arXiv research

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 also derive a formula relating the ADM energy-momentum of any asymptotically…

New proof shows equality in spacetime mass theorem.

In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbatio…

Proves critical points of ADM mass correspond to specific initial data sets.

We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-Ó Murchadha-Regge-T…

Paper bounds mass of 3D Einstein data using spacetime harmonic functions.

Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.

We study the limit of quasilocal mass defined in [4] and [5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted slice of the Schwarzchild solution is computed explicitly and shown to give the …

We study the limit of quasilocal energy defined in [7] and [8] for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi-Sachs e…

We affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight. Namely, if an asymptotically flat initial data set satisfies the dominant energy condition and has $E=|P|$, then $E=|P|=0$, where $(E, P)$ is the ADM energy-momentum vector. The dimensional restriction can be removed…

New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.

New methods for constructing null fluid metrics and solving optical lift conjectures.

New definition of angular momentum avoids supertranslation ambiguity.

We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\underline{\mathcal{N}}_0$. $\underline{\mathcal{N}}_0$ terminates at past null infinity $\mathcal{I}^-$ and $\mathcal{S}_0:=\partial\underline{\mathcal{N}}_0$…

Study linear perturbations in Schwarzschild black hole spacetime.

Given a spacelike 2-surface $Σ$ in a spacetime $N$ and a constant future timelike unit vector $T_0$ in $\R^{3,1}$, we derive upper and lower estimates of Wang-Yau quasilocal energy $E(Σ, X, T_0)$ for a given isometric embedding $X$ of $Σ$ into a flat 3-slice in $\R^{3,1}$. The quantity $E(Σ, X, T_0)$ itself depends …

One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum …

We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the initial data satisfies the inequality $E \ge |P|$. Previously, this theorem was proven…

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and po…

The paper proves positive energy-momentum theorems for charged AdS initial data sets.

Derives energy-momentum tensor from Standard Model, examines energy conditions.

The paper shows how to create scalar flat metrics with very large ADM mass.

The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.

This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: …

In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-para…

Paper solves Einstein vacuum equations gluing problem with applications.

In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given tensor $A$, a new tensor quadratic in $A$ and ``positive'', in the sense that it is …

We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy-momentum-Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.

New ADM mass definition for weakly regular manifolds.

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious argume…

Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of…

Generalizes energy-momentum method for non-autonomous Hamiltonian systems.

In this paper, we investigate the behavior of ADM mass and Einstein-Hilbert functional under the Yamabe flow. Through studying the Yamabe flow by weighted spaces, we show that ADM mass and Einstein-Hilbert functional are well-defined and monotone non-increasing under the Yamabe flow on $n$-dimensional, $n\geq 3$, asymp…

New relation found between ADM mass and generalized Komar energy for dynamical spacetimes.

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov's classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.

Study shows a mass quantity for $C^0$ metrics that agrees with ADM mass.

Proves existence of Yang-Mills fields for specific curvature conditions.

Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.

In a vacuum spacetime equips with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total linear momentum and the Bondi momentum. The relation between the ADM total energy and the Bondi mass in t…

Constructs initial data for multiple black holes with specified ADM parameters.

New mass definition linked to ADM mass for general metrics.

New method for studying $t$-dependent Hamilton equations on cosymplectic manifolds.

We give some lower estimates of the ADM mass of an asymptotically flat (AF) Riemannian manifold without assuming that the scalar curvature of the manifold is nonnegative. Some sufficient conditions for an AF manifold to have nonnegative ADM mass are obtained. We also give some lower estimates of the Brown-York mass of …

By using variational calculus and exterior derivative formalism, we proposed in two previous joint papers with S. Siparov a new geometric approach for electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge …

We show that it is natural to consider the energy-momentum tensor associated with a spinor field as the second fundamental form of an isommetric immersion. In particular we give a generalization of the warped product construction over a Riemannian manifold leading to this interpretation. Special sections of the spinor …

Predicts financial asset dependencies using spatiotemporal patterns.

Mathematical framework for field theories on Finsler spacetimes.

Paper proves flat 3-manifolds with positive mass have unique isoperimetric surfaces.