Possible Einstein’s cluster models in embedding class one spacetime

2021 ◽  
pp. 2150106
Author(s):  
Ksh. Newton Singh ◽  
Farook Rahaman ◽  
Modhuchandra Laishram ◽  
Rakesh Sharma
Keyword(s):  
Cluster Model ◽  
State Parameter ◽  
Static Stability ◽  
Compact Stars ◽  
Energy Conditions ◽  
Cluster Solution ◽  
Matter Distribution ◽  
Embedding Class One ◽  
First Time ◽  
Tov Equation

For the first time, we present Einstein’s cluster model in embedding class one spacetime. This paper shows that for any neutral configurations there is only one Einstein cluster solution in embedding class one. In fact, one can find two solutions where the first solution i.e. [Formula: see text] and [Formula: see text] is an unphysical one as it has zero density profile as well as violates the Pandey–Sharma condition (i.e. not a class one solution). However, the second solution can describe matter distribution representing Einstein’s cluster which is in static and equilibrium as it satisfies the static stability criterion and TOV-equation. The second solution not only satisfies the above conditions, but also satisfies the energy conditions. The equation of state parameter [Formula: see text] is less than unity signifying that it can represent physical matters. Further, we have also shown that the Einstein’s clusters may also exhibit the properties of compact stars.

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 Conformally symmetric relativistic star

2017 ◽  
Vol 32 (08) ◽  
pp. 1750053 ◽  
Author(s):  
Farook Rahaman ◽  
Sunil D. Maharaj ◽  
Iftikar Hossain Sardar ◽  
Koushik Chakraborty
Keyword(s):  
Conformal Symmetry ◽  
Compact Object ◽  
Radial Pressure ◽  
Compact Stars ◽  
Energy Conditions ◽  
Anisotropic Pressure ◽  
Matter Distribution ◽  
Strong Energy ◽  
Principal Directions ◽  
The Masses

We investigate whether compact stars having Tolman-like interior geometry admit conformal symmetry. Taking anisotropic pressure along the two principal directions within the compact object, we obtain physically relevant quantities such as transverse and radial pressure, density and redshift function. We study the equation of state (EOS) for the matter distribution inside the star. From the relation between pressure and density function of the constituent matter, we explore the nature and properties of the interior matter. The redshift function and compactness parameter are found to be physically reasonable. The matter inside the star satisfies the null, weak and strong energy conditions. Finally, we compare the masses and radii predicted from the model with corresponding values in some observed stars.

A study of anisotropic compact stars based on embedding class 1 condition

2019 ◽  
Vol 28 (09) ◽  
pp. 1950116 ◽  
Author(s):  
S. K. Maurya ◽  
Debabrata Deb ◽  
Saibal Ray ◽  
P. K. F. Kuhfittig
Keyword(s):  
Stellar Model ◽  
Einstein Equations ◽  
Compact Stars ◽  
Energy Conditions ◽  
Physical Parameters ◽  
Matter Distribution ◽  
Generalized Model ◽  
Anisotropic Factor ◽  
Class 1 ◽  
Metric Functions

This paper discusses a generalized model for compact stars, assumed to be anisotropic in nature due to the presence of highly dense and ultra-relativistic matter distribution. After embedding the 4D Riemannian space locally and isometrically into a 5D pseudo-Euclidean space, we solve the Einstein equations by employing a class of physically acceptable metric functions. The physical properties determined include the anisotropic factor showing that the anisotropy is zero at the center and maximum at the surface. Other boundary conditions yield the values of various parameters needed for rendering the numerous plots and also led to the EOS parameters. It is further determined that the usual energy conditions are satisfied and that the compact structures are stable, based on several criteria, viz., the equilibrium of forces, Herrera cracking concept, adiabatic index, etc. We note that the proposed stellar model satisfies the Buchdahl condition. Finally, the values of the numerous constants and physical parameters are determined, specifically for the compact stellar object [Formula: see text], which we choose as a representative of the compact stars to present the analysis of the obtained results. Finally, we show that the present generalized model can justify most of the compact stars including white dwarfs and ultra-dense compact stars for a suitable tuning of the parametric values of [Formula: see text].

