Related papers: Time vector defined in imaginary space of spatial …
A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These…
Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields…
The paper presents a relativistic space-time diagram, which displays in true values the space (Cartesian and polar) and the time coordinates of the same event detected from two inertial reference frames in relative motion related by the…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
This essay summarizes the efforts required to build a program of a unified, low-dimension topology that allows characterizing all these flat space-times. Since spatiotemporal manifolds are topological spaces equipped with metrics, their…
This paper presents a pedagogical introduction to the issue of how to implement Lorentz transformations in relativistic visualization. The most efficient approach is to use the even geometric algebra in 3+1 spacetime dimensions, or…
We present a topological classification of vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology…
Einstein's general relativity relates the curvature of space time, a second order differential property, to the stress-energy-momentum tensor. In this paper we ask whether it is possible to develop a first order theory relating space-time…
We study an analytical solution to the Einstein's equations in 2+1-dimensions. The space-time is dynamical and has a line symmetry. The matter content is a minimally coupled, massless, scalar field. Depending on the value of certain…
I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn…
In the framework of Lagrangian perturbation theory in general relativity we discuss the possibility to split the Einstein equations, written in terms of spatial Cartan coframes within a 3+1 foliation of spacetime, into gravitoelectric and…
We introduce a definition of symmetry generating vector fields on manifolds which are equipped with a first-order reductive Cartan geometry. We apply this definition to a number of physically motivated examples and show that our newly…
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead…
The formulation of General Relativity in which the 4-dimensional space-time is embedded in a flat host space of higher dimension is reconsidered. New classes of embeddings (modeled after Nash's classical free embeddings) are introduced.…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
We reformulate the general theory of relativity in the language of Riemann-Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed…
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…