scholarly journals Singularities in Static Spherically Symmetric Configurations of General Relativity with Strongly Nonlinear Scalar Fields

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 72
Author(s):  
Oleksandr Stashko ◽  
Valery I. Zhdanov
Keyword(s):  
Scalar Field ◽  
Asymptotic Properties ◽  
Field Potential ◽  
Scalar Fields ◽  
Einstein Equations ◽  
Large Field ◽  
Spherically Symmetric ◽  
Schwarzschild Solution ◽  
Naked Singularities ◽  
Strongly Nonlinear

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly nonlinear scalar field, which allow the appearance of singularities of a new type (“spherical singularities”) outside the center of curvature coordinates. As the example, we consider a scalar field potential ∼sinh(ϕ2n),n>2, which grows rapidly for large field values. The space-time is assumed to be asymptotically flat. We fulfill a numerical investigation of solutions with different n for different parameters, which define asymptotic properties at spatial infinity. Depending on the configuration parameters, we show that the distribution of the stable circular orbits of test bodies around the configuration is either similar to that in the case of the Schwarzschild solution (thus mimicking an ordinary black hole), or it contains additional rings of unstable orbits.

scholarly journals Spherically Symmetric Configurations in General Relativity in the Presence of a Linear Massive Scalar Field: Separation of a Distribution of Test Body Circular Orbits

2019 ◽  
Vol 64 (3) ◽  
pp. 189 ◽  
Author(s):  
O. S. Stashko ◽  
V. I. Zhdanov
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Scalar Fields ◽  
Test Body ◽  
Einstein Equations ◽  
Strength Parameter ◽  
Spherically Symmetric ◽  
Massive Scalar ◽  
Circular Orbits ◽  
Massive Scalar Field

We study static spherically symmetric configurations in the presence of linear massive scalar fields within General Relativity. Static solutions of the Einstein equations are considered under conditions of asymptotic flatness. Each solution is fixed by the configuration mass and the field strength parameter, which are defined at spatial infinity. The metric coefficients and the scalar field for a specific configuration are obtained numerically. Then we study the time-like geodesics describing the test particle motion. The focus is on the distribution of stable circular orbits (SCOs) of the test particles around a configuration. We found that, for the continuum of configuration parameters, there exist two unlinked regions of SCOs that are separated by some annular region, where SCOs do not exist.

scholarly journals GLOBAL MONOPOLES AND SCALAR FIELDS AS THE ELECTROGRAVITY DUAL OF SCHWARZSCHILD SPACE–TIME

2001 ◽  
Vol 16 (18) ◽  
pp. 1193-1200 ◽  
Author(s):  
NARESH DADHICH ◽  
NARAYAN BANERJEE
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Scalar Fields ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Schwarzschild Solution ◽  
State Formula ◽  
Global Monopoles ◽  
First Time

We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, [Formula: see text]. This property was however known for the global monopole space–time while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos–Zannias scalar field solution is dual to flat space.

scholarly journals A Riccati equation based approach to isotropic scalar field cosmologies

2014 ◽  
Vol 23 (07) ◽  
pp. 1450063 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
M. K. Mak
Keyword(s):  
Scalar Field ◽  
Evolution Equation ◽  
Interaction Potential ◽  
Arbitrary Function ◽  
Field Potential ◽  
Type Equation ◽  
Scalar Fields ◽  
Cosmological Models ◽  
Late Time ◽  
Field Equations

Gravitationally coupled scalar fields ϕ, distinguished by the choice of an effective self-interaction potential V(ϕ), simulating a temporarily nonvanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work, we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation. The solutions correspond to cosmological models in which the Hubble function is proportional to the scalar field potential plus a linearly decreasing function of time, models with the time variation of the scalar field potential proportional to the potential minus its square, models in which the potential is the sum of an arbitrary function and the square of the function integral, and models in which the potential is the sum of an arbitrary function and the derivative of its square root, respectively. The cosmological properties of all models are investigated in detail, and it is shown that they can describe the inflationary or the late accelerating phase in the evolution of the universe.

scholarly journals Singularities in Inflationary Cosmological Models

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 491
Author(s):  
Leonardo Fernández-Jambrina
Keyword(s):  
Scalar Field ◽  
Field Potential ◽  
Fractional Power ◽  
Scalar Fields ◽  
Big Bang ◽  
Cosmological Models ◽  
Accelerated Expansion ◽  
Type Iv ◽  
Big Crunch ◽  
Expansion Of The Universe

