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 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].

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.

Cosmological constant Λ in f(R,T) modified gravity

2016 ◽  
Vol 13 (05) ◽  
pp. 1650058 ◽  
Author(s):  
Gyan Prakash Singh ◽  
Binaya Kumar Bishi ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Modified Gravity ◽  
Bianchi Type ◽  
Field Equations ◽  
Type Iii ◽  
Expansion Scalar ◽  
Modified Theory Of Gravity ◽  
Shear Scalar ◽  
Modified Theory

In this paper, we have studied the Bianchi type-III cosmological model in the presence of cosmological constant in the context of [Formula: see text] modified theory of gravity. Here, we have discussed two classes of [Formula: see text] gravity, i.e. [Formula: see text] and [Formula: see text]. In both classes, the modified field equations are solved by the relation expansion scalar [Formula: see text] that is proportional to shear scalar [Formula: see text] which gives [Formula: see text], where [Formula: see text] and [Formula: see text] are metric potentials. Also we have discussed some physical and kinematical properties of the models.

scholarly journals Comparative Analysis of Standard ΛCDM and ΛCS Models

2021 ◽  
Vol 57 (11) ◽  
pp. 1169
Author(s):  
V.E. Kuzmichev ◽  
V.V. Kuzmichev
Keyword(s):  
Cosmological Constant ◽  
Semiclassical Approximation ◽  
Cosmic Strings ◽  
Cosmological Parameters ◽  
Einstein Equations ◽  
Scale Transformation ◽  
De Sitter ◽  
Field Equations ◽  
Low Velocity ◽  
Sitter Model

We draw a comparison of time-dependent cosmological parameters calculated in the standard ΛCDM model with those of the model of a homogeneous and isotropic Universe with non-zero cosmological constant filled with a perfect gas of low-velocity cosmic strings (ΛCS model). It is shown that pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch, when the global geometry and the total amount of matter in the Universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the time evolution of the equation of state of matter caused by the processes of redistribution of the energy between matter components. In the present article, the exact solutions of the Einstein equations for the ΛCS model are found. It is demonstrated that this model is equivalent to the open de Sitter model. After the scale transformation of the time variable of the ΛCS model, the standard ΛCDM and ΛCS models provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early Universe.

Embedded class solutions of an anisotropic object in Rastall gravity

2020 ◽  
Vol 35 (21) ◽  
pp. 2050109
Author(s):  
G. Mustafa ◽  
Tie-Cheng Xia
Keyword(s):  
Current Model ◽  
Compact Model ◽  
Physical Parameters ◽  
Equilibrium Stability ◽  
Field Equations ◽  
Energy Bounds ◽  
Extended Field ◽  
Metric Functions ◽  
Metric Function ◽  
Tov Equation

In this current work, we explore an anisotropic compact model with radius 9.1 km and mass 2.01 [Formula: see text] in the regime of Karmarkar condition in Rastall theory. To solve the extended field equations for the Rastall framework we have employed the Karmarkar condition. We investigate a comparative discussion to show the physical acceptance of Karmarkar condition in Rastall theory. Our obtained solutions, i.e. metric functions, density function and both the pressure components have well-behaved nature. The energy bounds and the equilibrium stability in the background of modified TOV equation (for Rastall proposal) are also discussed in this study. The parameter [Formula: see text] from [Formula: see text] metric function has some important role in this current model. All the calculated properties have different natures for [Formula: see text] to [Formula: see text]. In this current study we also discuss some physical parameters of this current model to check the validity of the model. In the end, it is concluded that our model is acceptable physically and geometrically.

scholarly journals Null hypersurfaces in de Sitter and anti-de Sitter cosmologies

2018 ◽  
Vol 27 (04) ◽  
pp. 1850045
Author(s):  
P. A. Hogan
Keyword(s):  
Cosmological Constant ◽  
Gravitational Waves ◽  
Constant Curvature ◽  
Focus Attention ◽  
De Sitter ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Null Hypersurfaces ◽  
Einstein's Field Equations ◽  
Line Elements

The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in spacetimes of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision spacetime is a solution of Einstein’s field equations with a cosmological constant, and the second originated in the generalization of plane fronted gravitational waves with parallel rays to include a cosmological constant.

scholarly journals A RELATIVISTIC DESCRIPTION OF GENTRY'S NEW REDSHIFT INTERPRETATION

1999 ◽  
Vol 14 (12) ◽  
pp. 779-790
Author(s):  
T. SHIMIZU ◽  
K. WATANABE
Keyword(s):  
Mass Function ◽  
Space Time ◽  
Model Parameters ◽  
De Sitter ◽  
Coordinate Origin ◽  
Walker Metric ◽  
New Interpretation ◽  
Metric Function ◽  
Static Form ◽  
Friedmann Robertson Walker

