We adapt Sbierski's proof of C^0-inextendibility of the maximal analytic Schwarzschild spacetime to a broad class of warped-product black hole spacetimes with a static exterior region. These spacetimes are globally hyperbolic, have a codimension-two Riemannian fibre and a radial coordinate (r), which serves as the warping function of the fibre. They admit a spacetime singularity as r → 0, characterised by the divergence of the Kretschmann scalar. This class encompasses nonvacuum black hole models and geometries beyond spherical symmetry. Under suitable assumptions, including that the fibre is closed (compact without boundary), connected, homogeneous, and orientable, we establish future C^0-inextendibility for spacetimes in this class. The result further extends to spacetimes possessing more than one regular black hole horizon.

Recently there has been an interest in exploring black holes that are regular in that the central curvature singularity is avoided. Here, we give a recipe to obtain a regular black hole spacetime from the unhindered gravitational collapse from regular initial data of a spherically symmetric perfect fluid. While the classic Oppenheimer-Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the centre, we show here that there are classes of regular initial conditions when collapse gives rise to a regular black hole.

A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if at least one of these causal geodesics is past incomplete. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I matter fields in an arbitrarily finite number of dimensions. In the spirit of Joshi and Dwivedi (1993 Phys. Rev. D 47 5357), and Goswami and Joshi (2007 Phys. Rev. D 76 084026), beginning with regular initial data, we derive two distinct (but not mutually exclusive) conditions, which we call the positive root condition (PRC) and the simple positive root condition (SPRC), that serve as necessary and sufficient conditions, respectively, for the existence of naked singularities. In doing so, we generalize the results of both the aforementioned works. We further restrict the PRC and the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak (1985 J. Geom. Phys. 2 127) on all causal curves that satisfy the causal convergence condition. The CGC then gives a sufficient condition ensuring that the naked singularities implying the PRC and implied by the SPRC, are of strong curvature type and hence correspond to the inextendibility of the spacetime. Using the CGC, we extend the results of Mosani et al (2020 Phys. Rev. D 101 044052) (that hold for dimension N = 4) to the case N = 5, showing that strong curvature naked singularities can occur in this case. However, for the case , we show that past-incomplete causal curves that identify naked singularities do not satisfy the CGC. These results shed light on the validity of the cosmic censorship conjectures in arbitrary dimensions.

In the case of unhindered gravitational collapse of matter cloud governed by the Lemaitre-Tolman-Bondi (LTB) spacetime, the end-state singularity is either locally visible, globally visible or completely hidden. We have a past-null singularity in the first two cases while a future-spacelike singularity in the last case. Here, we show an example of a gravitational collapse model whose end-state is a future-null-singularity (it has a causal property that is unlike the cases involving LTB spacetime). We depict such a distinct causal structure of the singularity by conformal diagrams.

A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if at least one of these causal geodesics is past incomplete. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I matter fields in an arbitrarily finite number of dimensions. In the spirit of Joshi and Dwivedi (1993 Phys. Rev. D 47 5357), and Goswami and Joshi (2007 Phys. Rev. D 76 084026), beginning with regular initial data, we derive two distinct (but not mutually exclusive) conditions, which we call the positive root condition (PRC) and the simple positive root condition (SPRC), that serve as necessary and sufficient conditions, respectively, for the existence of naked singularities. In doing so, we generalize the results of both the aforementioned works. We further restrict the PRC and the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak (1985 J. Geom. Phys.2 127) on all causal curves that satisfy the causal convergence condition. The CGC then gives a sufficient condition ensuring that the naked singularities implying the PRC and implied by the SPRC, are of strong curvature type and hence correspond to the inextendibility of the spacetime. Using the CGC, we extend the results of Mosani et al (2020 Phys. Rev. D 101 044052) (that hold for dimension N = 4) to the case N = 5, showing that strong curvature naked singularities can occur in this case. However, for the case N >= 6 , we show that past-incomplete causal curves that identify naked singularities do not satisfy the CGC. These results shed light on the validity of the cosmic censorship conjectures in arbitrary dimensions.

