In this article the method of conformal transformation is used to generate perfect fluid solutions of Einstein’s equations from vacuum spacetimes. The conditions on the conformal factor in order to generate a perfect fluid spacetime are presented. With Minkowski as a seed spacetime, these conditions are applied and a particular solution is found. It belongs to the family of Stephani spacetimes ...

In the framework of metric-free electrodynamics, we start with a linear spacetime relation between the excitation 2-form H = (D,H) and the field strength 2-form F = (E,B). This linear relation is constraint by the so-called closure relation. We solve this system algebraically and extend a previous analysis such as to include also singular solutions. Using the recently derived fourth order Fresn...

These notes show how observers can set up a coordinate system and measure the spacetime geometry using clocks and lasers. The approach is similar to that of special relativity, but the reader must not be misled. Spacetime diagrams with rectilinear axes do not imply flat spacetime any more than flat maps imply a flat earth. Cartography provides an excellent starting point for understanding the m...

where Rij is the Ricci curvature tensor of the metric and R is its scalar curvature. This equation tells us how the metric tensor gij (i.e. the field mediating the gravitation) is obeying to constraints imposed by the energy-momentum tensor Tij , which encodes informations about the distribution of energy and momentum in spacetime. For simplicity we will assume in the following that Tij = 0, i....

This work describes the formulation of the manifestly ghost-free (spacetime) light-cone gauge for bosonic string theory with non-trivial spacetime metric, antisymmetric tensor, dilaton and tachyon fields. The action is a general two-dimensional sigma model, corresponding to a closed string theory with a second order action in the Polyakov picture. The spacetime fields must have a symmetry gener...

Several approaches to quantum gravity (including the model of superplastic vacuum; Diakonov tetrads emerging as bilinear combinations fermionis fields; BF-theories gravity; and effective acoustic metric) suggest that in general relativity metric must have dimension 2, i.e., [g??] = 1/[L]2, irrespective spacetime. This leads “dimensionless physics” discussed [1]. Here we continue exploit this un...

The really novel feature of General Relativity (henceforth abbreviated GR), as compared to other field theories in physics, is that spacetime is not a fixed background arena that merely stages physical processes. Rather, spacetime is itself a dynamical entity, meaning that its properties depend in parts on its specific matter content. Hence, contrary to the Newtonian picture, in which spacetime...

The theory of gauge-invariant non-spherical metric perturbations of a Schwarzschild spacetime is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this paper is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equatio...

We report on the first results of self-consistent second order metric perturbations produced by a point particle moving in the Schwarzschild spacetime. The second order waveforms satisfy a wave equation with an effective source term build up from products of first order metric perturbations and its derivatives. We have explicitly regularized this source term at the particle location as well as ...