Research ArticleNo Access

Complexity factors for static axial system in self-interacting Brans–Dicke gravity

M. Sharif

http://orcid.org/0000-0001-6845-3506

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

E-mail Address: msharif.math@pu.edu.pk

Search for more papers by this author

and

Amal Majid

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

E-mail Address: amalmajid89@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S0219887819501743Cited by:15 (Source: Crossref)

Abstract

This paper explores the physical attributes of a static axial source that induce complexity within the fluid in the background of self-interacting Brans–Dicke theory. Bel’s approach is used to split the Riemann tensor and construct structure scalars that involve physical features of the fluid in the presence of scalar field. Using the evolution equations derived from Bianchi identities as well as structure scalars, five complexity factors are identified which include constraints on the scalar field. Finally, the conditions of vanishing complexity are used to present solutions for an anisotropic inhomogeneous spheroid. It is concluded that scalar field is an additional source of complexity.

Keywords:

References

1. E. Diaz et al., 2dFGRS and SDSS galaxy group density profiles, Astrophys. J. 629 (2005) 158–171. Web of Science, Google Scholar
2. A. N. Kolmogorov, Three approaches to the definition of the concept “quantity of information”, Probl. Peredachi Inf. 1 (1965) 3–11; J. Grassberger, Toward a quantitative theory of self-generated complexity, Int. J. Theor. Phys. 25 (1986) 907–938; P. W. Anderson, Is complexity physics? Is it science? What is it? Phys. Today 44 (1991) 9–11; G. Parisi, Statistical physics and biology, Phys. World 6 (1993) 42–47. Google Scholar
3. R. Lopez-Ruiz, H. L. Mancini and X. Calbet, A statistical measure of complexity, Phys. Lett. A 209 (1995) 321–325; X. Calbet and R. Lopez-Ruiz, Tendency towards maximum complexity in a nonequilibrium isolated system, Phys. Rev. E 63 (2001) 066116; R. G. Catalan, J. Garay and R. Lopez-Ruiz, Features of the extension of a statistical measure of complexity to continuous systems, Phys. Rev. E 66 (2002) 011102; J. Sañudo and R. Lopez-Ruiz, Statistical complexity and Fisher-Shannon information in the H-atom, Phys. Lett. A 372 (2008) 5283–5286. Google Scholar
4. J. Sañudo and A. F. Pacheco, Complexity and white-dwarf structure, Phys. Lett. A 373 (2009) 807–810; K. Ch. Chatzisavvas et al., Complexity and neutron stars structure, Phys. Lett. A 373 (2009) 3901–3909; R. A. de Souza, M. G. B. de Avellar and J. E. Horvath, Statistical measure of complexity in compact stars with global charge neutrality, preprint (2013), arXiv:astro-ph.SR 1308.3519; M. G. B. de Avellar et al., Information theoretical methods as discerning quantifiers of the equations of state of neutron stars, Phys. Lett. A 378 (2014) 3481–3487. Google Scholar
5. L. Herrera, New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case, Phys. Rev. D 97 (2018) 044010. Web of Science, Google Scholar
6. L. Herrera, A. Di Prisco and J. Ospino, Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions, Phys. Rev. D 98 (2018) 104059. Web of Science, Google Scholar
7. M. Sharif and I. I. Butt, Complexity factor for charged spherical system, Eur. Phys. J. C 78 (2018) 688. Web of Science, Google Scholar
8. M. Sharif and I. I. Butt, Complexity factor for static cylindrical system, Eur. Phys. J. C 78 (2018) 850. Web of Science, Google Scholar
9. J. H. Young and S. L. Bentley, Exact solution to the Einstein–Maxwell field equations for a charge and mass distribution with a quadrupole moment, Phys. Rev. D 11 (1975) 3388–3391. Web of Science, Google Scholar
10. L. Herrera, A. Di Prisco and J. Ibanez, Axially symmetric static sources: A general framework and some analytical solutions, Phys. Rev. D 87 (2013) 024014. Web of Science, Google Scholar
11. M. Sharif and M. Z. Bhatti, Stability analysis of restricted non-static axial symmetry, J. Cosmol. Astropart. Phys. 11 (2013) 014. Web of Science, Google Scholar
12. L. Herrera, A. Di Prisco and J. Ospino, Complexity factors for axially symmetric static sources, Phys. Rev. D 99 (2019) 044049. Web of Science, Google Scholar
13. C. Brans and R. H. Dicke, Mach’s principle and a relativistic theory of gravitation, Phys. Rev. 124 (1961) 925–935. Web of Science, Google Scholar
14. E. J. Weinberg, Some problems with extended inflation, Phys. Rev. D 40 (1989) 3950–3959. Web of Science, Google Scholar
15. C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativ. 4 (2001) 4. Google Scholar
16. J. Khoury and A. Weltman, Chameleon cosmology, Phys. Rev. D 69 (2004) 044026. Web of Science, Google Scholar
17. M. Sharif and R. Manzoor, Self-gravitating spherically symmetric fluid models in Brans-Dicke gravity, Gen. Relativ. Gravit. 47 (2015) 98; Structure scalars and anisotropic spheres in Brans–Dicke gravity, Phys. Rev. D 91 (2015) 024018; Structure scalars and cylindrical systems in Brans-Dicke gravity, Astrophys. Space Sci. 359 (2015) 17. Google Scholar
18. M. Sharif and R. Manzoor, Static axially symmetric models and structure scalars in self-interacting Brans–Dicke gravity, Commun. Theor. Phys. 68 (2017) 39–48. Web of Science, Google Scholar
19. G. Abbas and H. Nazar, Complexity factor for static anisotropic self-gravitating source in f(R) gravity, Eur. Phys. J. C 78 (2018) 510; Complexity factor for anisotropic source in non-minimal coupling metric f(R) gravity, Eur. Phys. J. C 78 (2018) 957. Google Scholar
20. Y. Fujii and K. Maeda, The Scalar–Tensor Theory of Gravitation (Cambridge University Press, Cambridge, 2003). Google Scholar
21. C. S. Trendafilova and S. A. Fulling, Static solutions of Einstein’s equations with cylindrical symmetry, Eur. J. Phys. 32 (2011) 1663–1667; G. Abbas, S. Nazeer and M. A. Meraj, Cylindrically symmetric models of anisotropic compact stars, Astrophys. Space Sci. 354 (2014) 449–455. Google Scholar
22. H. Bondi, The contraction of gravitating spheres, Proc. R. Soc. Lond. A 281 (1964) 39–48. Web of Science, Google Scholar
23. R. Penrose, General Relativity, An Einstein Centenary Survey (Cambridge University Press, Cambridge, 1979). Google Scholar
24. L. Bel, Inductions électromagnétique et gravitationnelle, Ann. Inst. Henri Poincaré 17 (1961) 37. Google Scholar
25. M. Sharif and A. Majid, Complexity factor for static sphere in self-interacting Brans–Dicke gravity, to appear in Chin. J. Phys. (2019). Google Scholar
26. M. Sharif and A. Majid, Complexity factor for cylindrical system in Brans–Dicke gravity, submitted for publication. Google Scholar