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The singularity theorem by Hawking and Penrose qualifies Schwarzschild black-holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows to probe the…
We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion)…
Non--minimal repulsive singularities (``repulsons'') in extended supergravity theories are investigated. The short distance antigravity properties of the repulsons are tested at the classical and the quantum level by a scalar…
We discuss the opportunity that the singularity inside a Schwarzschild black hole could be replaced by a regular bounce, described as a regular minimum of the spherical radius (instead of zero) and a regular maximum of the longitudinal…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear…
The concept of individuality in quantum mechanics shows radical differences from the one used in classical physics. In particular, it is not possible to consider the fundamental particles described by quantum theory as individual…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter "power-law" metrics we identify those parameters for which the spacetimes have classical…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
Schwarzschild black-hole interiors border on space-like singularities representing classical information leaks. We show that local quantum physics is decoupled from these leaks due to dynamically generated boundaries, called Zeno borders.…
We examine the Schwarzschild interior of a black hole, incorporating quantum gravitational modifications due to loop quantum gravity. We consider an improved loop quantization using techniques that have proven successful in loop quantum…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
We investigate the properties of the Schwarzschild black hole geometry involving leading one-loop long-distance quantum effects, which arise within the framework of effective field theories of gravity. Our analysis reveals that geodesic…
A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an…
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
Classical general relativity predicts that a contracting, spherically symmetric matter system with a large-enough mass will result in the formation of a trapped region whose outer boundary is an apparent horizon where the gravitational…
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…