Structure of spherically symmetric objects: a study based on structure scalars

2022 ◽  
Vol 97 (2) ◽  
pp. 025301
Author(s):  
Z Yousaf
Keyword(s):  
Energy Density ◽  
Constant Curvature ◽  
Spherical Geometry ◽  
Vital Role ◽  
Spherically Symmetric ◽  
Irregular Distribution ◽  
Structure Scalars ◽  
Tidal Forces

Abstract The aim of this paper is to explore the consequences of extra curvature terms mediated from f(R, T, Q) (where Q ≡ R μ ν T μ ν ) theory on the formation of scalar functions and their importance in the study of populations who are crowded with regular relativistic objects. For this purpose, we model our system comprising of non-rotating spherical geometry formed due to gravitation of locally anisotropic and radiating sources. After considering a particular f(R, T, Q) model, we form a peculiar relation among Misner-Sharp mass, tidal forces, and matter variables. Through structure scalars, we have modeled shear, Weyl, and expansion evolutions equations. The investigation for the causes of the irregular distribution of energy density is also performed with and without constant curvature conditions. It is deduced that our computed one of the f(R, T, Q) structure scalars (Y T ) has a vital role to play in understanding celestial mechanisms in which gravitational interactions cause singularities to emerge.

Stellar systems and structure scalars

2019 ◽  
Vol 97 (5) ◽  
pp. 465-471 ◽  
Author(s):  
S. Ahmad ◽  
A. Rehman Jami ◽  
I. Ahmad ◽  
H. Sadia
Keyword(s):  
Riemann Tensor ◽  
Matter Content ◽  
Anisotropic Pressure ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Structure Scalars ◽  
Tidal Forces ◽  
Stress Energy ◽  
Symmetric Geometry

The work is devoted to analyzing the effects of dark source polynomial curvature corrections in the mathematical modeling of radiating stars. In this scenario, we have used a particular f(R, T) model and consider the spherically symmetric geometry of relativistic interior. We assumed that our geometry is coupled with anisotropic shearing matter distribution undergoing radiating epoch with free streaming and diffusion approximation. We have calculated spherically symmetric total matter content with the help of Misner–Sharp formalism. A particular relation among anisotropic pressure, shearing viscosity, radiating parameters, energy density, and tidal forces is obtained. We then expressed this equation with the help of f(R, T) structure scalar, the scalar obtained by orthogonal decomposition of the Riemann tensor. The role of the logarithmic Ricci and trace of stress–energy tensor terms are also observed through Weyl scalar, shear, expansion scalar differential equations.

scholarly journals Karmarkar scalar condition

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
J. Ospino ◽  
L. A. Núñez
Keyword(s):  
Differential Equation ◽  
Energy Density ◽  
Density Profile ◽  
Riemann Tensor ◽  
Orthogonal Decomposition ◽  
Algebraic Relation ◽  
Structure Scalars ◽  
Physical Variables ◽  
Adiabatic Case ◽  
Dissipative Dynamic

AbstractIn this work we present the Karmarkar condition in terms of the structure scalars obtained from the orthogonal decomposition of the Riemann tensor. This new expression becomes an algebraic relation among the physical variables, and not a differential equation between the metric coefficients. By using the Karmarkar scalar condition we implement a method to obtain all possible embedding class I static spherical solutions, provided the energy density profile is given. We also analyse the dynamic adiabatic case and show the incompatibility of the Karmarkar condition with several commonly assumed simplifications to the study of gravitational collapse. Finally, we consider the dissipative dynamic Karmarkar collapse and find a new solution family.

scholarly journals Macroscopic traversable wormholes with zero tidal forces inspired by noncommutative geometry

2015 ◽  
Vol 24 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Peter K. F. Kuhfittig
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Energy Density ◽  
Noncommutative Geometry ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Quantum Field ◽  
Tidal Forces ◽  
Traversable Wormholes ◽  
Asymptotic Flatness

This paper addresses the following issues: (1) the possible existence of macroscopic traversable wormholes, given a noncommutative-geometry background and (2) the possibility of allowing zero tidal forces, given a known density. It is shown that whenever the energy density describes a classical wormhole, the resulting solution is incompatible with quantum-field theory. If the energy density originates from noncommutative geometry, then zero tidal forces are allowed. Also attributable to the noncommutative geometry is the violation of the null energy condition. The wormhole geometry satisfies the usual requirements, including asymptotic flatness.

scholarly journals Exact charged black hole solutions in D-dimensions in f(R) gravity

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Zi-Yu Tang ◽  
Bin Wang ◽  
Eleftherios Papantonopoulos
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
General Solution ◽  
Constant Curvature ◽  
Black Hole Solution ◽  
Einstein Gravity ◽  
Charged Black Hole ◽  
Spherically Symmetric ◽  
Spherically Symmetric Metric ◽  
Black Hole Solutions

