Spatial Slice Research Articles

The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State

In this article, we study the 1 + 3 dimensional relativistic Euler equations on a pre-specified conformally flat expanding spacetime background with spatial slices that are diffeomorphic to $\mathbb{R}^3.$ We assume that the fluid verifies the equation of state $p = c_s^2 \rho,$ where $0 \leq c_s \leq \sqrt{1/3}$ is the speed of sound. We also assume that the inverse of the scale factor associated to the expanding spacetime metric verifies a $c_s-$dependent time-integrability condition. Under these assumptions, we use the vectorfield energy method to prove that an explicit family of physically motivated, spatially homogeneous, and spatially isotropic fluid solutions is globally future-stable under small perturbations of their initial conditions. The explicit solutions corresponding to each scale factor are analogs of the well-known spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker family. Our nonlinear analysis, which exploits dissipative terms generated by the expansion, shows that the perturbed solutions exist for all future times and remain close to the explicit solutions. This work is an extension of previous results, which showed that an analogous stability result holds when the spacetime is exponentially expanding. In the case of the radiation equation of state $p = (1/3)\rho,$ we also show that if the time-integrability condition for the inverse of the scale factor fails to hold, then the explicit fluid solutions are unstable. More precisely, we show that arbitrarily small smooth perturbations of the explicit solutions' initial conditions can launch perturbed solutions that form shocks in finite time. The shock formation proof is based on the conformal invariance of the relativistic Euler equations when $c_s^2 = 1/3,$ which allows for a reduction to a well-known result of Christodoulou.

On a partially reduced phase space quantization of general relativity conformally coupled to a scalar field

The purpose of this paper is twofold. On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on ‘loop quantum gravity without the Hamiltonian constraint’ with calculational details and extend the results to standard model matter, a cosmological constant, and non-compact spatial slices. On the other hand, we provide a discussion on the role of observables, focused on the situation of a symmetry exchange, which is key to our derivation. Furthermore, we comment on the relation of our model to reduced phase space quantizations based on deparametrization.

Time evolution of entanglement entropy from black hole interiors

We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.

Loop quantum gravity without the Hamiltonian constraint

We show that under certain technical assumptions, including the existence of a constant mean curvature (CMC) slice and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantized on a partially reduced phase space, meaning reduced only with respect to the Hamiltonian constraint and a proper gauge fixing. More precisely, we introduce, in close analogy to shape dynamics, the generator of a local conformal transformation acting on both, the metric and the scalar field, which coincides with the CMC gauge condition. A new metric, which is invariant under this transformation, is constructed and used to define connection variables which can be quantized by standard loop quantum gravity methods. Since this connection is invariant under the local conformal transformation, the generator of which is shown to be a good gauge fixing for the Hamiltonian constraint, the Dirac bracket associated with implementing these constraints coincides with the Poisson bracket for the connection. Thus, the well developed kinematical quantization techniques for loop quantum gravity are available, while the Hamiltonian constraint has been solved (more precisely, gauge fixed) classically. The physical interpretation of this system is that of general relativity on a fixed spatial CMC slice, the associated ‘time’ of which is given by the CMC. While it is hard to address dynamical problems in this framework (due to the complicated ‘time’ function), it seems, due to good accessibility properties of the CMC gauge, to be well suited for problems such as the computation of black hole entropy, where actual physical states can be counted and the dynamics is only of indirect importance. The corresponding calculation yields the surprising result that the usual prescription of fixing the Barbero–Immirzi parameter β to a constant value in order to obtain the well-known formula S = a(Φ)A/(4G) does not work for the black holes under consideration, while a recently proposed prescription involving an analytic continuation of β to the case of a self-dual space-time connection yields the correct result. Also, the interpretation of the geometric operators gets an interesting twist, which exemplifies the deep relationship between observables and the choice of a time function and has consequences for loop quantum cosmology.

Entanglement entropy in de Sitter space

We compute the entanglement entropy for some quantum field theories on de Sitter space. We consider a superhorizon size spherical surface that divides the spatial slice into two regions, with the field theory in the standard vacuum state. First, we study a free massive scalar field. Then, we consider a strongly coupled field theory with a gravity dual, computing the entanglement using the gravity solution. In even dimensions, the interesting piece of the entanglement entropy is proportional to the number of e-foldings that elapsed since the spherical region was inside the horizon. In odd dimensions it is contained in a certain finite piece. In both cases the entanglement captures the long range correlations produced by the expansion.

