Related papers: Approximate spacetime symmetries and conservation …
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
We consider both the co-ordinates and momenta to be non-commutative and define a non-commutative version of Lorentz symmetry which has a smooth limit to the standard Lorentz symmetry. The Poincar\acute{e} algebra in this spacetime has also…
It is shown that in the weak field approximation the new geometrical approach can lead to the linear field equations for the several independent fields. For the stronger fields and in the second order approximation the field equations…
In realistic situations, black hole spacetimes do not admit a global timelike Killing vector field. However, it is possible to describe the horizon in a quasilocal setting by introducing the notion of a quasilocal boundary with certain…
We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular we prove that their relative "energy" (defined as the conserved quantity associated to…
While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where…
Spherically symmetric spacetimes admit the so-called Kodama vector, which provides a locally conserved current and a preferred time even for dynamical spacetime without any time translation symmetry. A charge associated with this conserved…
It is shown using a space-time curvature classification and decomposition that for certain holonomy types of a space-time, proper projective vector fields cannot exist. Existence is confirmed, by example, for the remaining holonomy types.…
Relations between kinematics, geometry and law of reference frame motion are considered. We show, that kinematical tensors define geometry up to a space functional arbitrariness when integrability condition for spin tensor is satisfied.…
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries…
The new 4D geometry whose Killing vectors span the Poincar\'e algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincar\'e-invariant solution of the degenerate extension of the vacuum Einstein field…
In the framework of the quasigroup approach to conservation laws in general relativity, we show how the infinite-parametric Newman-Unti group of asymptotic symmetries can be reduced to the Poincare quasigroup. We compute Noether's charges…
Binary collisions in Fermi systems obey two fundamental symmetries corresponding to the space and time inversion and to the interchange of particles and holes. We show that beyond the local and instant approximation of scattering-in and…
In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static spacetimes by their matter inheritance symmetries. It is shown that when the energy-momentum tensor is degenerate,…
We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of…
We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive a new hierarchy of higher-order weighted energy estimates by…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
A subclassification of stationary spacetimes, endowed with one timelike and one spacelike Killing vectors, i.e., Petrov $G{_2}I$ on $T_2$ spaces, is proposed. Special attention deserves the Collison's theorem [1] and the branch of metrics…
The notion of spacetime symmetry is essential to describe gravitating physical systems like planets, stars, black holes, or the universe as a whole, since they possess, at least to good approximation, spherical, axial, or spatially…
The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed…