Integrability of the Minimal Strain Equations for the Lapse and Shift in 3+1 Numerical Relativity

Brady, Creighton and Thorne have argued that, in numerical relativity simulations of the inspiral of binary black holes, if one uses lapse and shift functions satisfying the ``minimal strain equations'' (MSE), then the coordinates might be kept co-rotating, the metric components would then evolve on the very slow inspiral timescale, and the computational demands would thus be far smaller than for more conventional slicing choices. In this paper, we derive simple, testable criteria for the MSE to be strongly elliptic, thereby guaranteeing the existence and uniqueness of the solution to the Dirichlet boundary value problem. We show that these criteria are satisfied in a test-bed metric for inspiraling binaries, and we argue that they should be satisfied quite generally for inspiraling binaries. If the local existence and uniqueness that we have proved holds globally, then, for appropriate boundary values, the solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and keeps the metric evolving slowly) will be the unique solution and thus should be reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the uniqueness of the solution to the Dirichlet problem clarified. New subsection on the nature of the boundary dat

No-horizon theorem for spacetimes with spacelike G1 isometry groups

We consider four-dimensional spacetimes $(M,{\mathbf g})$ which obey the Einstein equations ${\mathbf G}={\mathbf T}$, and admit a global spacelike $G_{1}={\mathbb R}$ isometry group. By means of dimensional reduction and local analyis on the reduced (2+1) spacetime, we obtain a sufficient condition on ${\mathbf T}$ which guarantees that $(M,{\mathbf g})$ cannot contain apparent horizons. Given any (3+1) spacetime with spacelike translational isometry, the no-horizon condition can be readily tested without the need for dimensional reduction. This provides thus a useful and encompassing apparent horizon test for $G_{1}$-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture, and signals possible violations of strong cosmic censorship.Comment: 8 pages, LaTeX, uses IOP package; published in Class. Quantum Gra

NIST cybersecurity framework compliance: A generic model for dynamic assessment and predictive requirements

Organizations have become increasingly dependent on information systems to perform their business as usual activities. Moreover, organizations have registered an increase in the number of cyber-attacks, namely: industrial espionage, confidential information leakage, digital theft or pure damage to corporate image and reputation. In order to try to mitigate these issues, organizations like the National Institute of Standards and Technology (NIST) have made an effort to establish a cybersecurity protection guide. This paper presents a baseline for developing a generic and flexible model for manipulating key factors inside organizations: Processes, Human Resources and Technology, and extrapolate the percentage of compliance with the NIST cybersecurity framework, measure the current cybersecurity risk and allocate financial investments towards specific compliance objectives and reduce the overlapping of existing resources.info:eu-repo/semantics/submittedVersio

Perturbative analysis of generalized Einstein's theories

The hypothesis that the energy-momentum tensor of ordinary matter is not conserved separately, leads to a non-adiabatic expansion and, in many cases, to an Universe older than usual. This may provide a solution for the entropy and age problems of the Standard Cosmological Model. We consider two different theories of this type, and we perform a perturbative analysis, leading to analytical expressions for the evolution of gravitational waves, rotational modes and density perturbations. One of these theories exhibits satisfactory properties at this level, while the other one should be discarded.Comment: 14 pages, Latex fil

Experimental and theoretical evidences for the ice regime in planar artificial spin ices

In this work, we explore a kind of geometrical effect in the thermodynamics of artificial spin ices (ASI). In general, such artificial materials are athermal. Here, We demonstrate that geometrically driven dynamics in ASI can open up the panorama of exploring distinct ground states and thermally magnetic monopole excitations. It is shown that a particular ASI lattice will provide a richer thermodynamics with nanomagnet spins experiencing less restriction to flip precisely in a kind of rhombic lattice. This can be observed by analysis of only three types of rectangular artificial spin ices (RASI). Denoting the horizontal and vertical lattice spacings by a and b, respectively, then, a RASI material can be described by its aspect ratio $\gamma$=a/b. The rhombic lattice emerges when $\gamma$=$\sqrt{3}$. So, by comparing the impact of thermal effects on the spin flips in these three appropriate different RASI arrays, it is possible to find a system very close to the ice regime