Related papers: Hawking Mass Monotonicity for Initial Data Sets
We summarize results on the Penrose inequality bounding the ADM-mass or the Bondi mass in terms of the area of an outermost apparent horizon for asymptotically flat initial data of Einstein's equations. We first recall the proof, due to…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We present a numerical investigation of the evolution of the Hawking mass for perturbed surfaces evolving under hypersurface-restricted uniformly expanding flows in Minkowski spacetime. Although monotonicity of the Hawking mass under…
In this sequel paper we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
The Hawking energy has a monotonicity property under the inverse mean curvature flow on totally umbilic hypersurfaces with constant scalar curvature in Einstein spaces. It grows if the hypersurface is spacelike, and decreases if it is…
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably.…
In this paper, we study the relation of the monotonicity of Hawking Mass and geometric flow problems. We show that along the Hamilton-DeTurck flow with bounded curvature coupled with the modified mean curvature flow, the Hawking mass of the…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied.…
We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding…
We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [26]. We establish, for a class of…
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays…
We refine the Lyapunov-Schmidt analysis developed in our recent paper arxiv:2101.12665 to study the geometric center of mass of the asymptotic foliation by area-constrained Willmore surfaces of initial data for the Einstein field equations.…
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…
A generalized dilaton action is considered of which the standard dilaton black hole and spherically reduced gravity are particular cases. The Arnowitt-Deser-Misner (ADM) and the Bondi-Sachs (BS) mass are calculated. Special attention is…
We obtain global existence results for the Cauchy problem associated to the Schrodinger-Debye system for a class of data with infinite mass (L2-norm). A smallness condition on data is assumed. Our results include data such as…
In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological constant, these invariants, unlike the total Hawking mass,…