Related papers: Complex geometry and fundamental physical law
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…
A method is presented to construct a particular, non-minimally coupled scalar-tensor theory such that a given metric is an exact vacuum solution in that theory. In contrast to the standard approach in studies of gravitational dynamics,…
Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers…
The classical theory of $G$-structures, which include almost-complex structures, explains the relationship between the curvature of compatible connections and integrability. This note is an effort to understand how the curvature of…
The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…
Scalar-tensor theories offer the prospect of explaining the cosmological evolution of the Universe through an effective description of dark energy as a quantity with a non-trivial evolution. In this work, we investigate this feature of…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
Kinetic mixing between the metric and scalar degrees of freedom is an essential ingredient in contemporary scalar-tensor theories. This often makes hard to understand their physical content, especially when derivative mixing is present, as…
A holomorphy potential is a complex valued function whose complex gradient, with respect to some K\"ahler metric, is a holomorphic vector field. Given $k$ holomorphic vector fields on a compact complex manifold, form, for a given K\"ahler…
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor…
The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value…
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…
Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the…