An Eternal gravitational collapse in f(R)f(R) theory of gravity and their astrophysical implications

In this work, we explore the eternal collapsing phenomenon of a stellar system (e.g., a star) within the framework of $f(R)$ gravity and investigate some new aspects of the continued homogeneous gravitational collapse with perfect fluid distribution. The exact solutions of field equations have been obtained in an independent way by the parameterization of the expansion scalar ($\Theta$) governed by the interior spherically symmetric FLRW metric. We impose the Darmois junction condition required for the smooth matching of the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star. The junction conditions demand that the pressure is non-vanishing at the boundary and is proportional to the non-linear terms of $f(R)$ gravity, and the mass function $m(t, r)$ is equal to Schwarzschild mass $M$. The eight massive stars, namely $Westerhout 49-2, BAT99-98, R136a1, R136a2, WR 24, Pismis 24-1$, $\lambda- Cephei$, and $\beta -Canis Majoris$ with their known astrophysical data (masses and radii) are used to estimate the numerical values of the model parameters which allows us to study the solutions numerically and graphically. Here we have discussed two $f(R)$ gravity models describing the collapse phenomenon. The singularity analysis of models is discussed via the apparent horizon and we have shown that stars tend to collapse for an infinite co-moving time in order to attain the singularity (an eternal collapsing phenomenon). We have also shown that our models satisfy the energy conditions and stability requirements for stellar systems

Black hole formation in gravitational collapse and their astrophysical implications

In this work, we have investigated a novel aspect of black hole (BH) formation during the collapse of a self-gravitating configuration. The exact solution of the Einstein field equations is obtained in a model-independent way by considering a parametrization of the expansion scalar ($\Theta$) in the background of spherically symmetric space-time geometry governed by the FLRW metric. Smooth matching of the interior solution with the Schwarzschild exterior metric across the boundary hypersurface of the star, together with the condition that the mass function $m(t,r)$ is equal to Schwarzschild mass $M$, is used to obtain all the physical and geometrical parameters in terms of the stellar mass. The four known massive stars namely $R136a3$, $Melnick$, $R136c$, and $R136b$ with their known astrophysical data (mass, radius, and present age) are used to study the physics of the model both numerically and graphically. We demonstrate that the formation of the apparent horizon occurs earlier than the singular state that is, the model of massive stars would inevitably lead to the formation of a BH as their end state. We have conducted an analysis indicating that the lifespans of massive stars are closely related to their respective masses. Our findings demonstrate that more massive stars exhibit considerably shorter lifespans in comparison to their lighter counterparts. Thus, the presented model corresponds to the evolutionary stages of astrophysical stellar objects and theoretically predicts their possible lifespan. We have also shown that our model satisfies the energy conditions and stability requirements via Herrera's cracking method

Dynamical complexity and the gravitational collapse of compact stellar objects

We investigate the dynamics of the gravitational collapse of a compact object via a complexity factor scalar which arises from the orthogonal splitting of the Riemann tensor. This scalar has the property of vanishing for systems which are isotropic in pressure and homogeneous in the energy density. In this way, the complexity factor can give further details of the progression of inhomogeneity as the collapse proceeds. Furthermore, we show that complexity may be used in comparing models and justifying their physical viability. Thus, it could become an integral part of the physical analysis of relativistic collapse in addition to energy conditions analysis, (in)stability, and recently investigated force dynamics

The role of density inhomogeneity and anisotropy in the final outcome of dissipative collapse

In this work, we employ the “horizon” function introduced by Ivanov (Int J Mod Phys D 25:1650049, 2016b) to study radiating stellar models with a generalized Vaidya exterior. Since the star is dissipating energy in the form of a radial heat flux, the radial pressure at the boundary is non-vanishing. We study the boundary condition which encodes the temporal behaviour of the model. Utilizing a scheme developed by Ivanov, we provide several solutions to the modified junction condition. We show that the presence of strings, allow for the collapse to a black hole or the complete burning of a star

Temporal evolution of a radiating star via Lie symmetries

In this work we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (Phys Rev D 40:670, 1989) in which they provided a particular solution of the temporal equation. This simple exact solution has been widely utilised in modeling dissipative collapse with the most notable result being prediction of the avoidance of the horizon as the collapse proceeds. We study the dynamics of dissipative collapse arising from the general solution obtained via the method of symmetries and of the singularity analysis. We show that the end-state of collapse for our model is significantly different from the widely used linear solution

The role of an equation of state in the dynamical (in)stability of a radiating star

Abstract The influence of an equation of state on the dynamical (in)stability of a sphere undergoing dissipative collapse is investigated for various forms of matter distributions. Employing a perturbative scheme we study the collapse of an initially static star described by the interior Schwarzschild solution. As the star starts to collapse it dissipates energy in the form of a radial heat flux to the exterior spacetime described by the Vaidya solution. By imposing a linear equation of state of the form $$p_r = \gamma \mu$$ pr=γμ on the perturbed radial pressure and density we obtain the complete gravitational behaviour of the collapsing star. We analyse the stability of the collapsing star in both the Newtonian as well as the post-Newtonian approximations

The role of an equation of state in the dynamical (in)stability of a radiating star

Abstract The influence of an equation of state on the dynamical (in)stability of a sphere undergoing dissipative collapse is investigated for various forms of matter distributions. Employing a perturbative scheme we study the collapse of an initially static star described by the interior Schwarzschild solution. As the star starts to collapse it dissipates energy in the form of a radial heat flux to the exterior spacetime described by the Vaidya solution. By imposing a linear equation of state of the form $$p_r = \gamma \mu$$ pr=γμ on the perturbed radial pressure and density we obtain the complete gravitational behaviour of the collapsing star. We analyse the stability of the collapsing star in both the Newtonian as well as the post-Newtonian approximations