Narrow Results

In our study, we delved into the profound ramifications of string tension on the collapse of a string fluid, culminating in the formation of a black hole within the realm of $f(R)$ gravity. A string fluid is a perfect fluid model, each whose particle admits a radially stretched string. The outer region for the collapsing object is assumed to be the Schwarzschild spacetime, while the fluid collapses in the internal region are supposed to be Friedman–Robertson–Walker spacetime. The junction conditions are developed leading to gravitational mass and energy. The time frame for apparent horizon and singularity formation was estimated, showing a black hole as the outcome. String tension emerged as a pivotal factor in prolonging horizon creation. Our findings illuminate the relation among $f(R)$ gravity, string tension, and collapse dynamics, enriching our understanding of cosmic phenomena.

Recently, there has been an interest in exploring black holes that are regular in the sense that the central curvature singularity is avoided. Here, we depict a method to obtain a regular black hole (RBH) spacetime from the unhindered gravitational collapse beginning with regular initial data of a spherically symmetric perfect fluid. In other words, we obtain the equilibrium (static) spacetime $(\mathcal{ℳ},\tilde{g})$ as a limiting case of the time-evolving (nonstationary) spacetime $(\mathcal{ℳ},g)$. In the spirit of P. S. Joshi, D. Malafarina and R. Narayan, Class. Quantum Grav. 31 (2014) 015002, our description of gravitational collapse is implicit in nature in the sense that we do not describe the data at each time-slice. Rather, we impose a condition in terms of geometric and matter variables for the collapse to have an end-state that is devoid of incomplete geodesics but admits a marginally trapped surface (MTS). The admission of MTS causally disconnects two mutually exclusive regions ${\widehat{\mathcal{ℳ}}}_1$ and ${\widehat{\mathcal{ℳ}}}_2\subset \mathcal{ℳ}$ in the sense that $\forall p\in {\widehat{\mathcal{ℳ}}}_2$, the causal past of p does not intersect ${\widehat{\mathcal{ℳ}}}_1$. While the classic Oppenheimer–Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the center, we show here that there are classes of regular initial conditions for which the collapse gives rise to a RBH.

In this paper, we perform a comprehensive analysis of conformal symmetries in the generalized Vaidya spacetime and establish several new results. First, a proper conformal Killing vector is shown to exist in the radial direction and interestingly the generalized Vaidya spacetimes with this symmetry are shown to be the subclass of those, which are embeddable in five-dimensional Euclidean space. The general form of the mass function that enables the proper and planar conformal symmetry in the $v$–$r$ plane is also determined. This treatment also includes earlier results. We also consider the gravitational collapse of these spacetimes with proper planar conformal symmetry in the context of cosmic censorship conjecture. We obtain an interesting and novel result that censorship is always obeyed for these spacetimes, and no locally naked central singularity forms as the end state of the continual collapse.

In practice, hypersurfaces are defined via functions of coordinates. As a result, causal classification of hypersurfaces bounding charts can be frame-dependent. We prove that if there exists any frame such that, at some (limiting) point, the metric is diagonal and a basis vector lies on a null hypersurface (defined by that frame) then the metric is degenerate and $C^0$-inextendible there. We apply this to Schwarzschild spacetimes. We show that volume-forms of all 1-submanifolds vanish in the limit of approaching the event horizon, then prove that any point of a 1-submanifold at which volume-forms would vanish (by continuity) cannot be contained in the 1-submanifold, or the manifold itself. This yields a geometric obstruction to the $C^0$-extendibility of curves and the manifold from the black hole exterior to the event horizon. The Ingoing Eddington–Finkelstein coordinate map is shown to fail to be a diffeomorphism at the event horizon, and thus cannot be used to extend the exterior. We discuss the implications for gravitational collapse spacetimes, and show that the geometry of curves inherited from the manifold precludes worldlines from ‘leaving the manifold’, providing new physical intuition for their incompleteness. Finally, the framework is shown not to further constrain extendibility of FLRW spacetimes.

End state of gravitational collapse and the related cosmic censorship conjecture continue to be amongst the most important open problems in gravitation physics today. My purpose here is to bring out several aspects related to gravitational collapse and censorship, which may help towards a better understanding of the issues involved. Possible physical constraints on gravitational collapse scenarios are considered. It is concluded that the best hope for censorship lies in analyzing the genericity and stability properties of the currently known classes of collapse models which lead to the formation of naked singularities, rather than black holes, as the final state of collapse and which develop from a regular initial data.

We investigate the end state of the gravitational collapse of an inhomogeneous dust cloud in higher dimensional spacetime. The naked singularities are shown to be developing as the final outcome of non-marginally bound collapse. The naked singularities are found to be gravitationally strong in the sense of Tipler.

In this paper, the role of anisotropy and inhomogeneity has been studied in quasi-spherical gravitational collapse. Also the role of initial data has been investigated in characterizing the final state of collapse. Finally, a linear transformation on the initial data set has been presented and its impact has been discussed.

The thin shell collapse leading to the formation of charged rotating black holes in three dimensions is analyzed in the light of a recently developed Hamiltonian formalism for these systems. It is proposed to demand, as a way to reconcile the properties of an infinitely extended solenoid in flat space with a magnetic black hole in three dimensions, that the magnetic field should vanish just outside the shell. The adoption of this boundary condition results in an exterior solution with a magnetic field different from zero at a finite distance from the shell. The interior solution is also found and assigns another interpretation, in a different context, to the magnetic solution previously obtained by Clément and Hirschmann and Welch.