New code for equilibriums and quasiequilibrium initial data of compact objects. II. Convergence tests and comparisons of binary black hole initial data

COCAL is a code for computing equilibriums or quasiequilibrium initial data of single or binary compact objects based on finite difference methods. We present the results of supplementary convergence tests of COCAL code using time symmetric binary black hole data (Brill-Lindquist solution). Then, we compare the initial data of binary black holes on the conformally flat spatial slice obtained from COCAL and KADATH, where KADATH is a library for solving a wide class of problems in theoretical physics including relativistic compact objects with spectral methods. Data calculated from the two codes converge nicely towards each other, for close as well as largely separated circular orbits of binary black holes. Finally, as an example, a sequence of equal mass binary black hole initial data with corotating spins is calculated and compared with data in the literature.

Fluctuating geometries,q-observables, and infrared growth in inflationary spacetimes

Infrared growth of geometrical fluctuations in inflationary spacetimes is investigated. The problem of gauge-invariant characterization of growth of perturbations, which is of interest also in other spacetimes such as black holes, is addressed by studying evolution of the lengths of curves in the geometry. These may either connect freely falling ``satellites,'' or wrap nontrivial cycles of geometries like the torus, and are also used in diffeomorphism-invariant constructions of two-point functions of field operators. For spacelike separations significantly exceeding the Hubble scale, no spacetime geodesic connects two events, but one may find geodesics constrained to lie within constant-time spatial slices. In inflationary geometries, metric perturbations produce significant and growing corrections to the lengths of such geodesics, as we show in both quantization on an inflating torus and in standard slow-roll inflation. These become large, signaling breakdown of a perturbative description of the geometry via such observables, and consistent with perturbative instability of de Sitter space. In particular, we show that the geodesic distance on constant time slices during inflation becomes nonperturbative a few e-folds after a given scale has left the horizon, by distances $\ensuremath{\sim}1/{H}^{3}\ensuremath{\sim}RS$, obstructing use of such geodesics in constructing IR-safe observables based on the spatial geometry. We briefly discuss other possible measures of such geometrical fluctuations.

ON THE SEMICLASSICAL LIMIT OF LOOP QUANTUM COSMOLOGY

We consider a k = 0 Friedman–Robertson–Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state solutions for each point on the space of classical states. We propose physical criteria that select from these coherent states, those that display semiclassical behavior, and study their properties in the deep Planck regime. Furthermore, we consider generalized squeezed states and compare them to the Gaussian states. The issue of semiclassicality preservation across the bounce is studied and shown to be generic for all the states considered. Finally, we comment on some implications these results have, depending on the topology of the spatial slice. In particular, we consider the issue of the recovery, within our class of states, of a scaling symmetry present in the classical description of the system when the spatial topology is noncompact.

TU-A-217A-03: Radiographic Tomosynthesis: Image Quality and Artifacts Reduction

Image quality of digital radiographictomosynthesis is influenced by the fundamentals of x‐ray physics, the unique system geometry, data acquisitionhardware and protocols, system calibrations, and reconstruction techniques. With the commercialization of at least two vendors, there is a renewed focus on this advanced application. This talk will provide an overview on the recent advances in IQ performance evaluation and enhancement and focus on these specific areas: in‐plane spatial resolution, slice sensitivity, noise and low contrast sensitivity, localization accuracy, out of focus structures, uniformity, and ripple artifacts. Various techniques to suppress, correct, or avoid the artifacts are presented. Future technologies to overcome the limitations of current tomosynthesis system will also be discussed. Learning Objectives: 1. Understand the image quality performance and measurement standards of digital radiographictomosynthesis. 2. Understand the root cause(s) of image artifacts present in digital radiographictomosynthesis. 3. Understand the various techniques to suppress, correct, or avoid the artifacts, and future technologies to overcome the limitations of current tomosynthesis system.

