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Entropy
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Complexity of Self-Gravitating Systems
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Complexity of Self-Gravitating Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (30 October 2022) | Viewed by 20378

Special Issue Editor

Prof. Dr. Luis Alfredo Herrera Cometta

E-Mail Website
Guest Editor
Instituto Universitario de Fisica Fundamental y Matemáticas, Universidad de Salamanca, 37008 ‎Salamanca, Spain
Interests: general relativity; relativistic astrophysics; causal dissipative theories; Information theory

Special Issue Information

Dear Colleagues,

In the past decades many efforts have been devoted towards a rigorous definition of complexity in different branches of science however in spite of all the work done so far there is not yet a consensus on a precise definition

The reason behind such interest stems from the fact that, at least at an intuitive level, complexity, no matter how we define it, is a physical concept deeply intertwined with fundamental aspects of the system. In other words, we expect that a suitable definition of complexity of the system could allow us to infer relevant conclusions about its behaviour.

Therefore it is of utmost relevance to provide a precise definition of an observable quantity which allows to measure such an important property of the system. Thus, when dealing with a situation that intuitively is judged as “complex”, we need to be able to quantify this complexity by defining an observable measuring it.

This special issue of Entropy is devoted to the discussion on the possible definition of complexity of self--gravitating systems and its applications.

We propose below a list of questions which we would like to see treated in the manuscripts submitted to this special issue. It is of course a partial list, and it goes without saying that any manuscript devoted to a subject related to the concept of complexity of self--gravitating systems but not mentioned in the list below, would also be welcomed.

  • Is there alternative definitions of complexity different from the one proposed in [1]
  • How can we extend the definition of complexity for vacuum space--times?
  • Besides the homologous and the quasi--homologous regime, could we define another pattern of evolution that could qualify as the simplest one?
  • Can we relate the complexity factor(s) in the non--spherically symmetric case, to the active gravitational mass, as in the spherically symmetric case?
  • Can we single out a specific family of exact axially symmetric static solutions satisfying the vanishing complexity factor(s) condition?
  • Can any of the above solutions be matched smoothly to any vacuum Weyl solution?
  • The definition of complexity proposed in [1] is not directly related to entropy or disequilibrium, although it is possible that such a link might exist after all. If so, how could such relationship be brought out?
  • Could it be possible to provide a definition of the arrow of time in terms of the complexity factor?
  • How the complexity factor is related to physical relevant properties of the source such as stability, or maximal degree of compactness.
  • How does the complexity factor evolves? Do physically meaningful systems prefer vanishing complexity factor?
  • Should a physically sound cosmological model have a vanishing complexity factor? Should it evolve in the homologous or quasi--homologous regime?
  • The complexity factor for a charged fluid is known, but what is the complexity factor for a different type of field (e.g., scalar field?).
  • How should we define the complexity factor in the context of other alternatives theories of gravity which have not been considered so far?
  • How to find new solutions satisfying the vanishing complexity factor?
  • What relevant physical features share solutions satisfying the vanishing complexity factor?
  • Is there a link between the concept of complexity and some kind of symmetry (e.g., motions, conformal motions, affine collineations, curvature collineations, matter collineations, etc) ?

[1]. Herrera, L. New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case. Phys. Rev. D 2018, 97, 044010.

Prof. Dr. Luis Alfredo Herrera Cometta
Guest Editor

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Published Papers (9 papers)

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Editorial

Jump to: Research

5 pages, 207 KiB  
Editorial
Complexity of Self-Gravitating Systems
by Luis Herrera
Entropy 2021, 23(7), 802; https://doi.org/10.3390/e23070802 - 24 Jun 2021
Cited by 16 | Viewed by 2144
Abstract
In recent decades many efforts have been made towards a rigorous definition of complexity in different branches of science (see [...] Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)

