Related papers: Equality of ADM mass and generalized Komar energy …
We derive expressions for the total Hamiltonian energy of gravitating systems in higher dimensional theories in terms of the Riemann tensor, allowing a cosmological constant $\Lambda \in \mathbb{R}$. Our analysis covers asymptotically…
The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two…
We construct the gravitating mass of an isolated composite system on asymptotically-flat spacetimes within conventional general relativity and investigate when this quantity is well defined. For stationary spacetimes, this quantity is known…
The ADM energy for asymptotically flat spacetimes or its generalizations to asymptotically non-flat spacetimes measure the energy content of a stationary spacetime, such as a single black hole. Such a stationary energy is given as a…
An asymptotically planar AdS spacetimes is characterized by its ADM mass and tensions. We define an additional ADM charge Q associated with the scaling Killing vector of AdS, show that Q is given by a certain sum over the ADM mass and…
There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of…
The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant)…
We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We…
The standard Komar charge is a $(d-2)$-form that can be defined in spacetimes admitting a Killing vector and which is closed when the vacuum Einstein equations are satisfied. Its integral at spatial infinity (the Komar integral) gives the…
We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. The one type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of…
In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an…
We apply the generalised Komar method proposed in [arxiv:2208.05494] to Taub-NUT-AdS spacetime in the theory of Einstein gravity plus a cosmological constant. Based on a generalised closed 2-form, we derive the total mass and NUT charge of…
In this paper, we investigate relations or differences among various conserved quantities which involve the matter Energy Momentum Tensor (EMT) in general relativity. These charges include the energy with Einstein's pseudo EMT, the…
The energy density of asymptotically flat gravitational fields can be calculated from a simple expression involving the trace of the torsion tensor. Integration of this energy density over the whole space yields the ADM energy. Such…
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to…
When a spacetime takes Bondi radiating metric, and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy-momentum is the past limit of the Bondi energy-momentum.…
We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic…
In the framework of the teleparallel equivalent of general relativity the energy density of asymptoticaly flat gravitational fields can be naturally and unambiguously defined. Upon integration of the energy density over the whole three…
The relation between uniformly accelerated laboratories and laboratories supported in a gravitational field lies at the conceptual core of the Equivalence Principle, yet its precise kinematical content beyond strictly local considerations…
We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy which is used in the original methods, and…