A regularity theorem for graphic spacelike mean curvature flows

For mean curvature flows in Euclidean spaces, Brian White proved a regularity theorem which gives C 2; estimates in regions of spacetime where the Gaussian density is close enough to 1. This is proved by applying Huisken’s monotonicity formula. Here we will consider mean curvature flows in semiEuclidean spaces, where each spatial slice is an m-dimensional graph in R mCn n satisfying a gradient bound stronger than the spacelike condition. By defining a suitable quantity to replace the Gaussian density ratio, we prove monotonicity theorems similar to Huisken’s and use them to prove a regularity theorem similar to White’s.

Numerical bifurcation analysis of conformal formulations of the Einstein constraints

The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to investigate further.

Quantum geons and noncommutative spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group $S_N$. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the commutative spacetime algebras of geons as well to noncommutative algebras. The latter support twisted actions of diffeos of geon spacetimes and associated twisted statistics. The notion of covariant fields for geons is formulated and their twisted versions are constructed from their untwisted versions. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli principle, seem to be the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.

Seeking for toroidal event horizons from initially stationary BH configurations

We construct and evolve non-rotating vacuum initial data with a ring singularity, based on a simple extension of the standard Brill–Lindquist multiple BH initial data, and search for event horizons with spatial slices that are toroidal when the ring radius is sufficiently large. While evolutions of the ring singularity are not numerically feasible for large radii, we find some evidence, based on configurations of multiple BHs arranged in a ring, that this configuration leads to singular limit where the horizon width has zero size, possibly indicating the presence of a naked singularity, when the radius of the ring is sufficiently large. This is in agreement with previous studies that have found that there is no apparent horizon surrounding the ring singularity when the ring's radius is larger than about twice its mass.

SU‐E‐J‐75: Clinical Commissioning and Quality Assurance Procedures for a Wide Bore MRI Unit Configured for Radiation Therapy Planning

Purpose: To develop a comprehensive protocol for the acceptance testing and clinical commissioning a wide bore (70cm) MRI‐Simulator for radiotherapy localization and planning.Methods: A GE 1.5T Optima 450W MR scanner was installed in our department in 2010. Standards derived from the ACR MRI Accreditation Program were used as reference for acceptance testing and commissioning. Commercially available phantoms were used to characterize magnetic field homogeneity, image intensity uniformity, high contrast spatial resolution, slice thickness, position accuracy and geometric accuracy. For 2D SE, GRE and 3D CUBE imaging sequences, in plane and through plane distortion and distortion correction accuracy with and without the GradWarp distortion algorithm provided the software was assessed. The test was performed using multi ROI at different locations off center with multiple slices using the Magphan® phantom. Couch position, couch load and laser system accuracy were also assessed. Daily QA procedures were developed for SNR, RF, isocenter position and the gradient linearity. Parameters derived from commissioning were utilized as baseline reference values for a comprehensive QA program. Results: For clinical commissioning, the MR scanner met the criteria established by the ACR MRI Accreditation Program .The results from ACR phantom showed that image quality specifications were met. The highest spatial frequencies were 9 lp/cm; visualized. The results from the monthly QA demonstrate that variations are within 1% of the commissioning data illustrating good self consistency as regards MRI simulator performance. In‐plane distortion measurements show that the distortion correction algorithm reduced the error to within acceptable (< 1mm at 30mm sup/inf to isocentre and within 2 mm at 120 mm off center) Conclusions: Analysis of the test results indicates consistent and reproducible operation of the wide bore MRI‐SIM unit. A comprehensive commissioning and QA protocol has been developed for use in the radiation oncology setting.

Abstract LB-359: Effects of space time fractionated radiation on normal tissue toxicity

