相关论文: On the Equivalence of Spacetimes, the Cartan-Karlh…

In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at…

In this paper we introduce an algorithm to determine the equivalence of five dimensional spacetimes, which generalizes the Karlhede algorithm for four dimensional general relativity. As an alternative to the Petrov type classification, we…

A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…

It was recently conjectured that a certain vacuum Kerr-Schild spacetime, which may be regarded as a self-dual analog of the Kerr metric, is equivalent to the self-dual Taub-NUT instanton. We confirm this conjecture by applying the…

A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean…

This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures.…

Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…

This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the…

Einstein's Equivalence Principle is used with the electromagnetic spectrum to translate meters and seconds into radians and seconds. Based on a unique geometric relationship, a new transformation of velocities and a changed Lorentz…

We employ the Cartan-Karlhede algorithm in order to completely characterize the class of G\"odel-like spacetimes for three-dimensional gravity. By examining the permitted Segre types (or P-types) for the Ricci tensor we present the results…

In this paper, we classify space-time curves up to Galilean group of transformations with Cartan's method of equivalence. As an aim, we elicit invariats from action of special Galilean group on space-time curves, that are, in fact,…

Using Cartan's equivalence method for point transformations we obtain from first principles the conformal geometry associated with third order ODEs and a special class of PDEs in two dimensions. We explicitly construct the null tetrads of a…

We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. These…

A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…

The equivalence principle can be tested by precision experiments based on classical and quantum systems, on the ground as well as in space. In many models, these tests are mostly equivalent in their ability to constrain physics beyond the…

In this paper, we carry out the equivalence problem for fifth-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. Two versions of equivalence problems have been…

In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…

Trajectories of light rays in a static spacetime are described by unparametrised geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate…

We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…

A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of Karlhede…