Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse

Exploration of a singular fluid spacetime

We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter w = p / ρ , there exist static, spherically-symmetric solutions with density profile ∝ 1 / r 2 , with the constant of proportionality fixed to be a special function of w. Like black holes, singular isothermal spheres possess a fixed mass-to-radius ratio independent of size, but no horizon cloaking the curvature singularity at r = 0 . For w = 1 , these solutions can be constructed from a homogeneous dilaton background, where the metric spontaneously breaks spatial homogeneity. We study the perturbative structure of these solutions, finding the radial modes and tidal Love numbers, and also find interesting properties in the geodesic structure of this geometry. Finally, connections are discussed between these geometries and dark matter profiles, the double copy, and holographic entropy, as well as how the swampland distance conjecture can obscure the naked singularity.

Hyperbolically Symmetric Versions of Lemaitre-Tolman-Bondi Spacetimes

We study fluid distributions endowed with hyperbolic symmetry, which share many common features with Lemaitre–Tolman–Bondi (LTB) solutions (e.g., they are geodesic, shearing, and nonconformally flat, and the energy density is inhomogeneous). As such, they may be considered as hyperbolic symmetric versions of LTB, with spherical symmetry replaced by hyperbolic symmetry. We start by considering pure dust models, and afterwards, we extend our analysis to dissipative models with anisotropic pressure. In the former case, the complexity factor is necessarily nonvanishing, whereas in the latter cases, models with a vanishing complexity factor are found. The remarkable fact is that all solutions satisfying the vanishing complexity factor condition are necessarily nondissipative and satisfy the stiff equation of state.

A non-static quantum inspired spacetime in f(R) gravity: Gravity's rainbow

In this note we explore a non-static spacetime in quantum regime in the background of f ( R ) gravity. The time dependent Vaidya metric which represents the spacetime of a radiating body like star is studied in an energy dependent gravity's rainbow, which is a UV completion of General Relativity. In our quest we have used gravitational collapse as the main tool. The focus is to probe the nature of singularity (black hole or naked singularity) formed out of the collapsing procedure. This is achieved via a geodesic study. For our investigation we have considered two different models of f ( R ) gravity, namely the inflationary Starobinsky's model and the power law model. Our study reveals the fact that naked singularity is as good a possibility as black hole as far as the central singularity is concerned. Via a proper fine tuning of the initial data, we may realize both black hole or naked singularity as the end state of the collapse. Thus this study is extremely important and relevant in the light of the Cosmic Censorship hypothesis. The most important result derived from the study is that gravity's rainbow increases the tendency of formation of naked singularities. We have also deduced the conditions under which the singularity will be a strong or weak curvature singularity. Finally in our quest to know more about the model we have performed a thermodynamical study. Throughout the study we have obtained results which involve deviation from the classical set-up. Such deviations are expected in a quantum evolution and can be attributed to the quantum fluctuations that our model suffers from. It is expected that this study will enhance our knowledge about quantization of gravity and subsequently about the illusive theory of quantum gravity.

Quantum evaporation of a naked singularity

We investigate here quantum effects in gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that nonperturbative semiclassical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before the singularity can form. Quantum gravitational effects thus censor naked singularities by avoiding their formation. Further, quantum gravity induced mass flux has a distinct feature which may lead to a novel observable signature in astrophysical bursts.

Generic cosmic-censorship violation in anti-de Sitter space

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.