arXiv research

Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.

Study spherical curves with curvature dependent on distance to a great circle.

This study classifies quadric surfaces in 3-sphere as Weingarten surfaces.

We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…

Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.

New method resolves ambiguity in measuring black hole merger angular momentum.

New method constructs axial vector fields and defines quasi-local spin-angular momentum.

Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.

The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.

New definition of angular momentum avoids supertranslation ambiguity.

Formulae track evolution of angular momentum and center of mass at null infinity.

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…

Study limits of quasi-local angular momentum at infinity of gravitating systems.

New memory effect discovered in gravitational wave behavior.

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …

We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which …

We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence…

Investigates physical properties on surfaces of rotation using Clairaut's theorem.

Study proves inequality linking black hole properties and angular momentum.

Study reveals dynamics of neural networks with normalization, weight decay, and SGD.

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…

A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate energy conditions, thus lending credence to the most general form of Bekenstein's b…

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

A lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which satisfy the weak energy condition. If, on the horizon, the given data agree to a certain extent with the associated model Ker…

Derives equations of motion for systems with angular momentum on Finsler geometries.

We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau \cite{CWY} for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi-Sachs expansion. Our result complements earlier work of Chen-Wang-Yau \cite{CWY2…

In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …

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 optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group…

This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the bundle of field configurations $Y$. Specifically, the generalized field momentum obs…

The paper derives theorems about curl eigenfields on a 3-sphere using angular momentum theory.

Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular this result does not require the res…

We prove a mass-angular momentum-charge inequality for a broad class of maximal, asymptotically flat, bi-axisymmetric initial data within the context of five-dimensional minimal supergravity. We further show that the charged Myers-Perry black hole initial data are the unique minimizers. In addition, we establish a rigi…

Establishes inequality for multiple black holes, proving mass lower bound.

In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and center of mass. Our assumption on the asymptotics is less stringent than any previo…

We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1)^2$ symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies $S^1 \times S^2$ and $L(p,q)$. In addition to t…

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a …

Study of spacelike singularities in spherical spacetimes with scalar matter.

We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the assumption of the maximal condition, and use a notion of size which is easily computab…

This paper proves a canonical foliation on null infinity for Kerr-like black holes.

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which p…

In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^{6}-$norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr-Newman data by proving convexity of the renormali…

We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As with previous inequalities of this type, the proof is reduced to minimizing an `ar…

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 quasi-local energy-momentum, this completes the definition of conserved quantities i…

For a stable marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant $Λ> 0$ and with matter satisfying the dominant energy condition, we prove that the area $A$ and the angular momentum $J$ satisfy the inequality $8π|J| \le A\sqrt{(1-ΛA/4π)(1-ΛA/12π)}$ which is saturated pre…

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is ra…

We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, $U(1)^2$-invariant initial data sets on simply connected four dimensional manifolds $Σ$. Moreover, we extend the local mass angular momenta inequality result Ref [1] for $U(1)^2$ invariant black holes to the case with nonzero stre…

Rolling systems limit to billiard models with no-slip collisions.

In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes.…