In this work, gravitational collapse has been studied for quasi-spherical spacetime with dust or anisotropic pressure as the matter content. A linear transformation on the initial data set and of the area radius shows the invariance of the physical parameters as well as the final fate of collapse, considering an arbitrary function of r as the initial area radius.

In this paper, the effect of a positive cosmological constant on spherically symmetric collapse with perfect fluid has been investigated. The matching conditions between static exterior and non-static interior spacetimes are given in the presence of a cosmological constant. We also study the apparent horizons and their physical significance. It is concluded that the cosmological constant slows down the collapse of matter and hence limit the size of the black hole. This analysis gives the generalization of the dust case to the perfect fluid. We recover the results of the dust case for p = 0.

An FRW brane model embedded in a conformally flat bulk is considered to study gravitational collapse for matter cloud in non-interacting combination of dark matter and dark energy. The form of dark energy is chosen as the decaying vacuum energy. Both expanding and contracting model of the universe are found for different time intervals with a time interval in between, which is a forbidden region.

Nuclear physics is an indispensable input for the investigation of high energy astrophysical phenomena involving compact objects. In this paper I take a gravitational collapse of massive stars as an example and show how the macroscopic dynamics is influenced by the properties of nuclei and nuclear matter. I will discuss two topics that are rather independent of each other. The first one is the interplay of neutrino-nuclei inelastic scatterings and the standing accretion shock instability in the core of core collapse supernovae and the second is concerning the neutrino emissions from black hole formations and their dependence on the equation of state at very high densities. In the latter, I will also demonstrate that future astronomical observations might provide us with valuable information on the equation of state of hot dense matter.

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with g₀₀ = 1. Israel's junction conditions are used to develop this formalism. The formulas for extrinsic curvature tensor are obtained. The general form of the surface energy–momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.

In this paper, the effect of electromagnetic field has been investigated on the spherically symmetric gravitational collapse with the perfect fluid in the presence of positive cosmological constant. Junction conditions between the static exterior and non-static interior spherically symmetric spacetimes are discussed. We study the apparent horizons and their physical significance. It is found that electromagnetic field reduces the bound of cosmological constant by reducing the pressure and hence collapsing process is faster as compared to the perfect fluid case. This work gives the generalization of the perfect fluid case to the charged perfect fluid. Results for the perfect fluid case are recovered.

We study the final outcome of gravitational collapse resulting from the plane symmetric charged Vaidya spacetime. Using the field equations, we show that the weak energy condition is always satisfied by collapsing fluid. It is found that the singularity formed is naked. The strength of singularity is also investigated by using Nolan's method. This turns out to be a strong curvature singularity in Tipler's sense and hence provides a counter example to the cosmic censorship hypothesis.

We explore the gravitational collapse of a spherically symmetric dust cloud in the Einstein–Gauss–Bonnet gravity without a cosmological constant, and obtain three families of LTB-like solutions. It is shown that the Gauss–Bonnet term has a profound influence on the nature of singularities, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the formation of a naked, massive and uncentral singularity, allowed in five-dimensional spacetime, is forbidden if D≥6. Moreover, such singularity is gravitational strong and a serious counterexample to CCH.

In this paper, the gravitational collapse has been studied in the context of higher-dimensional charged-Vaidya spacetime. It is shown that naked singularity always exists in this case and strong form of cosmic censorship is violated. This work extends the earlier studies on naked singularity formation in higher dimensions.

This paper is devoted to analyze the dynamics of plane symmetric gravitational collapse as well as energy density inhomogeneity in f(G) gravity. The field equations are constructed for dissipative isotropic source and Darmois junction conditions are used to discuss the process of collapse. We use Misner–Sharp mechanism to develop dynamical equation and couple it with transport equation to explore the impact of gravitational force on the collapsing rate. For constant f(G) model, we conclude that the rate of collapse slows down. Finally, we discuss the relationship between the Weyl tensor and physical quantities.

This paper investigates the phenomenon of gravitational collapse of Lemaitre–Tolman–Bondi (LTB) model in the presence of Brans–Dicke (BD) scalar field with nonzero potential field. We find a class of solutions by taking perfect fluid as well as scalar field and check the validity of weak energy conditions. It turns out that two different types of singularities are formed in the presence of scalar field. We conclude that the end state of gravitational collapse turns out to be a black hole (BH) contrary to general relativity (GR).

This paper is devoted to investigate the dynamics of the self-gravitating adiabatic and anisotropic source in 5D Einstein Gauss–Bonnet gravity. To this end, the source has been taken as Tolman–Bondi model which preserve inhomogeneity in nature. The field equations, Misner–Sharp mass and dynamical equations have formulated in Einstein Gauss–Bonnet gravity in 5D. The junction conditions have been explored between the anisotropic source and vacuum solution in Gauss–Bonnet gravity in detail. The Misner and Sharp approach has been applied to define the proper time and radial derivatives. Further, these helps to formulate general dynamical equations. The equations show that the mass of the collapsing system increases with the same amount as the effective radial pressure increases. The dynamical system preserves retardation which implies that system under-consideration goes to gravitational collapse.