Due to the accelerated expansion of the universe, the possibilities for the formation of singularities has changed from the classical Big Bang and Big Crunch singularities to include a number of new scenarios. In recent papers it has been shown that such singularities may appear in inflationary cosmological models with a fractional power scalar field potential. In this paper we enlarge the analysis of singularities in scalar field cosmological models by the use of generalised power expansions of their Hubble scalars and their scalar fields in order to describe all possible models leading to a singularity, finding other possible cases. Unless a negative scalar field potential is considered, all singularities are weak and of type IV.

scholarly journals STATIC SPHERICALLY SYMMETRIC SCALAR FIELD SPACETIMES WITH C0 MATCHING

2011 ◽  
Vol 26 (17) ◽  
pp. 1281-1290 ◽  
Author(s):  
SWASTIK BHATTACHARYA ◽  
PANKAJ S. JOSHI
Keyword(s):  
Scalar Field ◽  
Naked Singularity ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Curvature Singularity ◽  
Einstein Theory ◽  
Full Class ◽  
Strong Curvature

All the classes of static massless scalar field models currently available in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields coupled to gravity, which does not have any strong curvature singularity. This class of models contain a thin shell of singular matter, which has a physical interpretation. The central curvature singularity is, however, avoided which is common to all static massless scalar field spacetime models known so far. Our result thus points out that the full class of solutions in this case may contain non-singular models, which is an intriguing possibility.

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.

Some interactions of spherically symmetric massive scalar field with Brans–Dicke scalar field in Robertson–Walker universe

2019 ◽  
Vol 16 (04) ◽  
pp. 1950066 ◽  
Author(s):  
Kangujam Priyokumar Singh ◽  
Rajshekhar Roy Baruah
Keyword(s):  
Scalar Field ◽  
Cosmic Time ◽  
Scalar Fields ◽  
Cosmological Term ◽  
Physical Parameters ◽  
Spherically Symmetric ◽  
Massive Scalar ◽  
Field Equations ◽  
Massive Scalar Field ◽  
The Universe

Here in this work, we investigated the possible cosmological consequences of the interaction of Brans–Dicke scalar field and massive scalar field by considering spherically symmetric Robertson–Walker metric. The present problem can also be treated as an extension work of [K. Priyokumar et al., Interaction of gravitational field and Brans–Dicke field, Res. Astron. Astrophys. 16(4) (2016) 64; K. Priyokumar and M. Dewri, Interaction of electromagnetic field and Brans–Dicke field, Chinease J. Phys. 54 (2016) 845]. The exact solutions of the field equations are obtained with seven different cases. The behavior of the model and their contribution to the process of the evolution are examined in detail from some explicit and reasonable values of free parameter. We also presented the variations of certain physical parameters versus cosmic time graphically to compare our solutions with the present observational findings. When we studied further, it is found that the cosmological term [Formula: see text] takes a great role in the accelerating expansion of our universe when both scalar fields are exponentially increasing functions of time, while the cosmological term will not appear in the case when both the scalar fields are exponentially decreasing functions of time. Also, the scalar field is seen to have a tendency to increase the expansion of the universe, thereby flattening the universe.

scholarly journals GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC PERFECT FLUID WITH KINEMATIC SELF-SIMILARITY

2002 ◽  
Vol 11 (02) ◽  
pp. 155-186 ◽  
Author(s):  
C. F. C. BRANDT ◽  
L.-M. LIN ◽  
J. F. VILLAS DA ROCHA ◽  
A. Z. WANG
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Schwarzschild Solution ◽  
Naked Singularities

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

scholarly journals Velocity and velocity bounds in static spherically symmetric metrics

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Ivan Arraut ◽  
Davide Batic ◽  
Marek Nowakowski
Keyword(s):  
Radial Velocity ◽  
Density Profile ◽  
Local Minimum ◽  
Naked Singularity ◽  
Massless Particle ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Naked Singularities ◽  
Symmetric Metrics

AbstractWe find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.

The Schwarzschild solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Vacuum Solution ◽  
Matter Density ◽  
Einstein Equations ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Schwarzschild Solution ◽  
Newtonian Theory ◽  
Schwarzschild Metric ◽  
The Poisson Equation ◽  
Symmetric Spacetime

This chapter deals with the Schwarzschild metric. To find the gravitational potential U produced by a spherically symmetric object in the Newtonian theory, it is necessary to solve the Poisson equation Δ‎U = 4π‎Gρ‎. Here, the matter density ρ‎ and U depend only on the radial coordinate r and possibly on the time t. Outside the source the solution is U = –GM/r, where M = 4π‎ ∫ ρ‎r2dr is the source mass. In general relativity the problem is to find the ‘spherically symmetric’ spacetime solutions of the Einstein equations, and the analog of the vacuum solution U = –GM/r is the Schwarzschild metric.

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