
Surface Condition ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Field Equations ◽  
Spherical Source ◽  
Bonnet Gravity ◽  
Trapped Surface ◽  
Metric Functions ◽  
Definition Of ◽  
Metric Function

In this paper, we have studied gravitational collapse and expansion of nonstatic anisotropic fluid in 5D Einstein-Gauss-Bonnet gravity. For this purpose, the field equations have been modeled and evaluated for the given source and geometry. The two metric functions have been expressed in terms of parametric form of third metric function. We have examined the range of parameter β (appearing in the form of metric functions) for which Θ, the expansion scalar, becoming positive/negative leads to expansion/collapse of the source. The trapped surface condition has been explored by using definition of Misner-Sharp mass and auxiliary solutions. The auxiliary solutions of the field equations involve a single function that generates two types of anisotropic solutions. Each solution can be represented in term of arbitrary function of time; this function has been chosen arbitrarily to fit the different astrophysical time profiles. The existing solutions forecast gravitational expansion and collapse depending on the choice of initial data. In this case, wall to wall collapse of spherical source has been investigated. The dynamics of the spherical source have been observed graphically with the effects of Gauss-Bonnet coupling term α in the case of collapse and expansion. The energy conditions are satisfied for the specific values of parameters in both solutions; this implies that the solutions are physically acceptable.

Anisotropic compact stars model with generalized Bardeen–Hayward mass function

2021 ◽  
Vol 36 (26) ◽  
pp. 2150190
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Ksh. Newton Singh
Keyword(s):  
Surface Density ◽  
Mass Function ◽  
Static Stability ◽  
Compact Stars ◽  
Energy Conditions ◽  
Causality Condition ◽  
Field Equations ◽  
Regular Black Hole ◽  
Bag Constant ◽  
Tov Equation

A new compact stars nonsingular model is presented with the generalized Bardeen–Hayward mass function. Generalized Bardeen–Hayward described the regular black hole, however, due to its regularity or nonsingular nature we were inspired to construct an anisotropic compact stars model. Along with the ansatz mass function, we coupled it with a linear equation of state (EoS) to find the solutions of field equations. Indeed, the new solutions are physically viable in all physical ground. The energy conditions and Tolman–Oppenheimer–Volkoff (TOV)-equation are well satisfied signifying that the mass distribution is physically possible and at equilibrium. Also, the static stability criterion, the causality condition and Abreu’s stability condition hold good and therefore configurations are physically static stable. The same condition is further supported by the condition that the adiabatic index, which is greater than the Newtonian limit, i.e. [Formula: see text]. It is also noticed that the bag constant [Formula: see text] is proportional to the surface density in our model.

scholarly journals A new class of relativistic model of compact stars of embedding class I

2017 ◽  
Vol 26 (09) ◽  
pp. 1750090 ◽  
Author(s):  
Piyali Bhar ◽  
Ksh. Newton Singh ◽  
Tuhina Manna
Keyword(s):  
Compact Star ◽  
Mass Function ◽  
Static Stability ◽  
Compact Stars ◽  
Stable Region ◽  
Energy Conditions ◽  
Arbitrary Form ◽  
Star Model ◽  
Field Equations ◽  
Anisotropic Matter

In the present paper, we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function [Formula: see text] and solved the Einstein’s relativistic field equations with the help of Karmarkar condition for an anisotropic matter distribution. The physical properties of our model such as pressure, density, mass function, surface red-shift, gravitational redshift are investigated and the stability of the stellar configuration is discussed in details. Our model is free from central singularities and satisfies all energy conditions. The model we present here satisfy the static stability criterion, i.e. [Formula: see text] for [Formula: see text][Formula: see text]g/cm3(stable region) and for [Formula: see text][Formula: see text]g/cm3, the region is unstable i.e. [Formula: see text].

scholarly journals Charged wormholes in f(R,T)-extended theory of gravity

2019 ◽  
Vol 28 (08) ◽  
pp. 1950098 ◽  
Author(s):  
P. H. R. S. Moraes ◽  
W. de Paula ◽  
R. A. C. Correa
Keyword(s):  
Degrees Of Freedom ◽  
Matter Content ◽  
Nonlinear Electrodynamics ◽  
Energy Conditions ◽  
Field Equations ◽  
Extended Theory ◽  
Extended Theories Of Gravity ◽  
Theories Of Gravity ◽  
Theory Of Gravity ◽  
Physical Quantities