Research

Jump to: Editorial

16 pages, 326 KiB  
Article
Charged Shear-Free Fluids and Complexity in First Integrals
by Sfundo C. Gumede, Keshlan S. Govinder and Sunil D. Maharaj
Entropy 2022, 24(5), 645; https://doi.org/10.3390/e24050645 - 4 May 2022
Cited by 3 | Viewed by 1595
Abstract
The equation yxx=f(x)y2+g(x)y3 is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the [...] Read more.
The equation yxx=f(x)y2+g(x)y3 is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the Einstein–Maxwell system for a charged shear-free matter distribution. We integrate this equation and find a new first integral. For this solution to exist, two integral equations arise as integrability conditions. The integrability conditions can be transformed to nonlinear differential equations, which give explicit forms for f(x) and g(x) in terms of elementary and special functions. The explicit forms f(x)∼1x51−1x−11/5 and g(x)∼1x61−1x−12/5 arise as repeated roots of a fourth order polynomial. This is a new solution to the Einstein-Maxwell equations. Our result complements earlier work in neutral and charged matter showing that the complexity of a charged self-gravitating fluid is connected to the existence of a first integral. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
19 pages, 371 KiB  
Article
A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity
by Z. Yousaf, M. Z. Bhatti, Maxim Khlopov and H. Asad
Entropy 2022, 24(2), 150; https://doi.org/10.3390/e24020150 - 19 Jan 2022
Cited by 13 | Viewed by 2036
Abstract
This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric f(R) gravity to carry out our analysis. It is noticed that the matter distribution cannot fill [...] Read more.
This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric f(R) gravity to carry out our analysis. It is noticed that the matter distribution cannot fill the region close to the center of symmetry, thereby implying the existence of an empty core. Moreover, the evaluation of the effective energy density reveals that it is inevitably negative, which could have utmost relevance in understanding various quantum field events. To derive the structure scalars, we perform the orthogonal splitting of the Riemann tensor in this modified gravity. Few relationships among matter variables and both Tolman and Misner Sharp are determined. Through two generating functions, some hyperbolically symmetric cosmological models, as well as their physical interpretations, are studied. To delve deeply into the role of f(R) terms, the model of the less-complex relativistic system of Einstein gravity is presented. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
12 pages, 273 KiB  
Article
First Integrals of Shear-Free Fluids and Complexity
by Sfundo C. Gumede, Keshlan S. Govinder and Sunil D. Maharaj
Entropy 2021, 23(11), 1539; https://doi.org/10.3390/e23111539 - 19 Nov 2021
Cited by 5 | Viewed by 1831
Abstract
A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of yxx=f(x)y2, find new solutions, and generate a new [...] Read more.
A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of yxx=f(x)y2, find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function f(x). We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of f(x)∼1x51−1x−15/7 which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
19 pages, 1076 KiB  
Article
A Tolman-like Compact Model with Conformal Geometry
by Didier Kileba Matondo and Sunil D. Maharaj
Entropy 2021, 23(11), 1406; https://doi.org/10.3390/e23111406 - 26 Oct 2021
Cited by 9 | Viewed by 1731
Abstract
In this investigation, we study a model of a charged anisotropic compact star by assuming a relationship between the metric functions arising from a conformal symmetry. This mechanism leads to a first-order differential equation containing pressure anisotropy and the electric field. Particular forms [...] Read more.
In this investigation, we study a model of a charged anisotropic compact star by assuming a relationship between the metric functions arising from a conformal symmetry. This mechanism leads to a first-order differential equation containing pressure anisotropy and the electric field. Particular forms of the electric field intensity, combined with the Tolman VII metric, are used to solve the Einstein–Maxwell field equations. New classes of exact solutions generated are expressed in terms of elementary functions. For specific parameter values based on the physical requirements, it is shown that the model satisfies the causality, stability and energy conditions. Numerical values generated for masses, radii, central densities, surface redshifts and compactness factors are consistent with compact objects such as PSR J1614-2230 and SMC X-1. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
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19 pages, 358 KiB  
Article
Inhomogeneous and Radiating Composite Fluids
by Byron P. Brassel, Sunil D. Maharaj and Rituparno Goswami
Entropy 2021, 23(11), 1400; https://doi.org/10.3390/e23111400 - 25 Oct 2021
Cited by 22 | Viewed by 1653
Abstract
We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust [...] Read more.
We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
17 pages, 315 KiB  
Article
Hyperbolically Symmetric Versions of Lemaitre–Tolman–Bondi Spacetimes
by Luis Herrera, Alicia Di Prisco and Justo Ospino
Entropy 2021, 23(9), 1219; https://doi.org/10.3390/e23091219 - 16 Sep 2021
Cited by 17 | Viewed by 1950
Abstract
We study fluid distributions endowed with hyperbolic symmetry, which share many common features with Lemaitre–Tolman–Bondi (LTB) solutions (e.g., they are geodesic, shearing, and nonconformally flat, and the energy density is inhomogeneous). As such, they may be considered as hyperbolic symmetric versions of LTB, [...] Read more.
We study fluid distributions endowed with hyperbolic symmetry, which share many common features with Lemaitre–Tolman–Bondi (LTB) solutions (e.g., they are geodesic, shearing, and nonconformally flat, and the energy density is inhomogeneous). As such, they may be considered as hyperbolic symmetric versions of LTB, with spherical symmetry replaced by hyperbolic symmetry. We start by considering pure dust models, and afterwards, we extend our analysis to dissipative models with anisotropic pressure. In the former case, the complexity factor is necessarily nonvanishing, whereas in the latter cases, models with a vanishing complexity factor are found. The remarkable fact is that all solutions satisfying the vanishing complexity factor condition are necessarily nondissipative and satisfy the stiff equation of state. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
13 pages, 467 KiB  
Article
Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems
by Mohammad Hossein Zhoolideh Haghighi, Sohrab Rahvar and Mohammad Reza Rahimi Tabar
Entropy 2021, 23(9), 1158; https://doi.org/10.3390/e23091158 - 2 Sep 2021
Viewed by 2717
Abstract
We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there [...] Read more.
We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
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20 pages, 2419 KiB  
Article
Anisotropic Strange Star in 5D Einstein-Gauss-Bonnet Gravity
by Mahmood Khalid Jasim, Sunil Kumar Maurya, Ksh. Newton Singh and Riju Nag
Entropy 2021, 23(8), 1015; https://doi.org/10.3390/e23081015 - 6 Aug 2021
Cited by 25 | Viewed by 3011
Abstract
In this paper, we investigated a new anisotropic solution for the strange star model in the context of 5D Einstein-Gauss-Bonnet (EGB) gravity. For this purpose, we used a linear equation of state (EOS), in particular pr=βρ+γ [...] Read more.
In this paper, we investigated a new anisotropic solution for the strange star model in the context of 5D Einstein-Gauss-Bonnet (EGB) gravity. For this purpose, we used a linear equation of state (EOS), in particular pr=βρ+γ, (where β and γ are constants) together with a well-behaved ansatz for gravitational potential, corresponding to a radial component of spacetime. In this way, we found the other gravitational potential as well as main thermodynamical variables, such as pressures (both radial and tangential) with energy density. The constant parameters of the anisotropic solution were obtained by matching a well-known Boulware-Deser solution at the boundary. The physical viability of the strange star model was also tested in order to describe the realistic models. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified TOV equation and the dynamical stability through the critical value of the radial adiabatic index. The mass-radius relationship was also established for determining the compactness and surface redshift of the model, which increases with the Gauss-Bonnet coupling constant α but does not cross the Buchdahal limit. Full article
(This article belongs to the Special Issue Complexity of Self-Gravitating Systems)
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