AbstractWe consider Maxwell-f(R) gravity and obtain an exact charged black hole solution with dynamic curvature in D-dimensions. Considering a spherically symmetric metric ansatz and without specifying the form of f(R) we find a general black hole solution in D-dimensions. This general black hole solution can reduce to the Reissner–Nordström (RN) black hole in D-dimensions in Einstein gravity and to the known charged black hole solutions with constant curvature in f(R) gravity. Restricting the parameters of the general solution we get polynomial solutions which reveal novel properties when compared to RN black holes. Specifically we study the solution in $$(3+1)$$ ( 3 + 1 ) -dimensions in which the form of f(R) can be solved explicitly giving a dynamic curvature and compare it with the RN black hole. We also carry out a detailed study of its thermodynamics.

scholarly journals SPHERICALLY SYMMETRIC MASSIVE SCALAR FIELDS IN GENERAL RELATIVITY

2010 ◽  
Vol 25 (07) ◽  
pp. 1429-1438 ◽  
Author(s):  
MOHAMMAD MEHRPOOYA ◽  
D. MOMENI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Scalar Fields ◽  
Matter Field ◽  
Massless Scalar ◽  
Special Choice ◽  
Spherically Symmetric ◽  
Elementary Functions ◽  
Field Equations ◽  
Tidal Forces

First, we review some attempts made to find the exact spherically symmetric solutions to Einstein field equations in the presence of scalar fields. Wyman's solution in both the static and the nonstatic scalar field is discussed, and it is shown why in the case of the nonstatic homogenous matter field the static metric cannot be represented in terms of elementary functions. We mention here that if the space–time is static, according to field equations, there are two options for fixing the scalar field: static (time-independent) and nonstatic (time-dependent). All these solutions are limited to the minimally coupled massless scalar fields and also in the absence of the cosmological constant. Then we show that if we are interested to have homogenous isotropic scalar field matter, we can construct a series solution in terms of the scalar field's mass and cosmological constant. This solution is static and possesses a locally flat case as a special choice of the mass of the scalar field and can be interpreted as an effective vacuum. Therefore, the mass of the scalar field eliminates any locally gravitational effect as tidal forces. Finally, we describe why this system is unstable in the language of dynamical systems.

HOLOGRAPHIC SPHERICALLY SYMMETRIC METRICS

2007 ◽  
Vol 16 (06) ◽  
pp. 1603-1641 ◽  
Author(s):  
MICHAEL PETRI
Keyword(s):  
Energy Density ◽  
Degrees Of Freedom ◽  
Mass Density ◽  
Entropy Density ◽  
Constant Factor ◽  
Spherically Symmetric ◽  
Scale Invariant ◽  
Total Energy Density ◽  
Boundary Area ◽  
Symmetric Metrics

The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

Complexity factors for static anisotropic axially symmetric fluid distributions in f(R) gravity

2020 ◽  
Vol 17 (03) ◽  
pp. 2050043
Author(s):  
G. Abbas ◽  
H. Nazar
Keyword(s):  
Energy Density ◽  
General Theory ◽  
Graphical Analysis ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Axially Symmetric ◽  
Structure Scalars ◽  
Isotropic Pressure

In this paper, we have analyzed the complexity factor for the most general axially symmetric static anisotropic fluid distributions in context of [Formula: see text] theory of gravity. For this purpose, we have studied three distinct complexity factors that are organized in terms of three scalar variables (structure scalars) comes from the orthogonal splitting of the curvature tensor. The vanishing of all complexity factors condition for what we choose the simplest fluid distribution that in which system having energy density is homogeneous with isotropic pressure. Although, it has been found that the complexity factors condition can also vanish when inhomogeneous energy density and anisotropy of the pressure cancel each other. Next, we express a class of exact solutions and their graphical analysis as compatible to our models that satisfies the vanishing condition of complexity factors. Finally, it is worth mentioning that these results can reproduce the results of General theory of Relativity under some constraints.

Spherically symmetric high-velocity plasma expansions into background gases

1986 ◽  
Vol 35 (2) ◽  
pp. 239-256 ◽  
Author(s):  
Tai-Ho Tan ◽  
Joseph E. Borovsky
Keyword(s):  
High Velocity ◽  
Spherical Geometry ◽  
Ion Acceleration ◽  
Spherically Symmetric ◽  
Laser Target ◽  
X Ray ◽  
Isothermal Expansion ◽  
Ambient Gases ◽  
Photo Ionization

Spherically symmetric plasmas with high expansion velocities have been produced by irradiating targets with eight beams from the Helios CO2 laser in the presence of gases at various pressures. Attention was given to the properties of the target-emitted ions in order to obtain information about the ion acceleration mechanisms in plasma expansions. Photo-ionization of the ambient gases by the soft X-ray emission from the laser-irradiated targets produced background plasmas, permitting plasma counterstreaming experiments to be performed in spherical geometry. Successful laser-target coupling in the presence of background gases is obtained, modification of the ion acceleration in accordance with isothermal-expansion models is observed, and an absence of collective coupling between collisionless counterstreaming plasmas is found.

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