Relativistic modeling of stellar objects using embedded class one spacetime continuum

2020 ◽  
Vol 35 (13) ◽  
pp. 2050097 ◽  
Author(s):  
Satyanarayana Gedela ◽  
Ravindra K. Bisht ◽  
Neeraj Pant
Keyword(s):  
Generalized Solution ◽  
Compact Stars ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Positive Real ◽  
Stellar Objects ◽  
Embedding Class One ◽  
Pressure Anisotropy ◽  
Static Criterion

In this paper, we explore a family of exact solutions to the Einstein field equations (EFEs) describing a spherically symmetric, static distribution of fluid spheres with pressure anisotropy in the setting of embedding class one spacetime continuum. A detailed theoretical analysis of this class of solutions for compact stars PSR J16142230, Her X-1, LMC X-4 and 4U 1538-52 is carried out. The solutions are verified by examining various physical aspects, viz., anisotropy, gravitational redshift, causality condition, equilibrium (TOV-equation), stable static criterion and energy conditions, in connection to their cogency. Due to the well-behaved nature of the solutions for a large range of positive real [Formula: see text] values, we develop models of above stellar objects and discuss their behavior with graphical representations of the class of solutions of the first two objects extensively. The solutions studied by Fuloria [Astrophys. Space Sci. 362, 217 (2017)] for [Formula: see text] and Tamta and Fuloria [Mod. Phys. Lett. A 34, 2050001 (2019), https://doi.org/10.1142/S0217732320500017 ] for [Formula: see text] are particular cases of our generalized solution.

scholarly journals Anisotropic compact stars via embedding approach in general relativity: new physical insights of stellar configurations

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Abdelghani Errehymy ◽  
Youssef Khedif ◽  
Mohammed Daoud
Keyword(s):  
General Relativity ◽  
Space Time ◽  
Compact Stars ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Interior Space ◽  
Exterior Space ◽  
New Family ◽  
Embedding Class One ◽  
Physical Tests

AbstractThe main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential $$\lambda (r)$$ λ ( r ) , and we obtained the other metric potential $$\nu (r)$$ ν ( r ) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars.

Wormhole solutions in modified f(R,φ,X) gravity

2021 ◽  
Vol 36 (04) ◽  
pp. 2150021
Author(s):  
M. Farasat Shamir ◽  
Adnan Malik ◽  
G. Mustafa
Keyword(s):  
Shape Function ◽  
Scalar Potential ◽  
Three Dimensional ◽  
State Parameter ◽  
Energy Conditions ◽  
Kinetic Term ◽  
Anisotropic Fluid ◽  
Shape Functions ◽  
Current Analysis ◽  
Static Space

This work aims to investigate the wormhole solutions in the background of [Formula: see text] theory of gravity, where [Formula: see text] is Ricci scalar, [Formula: see text] is scalar potential, and [Formula: see text] is the kinetic term. We consider spherically symmetric static space–time for exploring the wormhole geometry with anisotropic fluid. For our current analysis, we consider a particular equation of state parameter to study the behavior of traceless fluid and examine the physical behavior of energy density and pressure components. Furthermore, we also choose a particular shape function and explore the energy conditions. It can be noticed that energy conditions are violated for both shape functions. The violation of energy conditions indicates the existence of exotic matter and wormhole. Therefore, it can be concluded that our results are stable and realistic. The interesting feature of this work is to show two- and three-dimensional plotting for the analysis of wormhole geometry.

scholarly journals Compact stars in f(ℛ,𝒢,𝒯 ) gravity

2021 ◽  
Vol 36 (24) ◽  
pp. 2150165
Author(s):  
M. Ilyas
Keyword(s):  
Test Particle ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Conservation Equation ◽  
Compact Objects ◽  
Compact Stars ◽  
Energy Conditions ◽  
Field Equations ◽  
Physical Features ◽  
The Impact

