Stable charged radiating systems associated with tilted observers

Abstract

This paper is aimed to study the influence of electromagnetic field and tilted congruences on the dynamical features of self-gravitating system. We shall explore the stability of homogeneous energy density in the background of Maxwell–Palatini f(R) gravity. In this respect, we have considered an irrotational non-static planar geometry which is assumed to have two different types of gravitating sources. The role of tilted congruences and the geodesic motion of an evolving system is studied through the divergence of the entropy vector field. The condition for the emergence of Minskoskian cavity is also explored. In order to connect tilted and non-tilted reference frames with inflationary and inverse Ricci scalar corrections in the charged medium, few well-consistent relations are presented. It is concluded that effective electric charge is trying to increase the stability of regular energy density of the planar system.

Appendix

The expressions $\mathcal {K}_0$ and $\mathcal {K}_1$ arising in Eqs. (60) and (61) are given below

$$\begin{aligned} \mathcal {K}_0&=\frac{\mathcal {T}_{01}}{C^2}\left( \frac{2B'}{B} +\frac{2f'_R}{f_R}+\frac{C'}{C}\right) -\dot{\mathcal {T}}_{00} -\mathcal {T}_{00}\left( \frac{\dot{C}}{C}+\frac{3\dot{f_R}}{2f_R} +\frac{2\dot{B}}{B}\right) -\frac{\mathcal {T}_{11}}{C^2} \nonumber \\&\quad \times \left( \frac{\dot{C}}{C}+\frac{\dot{f_R}}{2f_R}\right) +\left( \frac{\mathcal {T}_{10}}{C^2}\right) '-\frac{2\mathcal {T}_{22}}{B^2}\left( \frac{\dot{B}}{B} +\frac{\dot{f_R}}{2f_R}\right) , \end{aligned}$$

(A1)

$$\begin{aligned} \mathcal {K}_1&=-\dot{\mathcal {T}}_{10} +\mathcal {T}_{00}\frac{f_R'}{2f_R}+ \left( 2\frac{B'}{B}+\frac{3f_R'}{2f_R}\right) \frac{\mathcal {T}_{11}}{C^2}-\mathcal {T}_{10} \left( \frac{\dot{C}}{C}+\frac{2\dot{f}_R}{f_R}+\frac{2\dot{B}}{B}\right) \nonumber \\&\quad +\left( \frac{\mathcal {T}_{11}}{C^2}\right) '-\frac{2}{B^2}\left( \frac{B'}{B}+\frac{f'_R}{2f_R}\right) \mathcal {T}_{22}. \end{aligned}$$

(A2)