Related papers: Recent progress and problems on the Bartnik quasi-…
This article provides a concise introduction to Bartnik's quasi-local mass, and surveys a selection of results pertaining to the understanding of it. The aim is to serve as both an entry point to the topic, and a quick reference of results…
This paper is a tribute to Robert Bartnik and his work and conjectures on quasi-local mass. We present a framework in which to clearly analyse Bartnik's static vacuum extension conjecture. While we prove that this conjecture is not true in…
Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik \cite{Bartnik_energy}. We show that, for any metric on $\bar{B}_1$ that is close enough to the…
In this study, we employ eth-operators and spin-weighted spherical harmonics to express the ADM mass of a static space-time based on the mean values of its components over a a radius-$r$ sphere. While initially derived for standard…
I review the status of lattice simulations relevant for phenomenological studies of B-physics. Results for much-studied quantities such as f_B, B_B and form-factors for semileptonic decays are presented as well as those for quantities which…
Bartnik's definition of gravitational quasilocal energy is analyzed. For a wide class of systems Bartnik's function is given by the ADM mass of some vacuous extension. As an example we calculate mass of a non central ball in Schwarzschild…
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial…
Bartnik's quasi-local mass is a functional on Bartnik data $(\mathbb S^2,\gamma,H,P,\omega^\perp)$, consisting of a metric $\gamma$, scalar functions $H$ and $P$, and a 1-form $\omega^\perp$ on the $2$-sphere $\mathbb S^2$. We construct…
It is conjectured that the full (spacetime) Bartnik mass of a surface $\Sigma$ is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed by $\Sigma$. Assuming this holds true for a 1-parameter…
We review the current status of determinations of the b-quark mass, m_b. We describe the theoretical tools required for determining m_b, with particular emphasis on effective field theories both in the continuum and on the lattice. We…
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications…
We present a review on the recent developments concerning rigorous mathematical results on Schr\"odinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon.
This article is a brief introduction to the rapidly evolving field of many-body localization. Rather than giving an in-depth review of the subject, our aspiration here is simply to introduce the problem and its general context, outlining a…
Recent experimental measurements and lattice QCD calculations are now reaching the precision (and accuracy) needed to over-constrain the CKM parameters $\bar\rho$ and $\bar\eta$. In this brief review, I discuss the current status of lattice…
In this paper, we obtain lower bounds for the Brown-York quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions for the existence of horizons for…
The present status of lattice calculations of $f_D$, $f_B$ and some mass splittings are discussed. When one includes the uncertainties due to discretization errors, the results do not yet have a sufficient precision to be relevant to…
The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the…
Investigation of the many-body condensed-matter systems allows us to connect the microscopic physics at the atomic energy scale and the macroscopic physics emerging in the low-energy corner. It gives some hints on the mechanisms of the…
In this paper we briefly review the advances and problems in the QCD theory of the $\eta_b$ mass.
The problem of quantum gravity is treated from a radically new viewpoint based on a detailed mathematical analysis of what the constitution of physical space is, which has been carried out by Michel Bounias and the author. The approach…