Metric perturbations from eccentric orbits on a Schwarzschild black hole: I. Odd-parity Regge-Wheeler to Lorenz gauge transformation and two new methods to circumvent the Gibbs phenomenon

We calculate the odd-parity, radiative ($\ell \ge 2$) parts of the metric perturbation in Lorenz gauge caused by a small compact object in eccentric orbit about a Schwarzschild black hole. The Lorenz gauge solution is found via gauge transformation from a corresponding one in Regge-Wheeler gauge. Like the Regge-Wheeler gauge solution itself, the gauge generator is computed in the frequency domain and transferred to the time domain. The wave equation for the gauge generator has a source with a compact, moving delta-function term and a discontinuous non-compact term. The former term allows the method of extended homogeneous solutions to be applied (which circumvents the Gibbs phenomenon). The latter has required the development of new means to use frequency domain methods and yet be able to transfer to the time domain while avoiding Gibbs problems. Two new methods are developed to achieve this: a partial annihilator method and a method of extended particular solutions. We detail these methods and show their application in calculating the odd-parity gauge generator and Lorenz gauge metric perturbations. A subsequent paper will apply these methods to the harder task of computing the even-parity parts of the gauge generator.Comment: 17 pages, 9 figures, Updated with one modified figure and minor changes to the text. Added DOI and Journal referenc

Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are initially made in the frequency domain and provide Fourier-harmonic modes for the gauge-invariant master functions that satisfy inhomogeneous versions of the Regge-Wheeler and Zerilli equations. These gravitational master equations have specific singular sources containing both delta function and derivative-of-delta function terms. We demonstrate in this paper successful application of the method of extended homogeneous solutions, developed recently by Barack, Ori, and Sago, to handle source terms of this type. The method allows transformation back to the time domain, with exponential convergence of the partial mode sums that represent the field. This rapid convergence holds even in the region of $r$ traversed by the point mass and includes the time-dependent location of the point mass itself. We present numerical results of mode calculations for certain orbital parameters, including highly accurate energy and angular momentum fluxes at infinity and at the black hole event horizon. We then address the issue of reconstructing the metric perturbation amplitudes from the master functions, the latter being weak solutions of a particular form to the wave equations. The spherical harmonic amplitudes that represent the metric in Regge-Wheeler gauge can themselves be viewed as weak solutions. They are in general a combination of (1) two differentiable solutions that adjoin at the instantaneous location of the point mass (a result that has order of continuity $C^{-1}$ typically) and (2) (in some cases) a delta function distribution term with a computable time-dependent amplitude.Comment: 25 pages, 5 figures, Updated with minor change

Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting

We present an extension of work in an earlier paper showing high precision comparisons between black hole perturbation theory and post-Newtonian (PN) theory in their region of overlapping validity for bound, eccentric-orbit, Schwarzschild extreme-mass-ratio inspirals. As before we apply a numerical fitting scheme to extract eccentricity coefficients in the PN expansion of the gravitational wave fluxes, which are then converted to exact analytic form using an integer-relation algorithm. In this work, however, we fit to individual $lmn$ modes to exploit simplifying factorizations that lie therein. Since the previous paper focused solely on the energy flux, here we concentrate initially on analyzing the angular momentum flux to infinity. A first step involves finding convenient forms for hereditary contributions to the flux at low-PN order, analogous to similar terms worked out previously for the energy flux. We then apply the upgraded techniques to find new PN terms through 9PN order and (at many PN orders) to $e^{30}$ in the power series in eccentricity. With the new approach applied to angular momentum fluxes, we return to the energy fluxes at infinity to extend those previous results. Like before, the underlying method uses a \textsc{Mathematica} code based on use of the Mano-Suzuki-Takasugi (MST) function expansion formalism to represent gravitational perturbations and spectral source integration (SSI) to find numerical results at arbitrarily high precision.Comment: 36 pages, 1 figur

Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI--for us its \emph{raison d'\^{e}tre}--is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.Comment: 15 pages, 7 figure

