A Remark on Boundary Effects in Static Vacuum Initial Data sets

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that the boundary of (M, g) has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that the boundary has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the area and mean curvature of the boundary. Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit

Critical points of Wang-Yau quasi-local energy

In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\Omega$ in a time-oriented spacetime $N$ satisfying the dominant energy condition. Suppose the induced metric on $\Sigma$ has positive Gaussian curvature and all boundary components of $\Omega$ have positive mean curvature. Suppose $H \le H_0$ where $H$ is the mean curvature of $\Sigma$ in $\Omega$ and $H_0$ is the mean curvature of $\Sigma$ when isometrically embedded in $R^3$. If $\Omega$ is not isometric to a domain in $R^3$, then 1. the Brown-York mass of $\Sigma$ in $\Omega$ is a strict local minimum of the Wang-Yau quasi-local energy of $\Sigma$, 2. on a small perturbation $\tilde{\Sigma}$ of $\Sigma$ in $N$, there exists a critical point of the Wang-Yau quasi-local energy of $\tilde{\Sigma}$.Comment: substantially revised, main theorem replaced, Section 3 adde

Quantisation of 2D-gravity with Weyl and area-preserving diffeomorphism invariances

The constraint structure of 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called ``quasi-light-cone'' gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2,R) residual symmetry. The string-like approach is applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2,R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained.Comment: 14 pages, Latex fil

Landau parameters for isospin asymmetric nuclear matter based on a relativistic model of composite and finite extension nucleons

We study the properties of cold asymmetric nuclear matter at high density, applying the quark meson coupling model with excluded volume corrections in the framework of the Landau theory of relativistic Fermi liquids. We discuss the role of the finite spatial extension of composite baryons on dynamical and statistical properties such as the Landau parameters, the compressibility, and the symmetry energy. We have also calculated the low lying collective eigenfrequencies arising from the collisionless quasiparticle transport equation, considering both unstable and stable modes. An overall analysis of the excluded volume correlations on the collective properties is performed.Comment: 24 pages, 6 figure