Related papers: Gordon Metric Revisited
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric.…
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic…
This paper introduces an alternative generalization of the static solution with quadrupole moment, the $\rm q$-metric, that describes a deformed compact object in the presence of the external fields characterized by multipole moments. In…
We introduce the geodesic complexity of a metric space, inspired by the topological complexity of a topological space. Both of them are numerical invariants, but, while the TC only depends on the homotopy type, the GC is an invariant under…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields…
The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations,…
Area metrics are an intriguing generalization of length metrics which appears in several quantum-gravity approaches. We describe the space of diffeomorphism-invariant area-metric actions quadratic in fluctuations and derivatives. A general…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
A recently proposed pregeometric auxiliary vector mediated gauge theory is studied in its canonical domain, by performing the Legendre transform on a curved background and by considering its covariant phase space, with further application…
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories. Certain steps towards the generic case…
Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing…
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…