相关论文: On the (1+3) threading of spacetime with respect t…
We introduce and develop the 1+3 covariant approach to relativity and cosmology to spacetimes of arbitrary dimensions that have nonzero torsion and do not satisfy the metricity condition. Focusing on timelike observers, we identify and…
The 1+3 covariant equations, embedded in an extended tetrad formalism and describing a space-time with an arbitrary energy-momentum distribution, are reconsidered. It is shown that, provided the 1+3 splitting is performed with respect to a…
We continue our research work started in "Kinematic Quantities and Raychaudhuri Equations in a $5D$ Universe" (Eur. Phys. J. C, 2015), and obtain in a covariant form, the equations of motion with respect to the $(1+1+3)$ threading of a $5D$…
I present a covariant approach to developing 1+3 formalism without an introduction of any basis or coordinates. In the formalism, a spacetime which has a timelike congruence is assumed. Then, tensors are split into temporal and spatial…
We discuss and prove a theorem which asserts that any n-dimensional semi-Riemannian manifold can be locally embedded in a (n+1)-dimensional space with a non-degenerate Ricci tensor which is equal, up to a local analytic diffeomorphism, to…
Conformally flat spacetimes with an elastic stress energy tensor given by a diagonal trace-free anisotropic pressure tensor are investigated using 1+3 formalism. We show how the null tetrad Ricci components are related to the pressure…
We develop an extension of special relativity in $1+3$ dimensional spacetime to account for superluminal inertial observers and show that such an extension rules out the conventional dynamics of mechanical point-like particles and forces…
We establish a new set of pointwise inequalities that order curvature invariants across various Petrov and Segre types of spacetimes. In arbitrary spacetime dimension, we systematically analyze inequalities among contractions of the Ricci…
Killing vector fields in three dimensions play important role in the construction of the related spacetime geometry. In this work we show that when a three dimensional geometry admits a Killing vector field then the Ricci tensor of the…
To confront relativity theory with observation, it is necessary to split spacetime into its temporal and spatial components. The (1+3) timelike threading approach involves restrictions on the gravitational potentials $(g_{\mu \nu})$, while…
We present a unified treatment of the slicing (3+1) and threading (1+3) decompositions of spacetime in terms of foliations. It is well-known how to decompose the metric and connection in the slicing picture; this is at the heart of any…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
Spacetimes which are conformally related to reducible 1+3 spacetimes are considered. We classify these spacetimes according to the conformal algebra of the underlying reducible spacetime, giving in each case canonical expressions for the…
Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such…
We have generalized the results of the previous work [arXiv:2302.12209] to the case of three-dimensional (3D) spacetime with two spatial and one temporal coordinates. We have found that the flat Minkowski 3D spacetime is "well-stitched",…
This papers aims at revisiting Minkowski space-time with a modified outlook and making it more consistent (III.8). The paper scrutinizes the special case of relativistic hypothesis (STR). The paper tries to solve the problems faced by…
A new approach to the model of the universe based on work by Rippl, Romero, Tavakol is presented. We have used the scheme for relating the vacuum (D + 1) dimensional theories to D dimensional theories for setting up a correspondence between…
We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence…
Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…