Abstract Purpose: Space-Time Fractionation (STF) proposed herein is a novel concept based on the long-standing clinical data of Spatially Fractionated GRID Radiotherapy. The conventional GRID therapy, or the recently proposed LATTICE therapy is generally intended for single-fraction treatment. The STF extends the concept to definitive, fractionated radiation therapy, aiming at maximum tumor control with significantly reduced normal tissue toxicity. Methods: In this fractionation scheme, treatment volume was divided into segments or slices, consecutively numbered 1,2,3,4,5,6,7,8…, with typical slice thickness of 1–2 cm. This formed the spatially fractionated structure. Alternated time fraction numbers (time fractionation), were delivered to their corresponding spatial segments, i.e., the odd fractions 1,3,5,7,9, … were delivered to spatial slices 1,3,5,7… and the even fractions 2,4,6,8,… were delivered to spatial slices 2,4,6,8. To demonstrate the normal tissue sparing effect, three groups of C57/BL6 mice (16/group) were used: untreated (UT); STF, 500cGy/fx × 10 (5x Position 1 + 5x Position 2) delivered through a block of multiple equally spaced open/closed slits of 2 mm width; Conventional 310cGy × 10, open field. The two irradiated groups having the same biological equivalent dose (BED) delivered to the whole abdomen. Two mice were sacrificed immediately, 24h and 7 days after radiation and intestines, kidneys and liver tissues were collected. The formalin fixed tissues were stained with hematoxylin and eosin and pathological analysis was carried out to assess the damage. Remaining mice were followed for overall survival. Results: Although mice from all the treatment groups survived for at least 90 days after the treatment, pathological analysis of the tissues clearly showed maximal damage with open field irradiation compared to STF. Intestinal epithelial cells from open field irradiated mice showed severe damage with cell loss in intestinal crypts and thus villi were shortened and blunted. Even one month after irradiation, amphophilic cytoplasm, variation in the size of the nuclei, clumping of chromatin and prominent nucleoli were observed in the intestinal tissues. Number of mitotic figures increased with time indicating regeneration but recovery was only partial. In case of the STF irradiated mice, negligible damage was observed at all the time points studied. Again, kidney tissues obtained from open field irradiated mice showed highly disorganized tubule cells structure compared to kidney tissue from mice subjected to STF. Currently, we are assessing the effects in the liver tissue. Conclusions: Results show that STF could be a new approach in treating advanced/recurrent cancers with improved local tumor control without increasing normal tissue toxicity. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 102nd Annual Meeting of the American Association for Cancer Research; 2011 Apr 2-6; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2011;71(8 Suppl):Abstract nr LB-359. doi:10.1158/1538-7445.AM2011-LB-359

Trumpet slices of the Schwarzschild-Tangherlini spacetime

We study families of time-independent maximal and $1+\mathrm{log}$ foliations of the Schwarzschild-Tangherlini spacetime, the spherically symmetric vacuum black hole solution in $D$ spacetime dimensions, for $D\ensuremath{\ge}4$. We identify special members of these families for which the spatial slices display a trumpet geometry. Using a generalization of the $1+\mathrm{log}$ slicing condition that is parameterized by a constant $n$ we recover the results of Nakao, Abe, Yoshino, and Shibata in the limit of maximal slicing. We also construct a numerical code that evolves the Baumgarte-Shapiro-Shibata-Nakamura equations for $D=5$ in spherical symmetry using moving-puncture coordinates and demonstrate that these simulations settle down to the trumpet solutions.

Effect of improving spatial or temporal resolution on image quality and quantitative perfusion assessment with k‐t SENSE acceleration in first‐pass CMR myocardial perfusion imaging

k-t Sensitivity-encoded (k-t SENSE) acceleration has been used to improve spatial resolution, temporal resolution, and slice coverage in first-pass cardiac magnetic resonance myocardial perfusion imaging. This study compares the effect of investing the speed-up afforded by k-t SENSE acceleration in spatial or temporal resolution. Ten healthy volunteers underwent adenosine stress myocardial perfusion imaging using four saturation-recovery gradient echo perfusion sequences: a reference sequence accelerated by sensitivity encoding (SENSE), and three k-t SENSE–accelerated sequences with higher spatial resolution (“k-t High”), shorter acquisition window (“k-t Fast”), or a shared increase in both parameters (“k-t Hybrid”) relative to the reference. Dark-rim artifacts and image quality were analyzed. Semiquantitative myocardial perfusion reserve index (MPRI) and Fermi-derived quantitative MPR were also calculated. The k-t Hybrid sequence produced highest image quality scores at rest (P = 0.015). Rim artifact thickness and extent were lowest using k-t High and k-t Hybrid sequences (P < 0.001). There were no significant differences in MPRI and MPR values derived by each sequence. Maximizing spatial resolution by k-t SENSE acceleration produces the greatest reduction in dark rim artifact. There is good agreement between k-t SENSE and standard acquisition methods for semiquantitative and fully quantitative myocardial perfusion analysis. Magn Reson Med, 2010. © 2010 Wiley-Liss, Inc.