This work is to introduce a new kind of modified gravitational theory, named as [Formula: see text] (also [Formula: see text]) gravity, where [Formula: see text] is the Ricci scalar, [Formula: see text] is Gauss–Bonnet invariant and [Formula: see text] is the trace of the energy–momentum tensor. With the help of different models in this gravity, we investigate some physical features of different relativistic compact stars. For this purpose, we develop the effectively modified field equations, conservation equation, and the equation of motion for test particle. Then, we check the impact of additional force (massive test particle followed by a nongeodesic line of geometry) on compact objects. Furthermore, we took three notable stars named as [Formula: see text], [Formula: see text] and [Formula: see text]. The physical behavior of the energy density, anisotropic pressures, different energy conditions, stability, anisotropy, and the equilibrium scenario of these strange compact stars are analyzed through various plots. Finally, we conclude that the energy conditions hold, and the core of these stars is so dense.

Recommendations for the multilateral wells design selection in various geological conditions based on lessons learned

2021 ◽  
pp. 159-167
Author(s):  
A. A. Zernin ◽  
E. S. Ziuzev ◽  
A. S. Sergeev ◽  
R. M. Khismatullin ◽  
M. A. Starikov
Keyword(s):  
Lessons Learned ◽  
Energy Conditions ◽  
Reservoir Properties ◽  
Field Development ◽  
Well Design ◽  
Well Efficiency ◽  
Geological Conditions ◽  
Efficiency Estimation ◽  
Design Selection ◽  
First Time

The authors of the article have summarized the experience of multilateral well application, performed an efficiency analysis of multilateral wells vs horizontal wells in Rosneft Oil Company's fields with various subsurface architecture. The algorithm for multilateral well efficiency estimation, compared to other type of well completions, was developed. This algorithm is based on the selection of areas for well locations with similar reservoir properties, reservoir energy conditions, and reservoir development conditions to evaluate production startup parameters, decline rates, cumulative parameters for the areas of over 6 month production. A matrix of multilateral well applicability in various geological conditions was generated, and recommendations for preferable well design were made. This type of analysis was conducted for the first time due to collection of sufficient statistical data, because of a multiple increase in the amount of drilling complex wells in the recent years. The obtained results provide an opportunity to design an efficient field development system for new assets, perform an adjustment of brownfields development systems, select multilateral well design for certain geological conditions based on lessons learned.

A generalized anisotropic model for super dense stars

2021 ◽  
pp. 2150070
Author(s):  
Joaquin Estevez-Delgado ◽  
Gabino Estevez-Delgado ◽  
Noel Enrique Rodríguez Maya ◽  
José Martínez Peña ◽  
Aurelio Tamez Murguía
Keyword(s):  
Radial Pressure ◽  
Compact Stars ◽  
Anisotropic Model ◽  
Speed Of Light ◽  
Matter Distribution ◽  
Sphere Model ◽  
Tangential Pressure ◽  
Relativistic Fluid ◽  
Causal Condition ◽  
Dense Stars

A static anisotropic relativistic fluid sphere model with regular geometry and finite hydrostatic functions is presented. In the interior of the sphere, the density, radial pressure and tangential pressure are positives, monotonically decreasing with increasing radius and the radial pressure vanishes at the surface of the matter distribution and is joined continuously to the exterior Schwarzschild’s solution at this surface. The speeds of the radial and tangential sound are positive and lower than the speed of light, that is, the causal condition is not violated, and also the behavior of these guarantees that the model is potentially stable. Furthermore, the range of the compactness ratio is characteristic of compact stars and it is shown that the effect of the anisotropy generates that the speed of the radial sound can behave as a function monotonically increasing or monotonically decreasing.

Sign in / Sign up

Export Citation Format

Share Document