Related papers: Topology change with Morse functions: progress on …
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Modified Newtonian dynamics (MOND) is a possible way to explain the flat galaxy rotation curves without invoking the existence of dark matter. It is however quite difficult to predict such a phenomenology in a consistent field theory, free…
We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie…
In present work we examine the implications on both, space-time measures and causal structure, of a generalization of the local causality postulate by asserting its validity to all motion regimes, the subluminal and superluminal ones. The…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
We address some issues of topological defect inflation. (1) We clarify the causal structure of an inflating magnetic monopole. The spacetime diagram shows explicitly that this model is free from the ``graceful exit'' problem, while the…
We show that superpositions of classical states in quantum gravity with fixed topology can lead to new classical states with a different topology. We study this phenomenon in a particular limit of the LLM geometries. In this limit, the UV…
In 1946, M. Morse proposed a conjecture that an analytic topologically transitive systems is metrically transitive. We prove this Morse conjecture for flows on a closed orientable surface of negative Euler characteristic. As a consequence,…
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the…
It is argued that the surface radius of a compact source can not be less than its gravitational radius due to the strong gravitational time dilation effects. The such "topological" difference between the Newtonian and relativistic gravity…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
The cold dark matter paradigm has been extremely successful for explaining a wide range of cosmological phenomena. Nevertheless, since evidence for non-baryonic dark matter remains indirect, all reasonable alternatives should be explored.…
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates the description and computation via Morse theory of key topological invariants. Here we establish checkable…
We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we…
The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the…
Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in…
A theory of topological gravity is a homotopy-theoretic representation of the Segal-Tillmann topologification of a two-category with cobordisms as morphisms. This note describes a relatively accessible example of such a thing, suggested by…
The trace anomaly and the cosmological constant problem are two typical breakdowns when applying the quantum principle to a general covariant or gravitational system. A quantum theory of spacetime reference frame is proposed and reviewed.…
Modified Newtonian Dynamics (MOND) is an alternative to the dark matter hypothesis that attempts to explain the "missing gravity" problem in astrophysics and cosmology through a modification to objects' dynamics. Since its conception in…
It was recently proposed that the effects usually attributed to particle dark matter on galaxy scales are due to the displacement of dark energy by baryonic matter, a paradigm known as emergent gravity. This formalism leads to predictions…