We study here the unhindered gravitational collapse of spatially homogeneous (SH) scalar fields $\phi$ with a potential $V_{s}(\phi)$, as well as vector fields $\tilde{A}$ with a potential $V_{v}(B)$ where $B=g(\tilde{A},\tilde{A})$ and $g$ is the metric tensor. We show that in both cases, classes of potentials exist that give rise to black holes or naked singularities depending on the choice of the potential. The strength of the naked singularity is examined, and they are seen to be strong, in the sense of Tipler, for a wide class of respective potentials. We match the collapsing scalar/vector field with a generalized Vaidya spacetime outside. We highlight that full generality is maintained within the domain of SH scalar or vector field collapse.

We investigate the global causal structure of the end state of a spherically symmetric marginally bound Lemaitre–Tolman–Bondi (LTB) (Lemaitre 1933 Ann. Soc. Sci. Brux. A 53 51, Tolman 1934 Proc. Natl Acad. Sci. USA 20 169–76, Bondi 1947 Mon. Not. Astron. Soc. 107 410) collapsing cloud (which is well studied in general relativity) in the framework of modified gravity having the generalized Lagrangian R + α R 2 in the action. Here R is the Ricci scalar, and α ⩾ 0 is a constant. By fixing the functional form of the metric components of the LTB spacetime, using up the available degree of freedom, we realize that the matching surface of the interior and the exterior metric are different for different values of α . This change in the matching surface can alter the causal property of the first central singularity. We depict this by showing a numerical example. Additionally, for a globally naked singularity to have physical relevance, a congruence of null geodesics should escape from such singularity to be visible to an asymptotic observer for infinite time. For this to happen, the first central singularity should be a nodal point. We here give a heuristic method to show that this singularity is a nodal point by considering the above class of theory of gravity, of which general relativity is a particular case.

We investigate here the locally naked singularity formed due to a spherically symmetric inhomogeneous collapsing cloud having non-zero isotropic pressure, in terms of its strength. Sufficient condition provided by Clarke and Krolak for it to be Tipler strong has been used to restrict the parameters that represent the non-linear relation between the physical radius and the radial coordinate of the outgoing radial null geodesic at the singular center. Studying end state of a collapsing cloud requires information about the dynamics of collapse, which is unknown in a general scenario. Hence we study small perturbations to the mass profile for inhomogeneous dust, which is possible using the formalism developed here. This perturbed mass profile, in turn, gives rise to non-zero pressure. We show the existence of a non-zero measure set of initial data giving rise to such strong curvature naked singularity.

We investigate here the final state of gravitational collapse of a non-spherical and non-marginally bound dust cloud as modeled by the Szekeres spacetime. We show that a directionally globally naked singularity can be formed in this case near the collapsing cloud boundary and not at its geometric center, as is typically the case for a spherical gravitational collapse. This singularity is a strong curvature naked singularity in the sense of Tipler criterion on gravitational strength. The null geodesics escaping from the singularity would be less scattered in this case in certain directions since the singularity is close to the boundary of the cloud, as is the case in the current scenario. The physical implications are pointed out.

What happens to a massive star at the end of its life cycle is one of the most important and intriguing questions in theoretical physics. An unhindered gravitational collapse of such a sufficiently massive star can give rise to a spacetime singularity. This thesis discusses the phenomenon of such unhindered gravitational collapse and the causal structure of the singularity thus formed.

We investigate the unhindered gravitational collapse of a homogeneous scalar field with nonzero potential, a two-dimensional analog of the Mexican hat-shaped Higgs field potential. The collapsing scalar field is surrounded by an exterior retarded (outgoing) generalized Vaidya spacetime. We prove that the density dependence on the scale factor cannot be expressed as an algebraic function in such a scenario. For a certain transcendental expression of the density of such field as a function of scale factor, we then show that the collapse evolves to a singularity at an infinite comoving time, which is equivalent to saying that the singularity is avoided altogether. An ultra high density region of the order of Planck length can, however, be reached in a finite comoving time. The absence of the formation of trapped surfaces makes this ultra high density region globally visible.

