BBO and the Neutron-Star-Binary Subtraction Problem

The Big Bang Observer (BBO) is a proposed space-based gravitational-wave (GW) mission designed primarily to search for an inflation-generated GW background in the frequency range 0.1-1 Hz. The major astrophysical foreground in this range is gravitational radiation from inspiraling compact binaries. This foreground is expected to be much larger than the inflation-generated background, so to accomplish its main goal, BBO must be sensitive enough to identify and subtract out practically all such binaries in the observable universe. It is somewhat subtle to decide whether BBO's current baseline design is sufficiently sensitive for this task, since, at least initially, the dominant noise source impeding identification of any one binary is confusion noise from all the others. Here we present a self-consistent scheme for deciding whether BBO's baseline design is indeed adequate for subtracting out the binary foreground. We conclude that the current baseline should be sufficient. However if BBO's instrumental sensitivity were degraded by a factor 2-4, it could no longer perform its main mission. It is impossible to perfectly subtract out each of the binary inspiral waveforms, so an important question is how to deal with the "residual" errors in the post-subtraction data stream. We sketch a strategy of "projecting out" these residual errors, at the cost of some effective bandwidth. We also provide estimates of the sizes of various post-Newtonian effects in the inspiral waveforms that must be accounted for in the BBO analysis.Comment: corrects some errors in figure captions that are present in the published versio

Microfield Dynamics of Black Holes

The microcanonical treatment of black holes as opposed to the canonical formulation is reviewed and some major differences are displayed. In particular the decay rates are compared in the two different pictures.Comment: 22 pages, 4 figures, Revtex, Minor change in forma

Curve matching with applications in medical imaging

In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of finding geodesics. These two methods are combined in a Riemannian gradient-based optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations

A numerical framework for sobolev metrics on the space of curves

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable properties not present in lower order metrics, but their discretization is still largely missing. In this paper, we present algorithms to numerically solve the geodesic initial and boundary value problems for these metrics. The combination of these algorithms enables one to compute Karcher means in a Riemannian gradient-based optimization scheme and perform principal component analysis and clustering. Our framework is sufficiently general to be applicable to a wide class of metrics. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing HeLa cell nuclei.All authors were partially supported by the Erwin Schr odinger Institute programme: In nite-Dimensional Riemannian Geometry with Applications to Image Matching and Shape Analysis. M. Bruveris was supported by the BRIEF award from Brunel University London. M. Bauer was supported by the FWF project \Geometry of shape spaces and related in nite dimensional spaces" (P246251

Second order elastic metrics on the shape space of curves

Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects

Theoretical survey of tidal-charged black holes at the LHC

We analyse a family of brane-world black holes which solve the effective four-dimensional Einstein equations for a wide range of parameters related to the unknown bulk/brane physics. We first constrain the parameters using known experimental bounds and, for the allowed cases, perform a numerical analysis of their time evolution, which includes accretion through the Earth. The study is aimed at predicting the typical behavior one can expect if such black holes were produced at the LHC. Most notably, we find that, under no circumstances, would the black holes reach the (hazardous) regime of Bondi accretion. Nonetheless, the possibility remains that black holes live long enough to escape from the accelerator (and even from the Earth's gravitational field) and result in missing energy from the detectors.Comment: RevTeX4, 12 pages, 4 figures, 5 tables, minor changes to match the accepted version in JHE

Simulation of underground gravity gradients from stochastic seismic fields

We present results obtained from a finite-element simulation of seismic displacement fields and of gravity gradients generated by those fields. The displacement field is constructed by a plane wave model with a 3D isotropic stochastic field and a 2D fundamental Rayleigh field. The plane wave model provides an accurate representation of stationary fields from distant sources. Underground gravity gradients are calculated as acceleration of a free test mass inside a cavity. The results are discussed in the context of gravity-gradient noise subtraction in third generation gravitational-wave detectors. Error analysis with respect to the density of the simulated grid leads to a derivation of an improved seismometer placement inside a 3D array which would be used in practice to monitor the seismic field.Comment: 24 pages, 12 figure