Wormholes (WHs) are a solution for General Relativity field equations which characterize a passage or tunnel that connects two different regions of spacetime and is filled by some sort of exotic matter that does not satisfy the energy conditions. On the other hand, it is known that in extended theories of gravity, the extra degrees of freedom once provided may allow the energy conditions to be obeyed and, consequently, the matter content of the WH to be nonexotic. In this work, we obtain, as a novelty in the literature, solutions for charged WHs in the [Formula: see text]-extended theory of gravity. We show that the presence of charge in these objects may be a possibility to respect some stability conditions for their metric. Also, remarkably, the energy conditions are respected in the present approach. In addition, we argue that our framework can be very useful to study the possibility of evolving [Formula: see text] and [Formula: see text]-dimensional WH spacetime within the context of nonlinear electrodynamics, which open a new window to probe the physical quantities in a WH-type solution.

Tolman mass of spherical fluids with electromagnetic field

2019 ◽  
Vol 34 (02) ◽  
pp. 1950012 ◽  
Author(s):  
M. Z. Bhatti ◽  
Z. Yousaf ◽  
A. Yousaf
Keyword(s):  
Gravitational Collapse ◽  
Mass Function ◽  
Physical Factors ◽  
Field Equations ◽  
Density Inhomogeneity ◽  
Local Anisotropy ◽  
Anisotropic Matter ◽  
Weyl Curvature Tensor ◽  
The Impact

Assuming a system with spherical symmetry in f(R) gravity filled with dissipative charged and anisotropic matter, we study the impact of density inhomogeneity and local anisotropy on the gravitational collapse in the presence of charge. For this purpose, we evaluated the modified Maxwell field equations, Weyl curvature tensor, and the mass function. Using Misner–Sharp mass formalism, we construct a relation between the Weyl tensor, density inhomogeneity, and local anisotropy. Specifically, we obtain the expression of modified Tolman mass which helps to analyze the influence of charge and dark source terms on different physical factors, also it helps to study the role of these factors on gravitational collapse.

GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

2003 ◽  
Vol 12 (07) ◽  
pp. 1315-1332 ◽  
Author(s):  
C. F. C. BRANDT ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA ◽  
R. CHAN
Keyword(s):  
Physical Properties ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Tangential Pressure

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

scholarly journals Embedding with Vaidya geometry

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
A. V. Nikolaev ◽  
S. D. Maharaj
Keyword(s):  
Equation Of State ◽  
Euclidean Space ◽  
Mass Function ◽  
Energy Conditions ◽  
Dimensional Euclidean Space ◽  
De Sitter ◽  
Radiating Star ◽  
Theory Of Gravity ◽  
Null String ◽  
Vaidya Metric

Abstract The Vaidya metric is important in describing the exterior spacetime of a radiating star and for describing astrophysical processes. In this paper we study embedding properties of the generalized Vaidya metric. We had obtained embedding conditions, for embedding into 5-dimensional Euclidean space, by two different methods and solved them in general. As a result we found the form of the mass function which generates a subclass of the generalized Vaidya metric. Our result is purely geometrical and may be applied to any theory of gravity. When we apply Einstein’s equations we find that the embedding generates an equation of state relating the null string density to the null string pressure. The energy conditions lead to particular metrics including the anti/de Sitter spacetimes.

Non-adiabatic gravitational collapse in f(R,T) gravity with Karmarkar condition for anisotropic fluid

2020 ◽  
Vol 35 (13) ◽  
pp. 2050103 ◽  
Author(s):  
Riaz Ahmed ◽  
G. Abbas
Keyword(s):  
Gravitational Collapse ◽  
Coupling Parameter ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Interior Solution ◽  
Spatial Presence ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Radiating Star

In this paper, we have used the Karmarkar condition to the spherically symmetric non-static radiating star experiencing dissipative gravitational collapse with a heat flux in the framework of [Formula: see text] gravity, (where [Formula: see text] is Ricci scalar which replaces Lagrangian density and [Formula: see text] is the trace of energy–momentum tensor). To obtain the ultimate results of the gravitational field equations in [Formula: see text] scenario, we take a linear form of the function as [Formula: see text]. In this connection, the Karmarkar condition along with boundary condition generates a model of radiating star and enables us to completely indicate the spatial presence of gravitational potentials. Vadiya’s exterior solution across a time-like hypersurface is smoothly matched to the interior solution which allows to study the physical conduct of our model under consideration. Furthermore, we have analyzed the energy conditions of radiating star in [Formula: see text] gravity and analyzed the physical behavior of thermodynamics parameters which provide a detailed discussion of the model. For coupling parameter [Formula: see text], we successfully obtain the standard results of General Relativity.

Sign in / Sign up

Export Citation Format

Share Document