Related papers: Mass angular momentum inequality for axisymmetric …
We present a numerical scheme for solving Einstein's Equations in the presence of a negative cosmological constant and an event horizon with planar topology. Our scheme allows for the introduction of a particular metric source at the…
We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant…
With the era of precision cosmology upon us, and upcoming surveys expected to further improve the precision of our observations below the percent level, ensuring the accuracy of our theoretical cosmological model is of the utmost…
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…
The paper deals with the scale discrepancy between the observed vacuum energy in cosmology and the theoretical quantum vacuum energy (cosmological constant problem). Here, we demonstrate that Einstein's equation and an analogy to particle…
We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang; and the Jang equation in Schoen-Yau, Eichmair and Jang. Then, we proved a…
A refined version of a recently introduced method for analysing the dynamics of an inhomogeneous irrotational dust universe is presented. A fully non-perturbative numerical computation of the time dependence of volume in this framework…
Generalized definitions for angular and linear momentum are given and shown to reduce to the ADM (at spatial infinity) definitions and the definitions at null infinity in the appropriate limit. These definitions are used to express angular…
Critical phenomena in gravitational collapse are characterized by the emergence of surprising structure in solution space, namely the appearance of universal power-laws and periodicities near the threshold of collapse, and a universal…
The trace-free version of the Einstein Gravitational equations, essentially equivalent to unimodular gravity, can solve the troubling issue of the huge discrepancy between quantum field theory estimates of the vacuum energy density and the…
The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational…
The first comprehensive analyses of Planck data reveal that the cosmological model with dark energy and cold dark matter can satisfactorily explain the essential physical features of the expanding Universe. However, the inability to…
Using realistic classical models of microscopic electric-charge electric dipoles and electric-current (Amperian) magnetic dipoles, it is proven that the Einstein-Laub macroscopic electromagnetic force on a macroscopic-continuum volume of…
We study connections among the ADM mass, positive harmonic functions tending to zero at infinity, and the capacity of the boundary of asymptotically flat $3$-manifolds with nonnegative scalar curvature. First we give new formulae that…
In this paper, we study the evolution of asymptotically AdS initial data for the spherically symmetric Einstein--massless Vlasov system for $\Lambda<0$, with reflecting boundary conditions imposed on timelike infinity $\mathcal{I}$, in the…
This paper revisits momentum in the context of min-max optimization. Momentum is a celebrated mechanism for accelerating gradient dynamics in settings like convex minimization, but its direct use in min-max optimization makes gradient…
We show that any polyhomogeneous asymptotically hyperbolic constant-mean-curvature solution to the vacuum Einstein constraint equations can be approximated, arbitrarily closely in H\"older norms determined by the physical metric, by…
We constrain several models of the early Universe that predict a statistical anisotropy of the cosmic microwave background (CMB) sky. We make use of WMAP9 maps deconvolved with beam asymmetries. As compared to previous releases of WMAP…
In relativistic physics, angular momentum is paired with a lesser known conserved quantity, the "mass moment", which appears as the time-space components of the angular momentum tensor. Calculations of mass moment in electromagnetic and…
The standard formulation of the cosmological constant problem is based on one critical assumption---the spacetime is homogeneous and isotropic, which is true only on cosmological scales. However, this problem is caused by extremely small…