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Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate…
The stellar stripping of satellites in cluster haloes is understood to play an important role in the production of intracluster light. Increasingly, cosmological simulations have been utilised to investigate its origin and assembly.…
Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced…
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature,…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…
We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner.…
I consider the appearance of shocks in hyperbolic formalisms of General Relativity. I study the particular case of the Bona-Masso formalism with zero shift vector and show how shocks associated with two families of characteristic fields can…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
Moving-puncture coordinates are commonly used in numerical simulations of black holes. Their properties for vacuum Schwarzschild black holes have been analyzed in a number of studies. The behavior of moving-puncture coordinates in…
The issue of consistency is crucial in quantum gravity. It has recently been intensively addressed for effective symmetry-reduced models. In this article, we exhaustively study the anomaly freedom of effective loop quantum cosmology with…
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…
Beyond convergence studies and comparison of different codes, there are essentially no controls on the accuracy in the non-linear regime of cosmological N body simulations, even in the dissipationless limit. We propose and explore here a…
Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial…
We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as "usual", "naked" and "truly naked" ones depending on the near-horizon behavior of transverse tidal forces…
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by…