White Matter Correlates of Apathy in HIV-Positive Subjects: A Diffusion Tensor Imaging Study

White Matter Correlates of Apathy in HIV-Positive Subjects: A Diffusion Tensor Imaging Study

Combining gravity with the forces of the standard model on a cosmological scale

We prove the existence of a spectral resolution of the Wheeler–DeWitt equation when the underlying spacetime is a Friedman universe with flat spatial slices and where the matter fields comprise the strong interaction, with SU(3) replaced by a general SU(n), n ⩾ 2, and the electro-weak interaction. The wavefunctions are maps from to a subspace of the antisymmetric Fock space, and one noteworthy result is that whenever the electro-weak interaction is involved, the image of an eigenfunction is in general not one dimensional; i.e. in general it makes no sense specifying a fermion and looking for an eigenfunction the range of which is contained in the one-dimensional vector space spanned by the fermion.

079 Effect of improving spatial or temporal resolution on image quality and quantitative perfusion assessment in first pass CMR myocardial perfusion imaging accelerated by k-t SENSE

<h3>Introduction</h3> First pass cardiac magnetic resonance (CMR) myocardial perfusion imaging (MPI) requires the rapid acquisition of large amounts of image data. The advanced acceleration technique, k-t SENSE, exploits spatiotemporal correlations to speed up data acquisition. In CMR MPI, k-t SENSE has been used to improve spatial resolution, temporal resolution or slice coverage with reductions in endocardial dark rim artefacts reported. To date, there has been no direct comparison of these strategies. <h3>Method</h3> Adenosine stress and rest MPI was performed using a 1.5T Philips Intera system. Ten healthy volunteers were scanned on four occasions using a different saturation recovery gradient echo perfusion sequence at each visit (abstract 079 table 1). The order of sequence utilisation varied for each volunteer. Image analysis was performed on the middle slice. Image quality was scored 0–3 (0-poor, 3-excellent) and breathing artefacts noted by two readers in consensus. Dark rim artefact was assessed by: thickness (mm), duration (frame count) and extent (area of artefact contoured and expressed as a percentage of myocardial area). Semi-quantitative myocardial perfusion reserve index (MPRI) and Fermi deconvolution derived myocardial perfusion reserve (MPR) were calculated using standard techniques for each sequence type in seven of the volunteers. Friedman Test and repeated measures Analysis of Variance Testing (with Bonferroni correction for pairwise comparisons) were used to compare non-parametric and parametric data respectively. <h3>Results</h3> Image quality at stress did not significantly differ between the sequences (abstract 079 table 2). At rest, the k-t Hybrid sequence showed highest quality. Rim artefact thickness was similar using REFERENCE and k-t Fast sequences but significantly lower using k-t High and k-t Hybrid sequences. Rim artefact extent was significantly higher for REFERENCE images, similar for k-t Fast and k-t Hybrid images and significantly lower for k-t High images. Although four-way comparison suggested differences at rest, rim artefact duration did not differ between sequences by pairwise analysis at stress or rest. MPRI and MPR results did not differ between the four sequences (Mean MPRI:REFERENCE 1.67, k-t High 1.87, k-t Fast 1.94, k-t Hybrid 1.71, p=0.265. Mean MPR:REFERENCE 2.49, k-t High 2.56, k-t Fast 2.53, k-t Hybrid 2.67, p=0.58). Breathing artefacts occurred in 57% of stress and 17% of rest k-t SENSE studies. No breathing artefacts were seen with REFERENCE data. <h3>Conclusion</h3> Although spatial and temporal resolution both influence the thickness and extent of dark rim artefact, maximising spatial resolution by k-t SENSE acceleration produces the greatest reduction in these parameters. Semi-quantitative and fully quantitative measures of myocardial perfusion were comparable between k-t SENSE and SENSE acceleration techniques.