Narrow Results

We introduce our numerical studies of gravitational collapses in five-dimensional (5D) space-time, with a purpose of studying the cosmic censorship hypothesis and the hoop conjecture. The first model is the collapse of spindle matter which was performed by Shapiro and Teukolsky (1991) who announced an appearance of a naked singularity in 4D. Comparing with 4D cases, we found that 5D collapses proceed more rapidly, the final configurations tend to be spherical, and apparent horizon (AH) forms in wider parameter ranges. We also observed positive evidence for formation of a naked singularity in highly spindle cases as well. The second model is the formation of black-ring in 5D. Our code does not include angular momentum, but the model would be helpful for basic understandings. We constructed an initial data sequence with ring-shaped matter, and observed the topology of AHs, if formed. We found a critical ring radius for ring-shaped AH, and it suggests a dynamical transition of AH topology from ring-shaped to spherical. We demonstrate such an example in time evolution.

Hawking’s singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a non-negative effective energy density (EED). The SEC ensures the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed even in the simplest of cases, like the Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and weighted local averages of energy densities such as quantum energy inequalities (QEIs). We present lower bounds of the EED for both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent QEIs valid for the class of Hadamard states. We also discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction, the spacetime is future timelike geodesically incomplete.

The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. Here, we provide motivation for an energy condition obeyed in semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. Using SNEC as an assumption we proceed to prove a singularity theorem. This theorem extends the Penrose singularity theorem to semiclassical gravity and has interesting applications to evaporating black holes.

We present recent results on the asymptotics of a brane-world that consists of a flat 3-brane embedded in a five-dimensional bulk. The bulk matter is modelled by a fluid that satisfies a nonlinear equation of state of the form p = γρ^λ, where p is the ‘pressure’ and ρ is the ‘density’ of the fluid. We show that for appropriate ranges of the parameters γ and λ, it is possible to construct a regular solution, compatible with energy conditions, that successfully localizes gravity on the brane. These results improve significantly previous findings of the study of a bulk fluid with a linear equation of state.

We consider singularities of static spherically symmetric objects in minimal dilatonic gravity. They are only partially studied and purely understood even in the simplest models of extended gravity. We introduce the proper form of the structure equations and derive a set of all singularities, which turn to form several types of sub-manifolds of the phase space. We also introduce for the first time the Lyapunov function for the corresponding system, its equation, and its basic properties. The dependence on the mass of the dark scalar is discussed.

Using exactly solvable models, it is shown that black hole singularities in different electrically charged configurations can be cured. Our solutions describe black hole space-times with a wormhole giving structure to the otherwise point-like singularity. We show that geodesic completeness is satisfied despite the existence of curvature divergences at the wormhole throat. In some cases, physical observers can go through the wormhole and in other cases the throat lies at an infinite affine distance.

In this work we present an overview on the absorption features of Bardeen regular black holes In particular, we compute the absorption cross section of planar massless scalar waves – for arbitrary frequencies – showing that it approaches the area of the black hole in the small-frequency regime and the capture cross section in the high-frequency regime. We also compare with the case of Reissner-Nordström black holes.

We analyze the causal structure of some big-bang and black hole singularities. We find that the topology of the lightcones remains intact, despite the fact that the metric is singular. The topology of the lightcones allows spacelike foliations of the singularities, which are therefore compatible with global hyperbolicity and causality. The fact that the lightcones at different events have the same topology no matter whether the events are at or outside the singularities suggests that the causal structure is more universal and fundamental than the metric, which is very different at the singularities.

Dirac fermions and electromagnetic fields are considered as the source of gravitation in the framework of standard Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. It is shown that all solutions for the scale-factor a(t) are non-singular, provided the cosmological constant Λ is set to be less than the positive inverse of a quantum scale.

The gravitational interaction is expected to be modified for very short distances. This is particularly important in situations in which the curvature of spacetime is large in general, such as close to the initial cosmological singularity. The gravitational dynamics is then captured by the higher curvature terms in the action, making it difficult to reliably extrapolate any prediction of general relativity. In this note we review pure Lovelock equations for Kasner-type metrics. These equations correspond to a single Nth order Lovelock term in the action in d = 2N + 1, 2N + 2 dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. These are classified in several isotropy types. Some of these families correspond to degenerate classes of solutions, such that their dynamics is not completely determined by the equations of pure Lovelock gravity. Instead, these Kasner solutions become sensitive to the subleading terms in the Lovelock series.

The question of whether timelike classical singularities can be “healed” in a quantum setting is addressed. Roberts apace-time and a class of self-similar, spherically-symmetric space-times are analyzed to determine if quantum wave probes detect the singularity. In cases in which they do not, we can say the singularity is “healed”.