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A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Królak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the causal structure and the curvature strength of the singularities. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.

This paper is a further development of the approach to weak cosmic censorship proposed by the authors in Ref. 5. We state and prove a modified version of that work's main result under significantly relaxed assumptions on the asymptotic structure of spacetime. The result, which imposes strong constraints on the occurrence of naked singularities of the strong curvature type, is in particular applicable to physically realistic cosmological models.

A five-dimensional Einstein spacetime with (non)vanishing cosmological constant is analyzed in detail. The metric is in close analogy with the four-dimensional massless uncharged C-metric in many aspects. The coordinate system, horizons and causal structures, relations to standard form of de Sitter, anti de Sitter and Minkowski vacua are investigated. After a boost and Kaluza–Klein reduction, we get an exact solution of four-dimensional Einstein–Maxwell–Liouville theory which reduces to a solution to Einstein–Liouville theory in the limit of zero boost velocity and to that of Einstein–Maxwell–dilaton theory in the case of zero cosmological constant.

We study the influence of the spin-torsion coupling prescription and we prove the causal propagation for the fields of the standard model.

In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear methods ineffective. Moreover, signals sampled from real world systems are noisy and short, posing additional constraints on the estimation of the underlying couplings. In this article, we compare a set of six recently introduced methods for quantifying the causal structure of bivariate time series extracted from systems with complex dynamical behavior. We discuss the usefulness of the methods for detecting asymmetric couplings and directional flow of information in the context of uni- and bidirectionally coupled deterministic chaotic systems.

In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (∂ϕ)²/2-V(ϕ), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the conventional stress tensor , the tensor which is quadratic in , and describing interaction with the bulk. For models under study, the tensor has zero divergence, allowing one to consider . Such a brane, whose 4D gravity is decoupled from the bulk geometry, may be called minimally coupled. Assuming , we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a cosmological constant in GR: Minkowski, Schwarzschild, (anti-) de Sitter and Schwarzschild–(anti-)de Sitter. A no-hair theorem, saying that, given a potential V≥0, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.

I argue that an approach which uses an appropriate admixture of both classical and semiclassical effects is essential for understanding the ultimate fate of gravitational collapse and the nature of black holes (BHs). I provide an example of a problem which pushes the boundaries of what is known in both the classical and semiclassical approaches: the evolution of the inner horizon of a BH. I show that solving this problem requires considering perturbations of both classical and semiclassical origins. In fact, it has been found that classical mass inflation might be counteracted by a semiclassical tendency for the inner horizon to inflate outward.

Constructive gravity allows to calculate the Lagrangian for gravity, provided one previously prescribes the Lagrangian for all matter fields on a spacetime geometry of choice. We explain the physical and mathematical foundation of this result and point out how to answer questions about gravity that previously could not be meaningfully asked.

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.

Astronomical observations of distant quasars may be important to test models for quantum gravity, which posit Planck-scale spatial uncertainties (‘spacetime foam’) that would produce phase fluctuations in the wavefront of radiation emitted by a source, which may accumulate over large path lengths. We show explicitly how wavefront distortions cause the image intensity to decay to the point where distant objects become undetectable if the accumulated path-length fluctuations become comparable to the wavelength of the radiation. We also reassess previous efforts in this area. We use X-ray and gamma-ray observations to rule out several models of spacetime foam, including the interesting random-walk and holographic models.