Related papers: Almost-Killing conserved currents: a general mass …

We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an $(n-2)$-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a…

We derive the analog of the Tolman - Oppenheimer - Volkoff equation in conformal Killing gravity in a static spherically symmetric spacetime, sourced by anisotropic fluid matter. It differs from the original equation by new dark terms…

A new family of conserved currents for vacuum space-times with a Killing vector is presented. The currents are constructed from the superenergy tensor of the Mars-Simon tensor and using the positivity properties of the former we find that…

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each…

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…

Non-spherical dynamical approximations and models for the gravitational collapse are used to extend the well-known Press \& Schechter (PS) approach, in order to determine analytical expressions for the mass function of cosmic structures.…

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the…

It has been known that warped-product spacetimes such as spherically symmetric ones admit the Kodama vector. This vector provides a locally conserved current made by contraction of the Einstein tensor, even though there is no Killing…

Conserved currents are discussed for static Conformal Killing Gravity, with explicit expressions in static spherical symmetry with anisotropic matter fluid or coupled to (non)linear electromagnetism. They are found in the reformulation of…

An invariant definition of mass in asymptotically de-Sitter space-times is given that relies on the existence of a time-like Killing vector on a sphere surrounding the mass but does not require going to an asymptotic region. In particular…

We find a relation between the ADM mass and a generalized Komar energy in asymptotically-flat spacetime. We do not need to assume the existence of either a Killing or even asymptotically-Killing vector field. Instead, our generalized Komar…

We exploit once again the analogy between the energy-momentum tensor and the so-called ``superenergy'' tensors in order to build conserved currents in the presence of Killing vectors. First of all, we derive the divergence-free property of…

For locally rotationally symmetric (LRS) spacetimes, we construct two equivalent forms of the Komar current derived from a conformal Killing vector. One is a kinematic construction and the other is in terms of the matter quantities on the…

For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined…

We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible…

A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection…

Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…

An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell…

This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [25,26,7] and define the quasi-local energy as differences of…

Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might…