We obtain a new expression of the Friedmann–Robertson–Walker metric, which is an analogue of a static chart of the de Sitter space–time. The reduced metric contains two functions, M(T, R) and Ψ(T, R), which are interpreted as, respectively, the mass function and the gravitational potential. We find that, near the coordinate origin, the reduced metric can be approximated in a static form and that the approximated metric function, Ψ(R) satisfies the Poisson equation. Moreover, when the model parameters of the Friedmann–Robertson–Walker metric are suitably chosen, the approximated metric coincides with exact solutions of the Einstein equation with the perfect fluid matter. We then solve the radial geodesics on the approximated space–time to obtain the distance-redshift relation of geodesic sources observed by the comoving observer at the origin. We find that the redshift is expressed in terms of a peculiar velocity of the source and the metric function, Ψ(R), evaluated at the source position, and one may think that this is a new interpretation of Gentry's new redshift interpretation.

scholarly journals Extension Rules of Newman–Janis Algorithm for Rotation Metrics in General Relativity

2020 ◽  
pp. 1-14
Author(s):  
Yu-Ching, Chou
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Kerr Metric ◽  
Tensor Structure ◽  
De Sitter ◽  
Field Equations ◽  
Null Tetrad ◽  
Axisymmetric Solutions ◽  
Metric Function ◽  
De Sitter Metric

Aims: The aim of this study is to extend the formula of Newman–Janis algorithm (NJA) and introduce the rules of the complexifying seed metric. The extension of NJA can help determine more generalized axisymmetric solutions in general relativity.Methodology: We perform the extended NJA in two parts: the tensor structure and the seed metric function. Regarding the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically equivalent; however, the latter is more concise. Regarding the seed metric function, we propose the extended rules of a complex transformation by r2/Σ and combine the mass, charge, and cosmologic constant into a polynomial function of r. Results: We obtain a family of axisymmetric exact solutions to Einstein’s field equations, including the Kerr metric, Kerr–Newman metric, rotating–de Sitter, rotating Hayward metric, Kerr–de Sitter metric and Kerr–Newman–de Sitter metric. All the above solutions are embedded in ellipsoid- symmetric spacetime, and the energy-momentum tensors of all the above metrics satisfy the energy conservation equations. Conclusion: The extension rules of the NJA in this research avoid ambiguity during complexifying the transformation and successfully generate a family of axisymmetric exact solutions to Einsteins field equations in general relativity, which deserves further study.

scholarly journals Quasi-normal modes and stability of Einstein–Born–Infeld black holes in de Sitter space

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Chong Oh Lee ◽  
Jin Young Kim ◽  
Mu-In Park
Keyword(s):  
Black Holes ◽  
Cosmological Constant ◽  
Normal Modes ◽  
Extremal Black Hole ◽  
Wkb Method ◽  
De Sitter ◽  
Charged Black Holes ◽  
Resonance Modes ◽  
Metric Functions ◽  
The Stability

Abstract We study gravitational perturbations of electrically charged black holes in (3+1)-dimensional Einstein–Born–Infeld gravity with a positive cosmological constant. For the axial perturbations, we obtain a set of decoupled Schrödinger-type equations, whose formal expressions, in terms of metric functions, are the same as those without cosmological constant, corresponding to the Regge–Wheeler equation in the proper limit. We compute the quasi-normal modes (QNMs) of the decoupled perturbations using the Schutz–Iyer–Will’s WKB method. We discuss the stability of the charged black holes by investigating the dependence of quasi-normal frequencies on the parameters of the theory, correcting some errors in the literature. It is found that all the axial perturbations are stable for the cases where the WKB method applies. There are cases where the conventional WKB method does not apply, like the three-turning-points problem, so that a more generalized formalism is necessary for studying their QNMs and stabilities. We find that, for the degenerate horizons with the “point-like” horizons at the origin, the QNMs are quite long-lived, close to the quasi-resonance modes, in addition to the “frozen” QNMs for the Nariai-type horizons and the usual (short-lived) QNMs for the extremal black hole horizons. This is a genuine effect of the branch which does not have the general relativity limit. We also study the exact solution near the (charged) Nariai limit and find good agreements even far beyond the limit for the imaginary frequency parts.

scholarly journals Collapse and expansion of plane symmetric charged anisotropic source

2017 ◽  
Vol 95 (2) ◽  
pp. 114-118 ◽  
Author(s):  
G. Abbas ◽  
S.M. Shah ◽  
M. Zubair
Keyword(s):  
Apparent Horizon ◽  
Field Equations ◽  
Plane Symmetric ◽  
Radial Heat ◽  
Symmetric Source ◽  
New Form ◽  
Metric Functions ◽  
Static Plane ◽  
Radial Heat Flux ◽  
Anisotropic Source

In this paper, we have investigated the final evolutionary stages of charged non-static plane symmetric anisotropic source. To this end, we have solved the Einstein–Maxwell field equations with the charged plane symmetric source. We have found that vanishing of radial heat flux in the gravitating source provides the parametric form of the metric functions. The new form of the metric functions can generate a class of physically acceptable solutions depending on the choice parameter. These solutions may be classified as expanding or collapsing solutions with the particular values of generating parameter. The gravitational collapse in this case ends with the formation of single apparent horizon while there exists two such horizons in the case of charged spherical anisotropic source.

Sign in / Sign up

Export Citation Format

Share Document