Amplified Sensitivity of Nitrogen-Vacancy Spins in Nanodiamonds using All-Optical Charge Readout

Nanodiamonds containing nitrogen-vacancy (NV) centers offer a versatile platform for sensing applications spanning from nanomagnetism to in-vivo monitoring of cellular processes. In many cases, however, weak optical signals and poor contrast demand long acquisition times that prevent the measurement of environmental dynamics. Here, we demonstrate the ability to perform fast, high-contrast optical measurements of charge distributions in ensembles of NV centers in nanodiamonds and use the technique to improve the spin readout signal-to-noise ratio through spin-to-charge conversion. A study of 38 nanodiamonds, each hosting 10-15 NV centers with an average diameter of 40 nm, uncovers complex, multiple-timescale dynamics due to radiative and non-radiative ionization and recombination processes. Nonetheless, the nanodiamonds universally exhibit charge-dependent photoluminescence contrasts and the potential for enhanced spin readout using spin-to-charge conversion. We use the technique to speed up a $T_1$ relaxometry measurement by a factor of five.Comment: 13 pages, 14 figure

Fabrication of (111)-Faced Single-Crystal Diamond Plates by Laser Nucleated Cleaving

Single-crystal diamond plates with surfaces oriented in a (111) crystal plane are required for high-performance solid-state device platforms ranging from power electronics to quantum information processing architectures. However, producing plates with this orientation has proven challenging. In this paper, we demonstrate a method for reliably and precisely fabricating (111)-faced plates from commercially available, chemical-vapor-deposition-grown, type-IIa single-crystal diamond substrates with (100) faces. Our method uses a nanosecond-pulsed visible laser to nucleate and propagate a mechanical cleave in a chosen (111) crystal plane, resulting in faces as large as 3.0 mm$\times$0.3 mm with atomically flat surfaces, negligible miscut angles, and near zero kerf loss. We discuss the underlying physical mechanisms of the process along with potential improvements that will enable the production of millimeter-scale (111)-faced single-crystal diamond plates for a variety of emerging devices and applications.Comment: 11 pages, 10 figures, 2 table

Structural validation of oral mucosal tissue using optical coherence tomography

Background: Optical coherence tomography (OCT) is a non-invasive optical technology using near-infrared light to produce cross-sectional tissue images with lateral resolution. Objectives: The overall aims of this study was to generate a bank of normative and pathological OCT data of the oral tissues to allow identification of cellular structures of normal and pathological processes with the aim to create a diagnostic algorithm which can be used in the early detection of oral disorders. Material and methods: Seventy-three patients with 78 suspicious oral lesions were referred for further management to the UCLH Head and Neck Centre, London. The entire cohort had their lesions surgically biopsied (incisional or excisional). The immediate ex vivo phase involved scanning the specimens using optical coherence tomography. The specimens were then processed by a histopathologist. Five tissue structures were evaluated as part of this study, including: keratin cell layer, epithelial layer, basement membrane, lamina propria and other microanatomical structures. Two independent assessors (clinician and pathologist trained to use OCT) assessed the OCT images and were asked to comment on the cellular structures and changes involving the five tissue structures in non-blind fashion. Results: Correct identification of the keratin cell layer and its structural changes was achieved in 87% of the cohort; for the epithelial layer it reached 93.5%, and 94% for the basement membrane. Microanatomical structures identification was 64% for blood vessels, 58% for salivary gland ducts and 89% for rete pegs. The agreement was “good” between the clinician and the pathologist. OCT was able to differential normal from pathological tissue and pathological tissue of different entities in this immediate ex vivo study. Unfortunately, OCT provided inadequate cellular and subcellular information to enable the grading of oral premalignant disorders. Conclusion: This study enabled the creation of OCT bank of normal and pathological oral tissues. The pathological changes identified using OCT enabled differentiation between normal and pathological tissues, and identification of different tissue pathologies. Further studies are required to assess the accuracy of OCT in identification of various pathological processes involving the oral tissues