Related papers: Exponential stretch-rotation (ESR) formulation of …
The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a…
It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating…
The extended semantic realism (ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
This paper completes and comments on some aspects of our previous publications. In ref [1], we have derived a set of space-time transformations referred to as the extended space-time transformations. These transformations, which assume the…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
We examine geometry and dynamics of classical spacetime derived from entanglement spectrum. The spacetime is a kind of canonical parameter space defined by the Fisher information metric. As a concrete example, we focus on the spectrum for…
In recent years, gravitational models motivated by quantum corrections to gravity which introduce higher order terms like $R^{2}$ or terms in which the Riemann tensor is not symmetric have been studied by several authors in the form of a…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a…
Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of…
The observable spacetime can be viewed as worldline coincidences (events) between a particle system and the observers of an extended (material) reference frame (ERF). Particle positions are then operationally well defined with respect to…
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
Since the early days of the theory of electromagnetism and of gravity the idea of space, then space-time, as a sort of physical continuum hovered the scientific community. Actually general relativity shows the strong similarity that exists…
A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics…
We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions…
It is well known that Einstein General Relativity can be expressed covariantly in bi-metric spacetime, without the uncertainties which arise from the effects of gravitational energy-momentum pseudo-tensors. However the effect that the…
We extend the geometrical ideas of the spacetime deformations to study the physical foundation of the post-Riemannian geometry. To this aim, we construct the theory of 'two-step spacetime deformation' as a guiding principle. We address the…
This remodeled form of Einstein's relativity theories retains and incorporates only experimentally proven principles. It is based on a generalized law for spinning and rotational motions, which is in fact the conservation law of momentum…