The global visibility of a singularity as an end state of the gravitational collapse of a spherically symmetric pressureless cloud is investigated. We show the existence of a non-zero measured set of parameters: the total mass and the initial mean density of the collapsing cloud, giving rise to a physically strong globally visible singularity as the end state for a fixed velocity function. The existence of such a set indicates that such singularity is stable under small perturbation in the initial data causing its existence. This is true for marginally as well as non-marginally bound cases. The possibility of the presence of such suitable parameters in the astrophysical setup is then studied: (1) The singularities' requirements at the centre of the M87 galaxy and at the centre of our galaxy (SgrA(*)) to be globally visible are discussed in terms of the initial size of the collapsing cloud forming them, presuming that such singularities are formed due to gravitational collapse. (2) The requirement for the primordial singularities formed due to a collapsing configuration after getting detached from the background universe at the time of matter-dominated era just after the time of matter-radiation equality, to be globally visible, is discussed. (3) The scenario of the collapse of a neutron star after reaching a critical mass, which is achieved by accreting the supernova ejecta expelled by its binary companion core progenitor, is considered. The primary aim of this paper is to show that globally visible singularities can form in astrophysical setups under appropriate circumstances.

We investigate here the local versus global visibility of a spacetime singularity formed due to the gravitational collapse of a spherically symmetric dust cloud having a nonzero velocity function. The conditions are investigated that ensure the global visibility of the singularity, in the sense that the outgoing null geodesics leave the boundary of the matter cloud in the future, whereas, in the past, these terminate at the singularity. Explicit examples of this effect are constructed. We require that this must be a strong curvature singularity in the sense of Tipler, to ensure the physical significance of the scenario considered. This may act as a counterexample to the weak cosmic censorship hypothesis.

Gravitational collapse of a spherically symmetric homogeneous perfect barotropic fluid with linear as well as polytropic-type Equation of State (EoS) has been investigated in the framework of a linear model of [Formula: see text] gravity. This modified gravity has the potential to explain the observed cosmic acceleration. The calculations have been done taking the transformed time coordinate [Formula: see text], where [Formula: see text] is the initial density of the fluid. For linear EoS [Formula: see text], the condition for being a true singularity, along with sufficient condition for the formation of apparent horizon covering the singularity has been derived. For a polytrope having the EoS [Formula: see text], the scale factor [Formula: see text] as a function of fluid density [Formula: see text] has been obtained which is then used to study the dynamics of the fluid. Role of the polytropic index [Formula: see text] and the constant of proportionality [Formula: see text] in the dynamics of the fluid is also studied. A new type of exotic matter field having varied dependence of scale factor on the density, and having the potential to give rise to bouncing cosmology, provided it is the dominating fluid in the universe, is obtained in this domain and is investigated. Energy conditions are discussed.

We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in R-2 gravity. We make our calculations using dimensionless time with characteristic timescale t(g) similar to (G(rho))(-1/2), where rho is a density of collapsing matter. The cases of matter, radiation and stiff matter are considered. We also account the possible existence of vacuum energy and its influence on gravitational collapse. In a case of R-2 gravity, we have additional degree of freedom for initial conditions of collapse. For barotropic equation of state (EoS) p = w rho, the result depends from the value of parameter w: for w > 1/3 the collapse occurs slowly in comparison with General Relativity while for w < 1/3, we have the opposite situation. Vacuum energy as expected slows down the rate of collapse and for some critical density gravitational contraction may change to expansion. It is interesting to note that for General Relativity such expansion is impossible. We also consider the collapse in the presence of so-called phantom energy. For description of phantom energy, we use Lagrangian in the form -X - V (where X and V are the kinetic and potential energy of the field, respectively) and consider the corresponding Klein-Gordon equation for phantom scalar field.

The gravitational collapse of a barotropic perfect fluid having the Equation of State (EoS) $p=k\rho$, where $k$ is constant, is studied here in the framework of general relativity. We examine the restrictions on the Misner-Sharp mass function, because of the introduction of such an EoS, in terms of the compatibility of a certain pair of quasi-linear partial differential equations, obtained from Einstein's field equations. We find that except when this system of PDEs reduces to ODEs because of additional symmetries imposed on the spacetimes, or when they become compatible with each other in some special situations, consistent solution to perfect fluid collapse with linear EoS is not available. The end state of collapse with no such constraint of EoS has also been investigated. Since considering arbitrary pressures in a collapsing cloud to study its end state is difficult as this requires information about the dynamics of collapse not known in general, we consider small perturbations to mass profiles corresponding to inhomogeneous dust collapse. This, in turn, provides small pressure perturbations to the otherwise pressureless fluid. The dependence of visibility or otherwise of the singularity on initial conditions of collapse, in the presence or absence of such perturbations is studied numerically. As long as no linear EoS is imposed on the matter field, no incompatibility issue between its corresponding pair of PDEs arise, unlike the case when $k$ is restricted to be a constant.