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Self-gravitating spherically symmetric systems with Q h condition in chameleonic Brans–Dicke gravity

  • Z. Yousaf ORCID logo EMAIL logo , M. Z. Bhatti ORCID logo and Sana Rehman

Abstract

This paper is asserted to explore the self-gravitating spherically symmetric anisotropic fluids in Chameleonic Brans–Dicke theory as dark energy matter. The dissipative and non-dissipative cases for the evolution of the system are discussed evidently satisfying the quasi-homologous condition with vanishing complexity (Y TF ) factor, which is identified in the trace free part of the electric Riemann tensor in splitting of the curvature tensor. We formulate different equations through conformal tensor, mass function, shear stress tensor, scalar field to govern self-gravitating systems. A few models describe center filled fluid distribution whereas some of them have cavities surrounding the center by means of matching conditions on the boundary as well as on inner surfaces. The temperature of the respective models is also discussed here. Finally, we conclude the work by comparing it with GR.


Corresponding author: Z. Yousaf, Department of Mathematics, University of the Punjab, Quaid-i-Azam Campus, Lahore, 54590, Pakistan, E-mail:

Funding source: National Research Project for Universities (NRPU), Higher Education Commission Pakistan

Award Identifier / Grant number: Project No. 8754/Punjab/NRPU/R&D/HEC/2017

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

The expressions ϱ1, ϱ2 and ϱ3 emerging in Eqs (111), (113) and (114) are given as

ϱ 1 = Z 1 ϕ 2 4 η 2 [ r η 2 1 ] 5 σ 2 4 σ 2 ( η r + c ́ ) Z 1 ϕ Z 1 ϕ ( η r + c ́ ) 2 σ 2 η ( η r + c ́ ) 2 Z 1 ϕ Z 1 ϕ . ϱ 2 = 2 σ 4 η 2 ( η r + c ́ ) σ ̇ A ϕ X ̇ ψ ϕ + 2 η 3 σ 2 ( η r + c ́ ) Z 1 ϕ 2 σ 2 σ 2 ( η r + c ́ ) 2 + σ 2 σ ̇ η 2 A ϕ X ψ ϕ ̇ η 3 2 η 2 + σ 2 ( η r + c ́ ) 2 + 2 η ( η r + c ́ ) Z 1 ϕ ( η r + c ́ ) 2 4 η 2 A ϕ X ψ ϕ ̇ σ 2 σ ̇ ( η r + c ́ ) 2 σ 2 σ 2 ( η r + c ́ ) 2 + σ 2 σ ̇ η 2 A ϕ X ψ ϕ ̇ + Z 1 ϕ 4 η 2 ( η r + c ́ ) ( η r + c ́ ) + 4 η 2 + σ 2 ( η r + c ́ ) . ϱ 3 = σ 2 η 2 η ( η r + c ́ ) 2 4 η 2 A ϕ X ψ ϕ ̇ 2 ( η r + c ́ ) Z 1 ϕ σ ̇ 2 η 2 σ 2 ( η r + c ́ ) 2 + σ 2 2 σ ̇ ( η r + c ́ ) 2 A ϕ X ψ ϕ ̇ + 2 η 2 + σ 2 ( η r + c ́ ) 2 + 2 η ( η r + c ́ ) Z 1 ϕ ( η r + c ́ ) 2 4 η 2 A ϕ X ψ ϕ ̇ ( η r + c ́ ) σ ̇ 2 η 2 σ 2 ( η r + c ́ ) 2 + σ 2 2 σ ̇ ( η r + c ́ ) 2 A ϕ X ψ ϕ ̇ .

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Received: 2022-05-26
Accepted: 2022-11-08
Published Online: 2022-11-28
Published in Print: 2023-02-23

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