Evolving a puncture black hole with fixed mesh refinement

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio

A Note on Tachyons in the D3+D3ˉD3+{\bar {D3}} System

The periodic bounce of Born-Infeld theory of $D3$-branes is derived, and the BPS limit of infinite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born--Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3: explanations and references added. Final version to appear in Mod. Phys. Lett.

Analysis of ``Gauge Modes'' in Linearized Relativity

By writing the complete set of $3 + 1$ (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and constraint error modes arise in a straightforward way in the analysis, and are of a form which will be controlled in any well specified convergent computational discretization of the differential equations.Comment: 11pages LaTe

`Operational' Energy Conditions

I show that a quantized Klein-Gordon field in Minkowski space obeys an `operational' weak energy condition: the energy of an isolated device constructed to measure or trap the energy in a region, plus the energy it measures or traps, cannot be negative. There are good reasons for thinking that similar results hold locally for linear quantum fields in curved space-times. A thought experiment to measure energy density is analyzed in some detail, and the operational positivity is clearly manifested. If operational energy conditions do hold for quantum fields, then the negative energy densities predicted by theory have a will-o'-the-wisp character: any local attempt to verify a total negative energy density will be self-defeating on account of quantum measurement difficulties. Similarly, attempts to drive exotic effects (wormholes, violations of the second law, etc.) by such densities may be defeated by quantum measurement problems. As an example, I show that certain attempts to violate the Cosmic Censorship principle by negative energy densities are defeated. These quantum measurement limitations are investigated in some detail, and are shown to indicate that space-time cannot be adequately modeled classically in negative energy density regimes.Comment: 18 pages, plain Tex, IOP macros. Expanded treatment of measurement problems for space-time, with implications for Cosmic Censorship as an example. Accepted by Classical and Quantum Gravit

Geometric Phase, Hannay's Angle, and an Exact Action Variable

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version

Generalization of the Darboux transformation and generalized harmonic oscillators

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N=2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution, which is related to the existence of coherent states in the system