Narrow Results

We present a static, isotropic fluid solution around a black hole and its effects on the field equations and the horizon. We offer the solutions, their descriptions and we comment on their shortcomings. We derive from the proposed metric the density, the pressure, the equation of state, the temperature near and far of the black hole and the equation of state parameter. We show that for a special case, when $r\to 0$ the solution behaves as $p=\frac{\rho }{3}$, the equation of state for radiation and for $r\to \infty$ we observe that $p=0$, the equation of state for dust.

We present a time-dependent isotropic fluid solution around a Schwarzschild black hole. We offer the solutions and discuss the effects on the field equations and the horizon. We derive the energy density, pressure and the equation of state parameter. In the second part, we generalize the rotating black hole solution to an expanding universe. We derive from the proposed metric the special solutions of the field equations for the dust approximation and the dark energy solution. We show that the presence of a rotating black hole does not modify the scale factor $b(t)=t^{2/3}$ law for dust, nor $b(t)=e^{\lambda t}$ and $p=-\rho$ for dark energy.

This paper aims to conduct an extensive examination of hyperbolically symmetrical static fluid distributions, wherein a precise analysis of their physical characteristics is carried out in the background of modified $f(G,T)$ gravity, where $G$ and $T$ stands for Gauss Bonnet invariant and energy-momentum trace, respectively. The outcomes reveal that the energy density exhibits negative value, thus implying that any utilization of such fluids necessitates extremely demanding circumstances where quantum effects would be significantly influential. Furthermore, it has been determined that these fluid distributions cannot take the vicinity surrounding their central point of symmetry and leave behind an empty vacuum cavity in its place. Additionally, an appropriate definition for mass function and the complexity factor is determined. Eventually, we exhibit a broad strategy for accomplishing particular solutions and showcase several instances of exact analytical solutions in the presence of $f(G,T)$ correction terms.