arXiv subjects

David Q. Aruquipa

Publications and source records attributed to David Q. Aruquipa.

5 recordsLinked to original sources

arXiv2026

Calculation of a regularized Teukolsky Green function in Schwarzschild spacetime

We obtain exact expressions for various factors involved in the Hadamard form of the retarded Green function for the (Bardeen-Press-)Teukolsky equation on Schwarzschild spacetime. We use these to improve on previous results for the calculation of this Green function. We work in a spacetime $\mathcal{M}_2\times\mathbb{S}^2$ conformal to Schwarzschild, in which the metric takes a direct product form. This allows us to derive a separable form for the direct (i.e., singular) part of the Hadamard form of the retarded Green function. The angular factor in this quantity is calculated explicitly. This shows an interesting interplay between geodesics of $\mathbb{S}^2$, spin-weighted spherical harmonics, and Euler angles. The $\mathcal{M}_2$ factor equates to a spin-dependent factor that satisfies a transport equation along geodesics, times the square root of the van Vleck determinant. Both terms are calculated in an exact form for constant radius orbits (which includes the cases of circular timelike geodesics and static worldlines of Schwarzschild spacetime). This separable form also allows us to obtain the multipolar $\ell$-modes of the direct part for electromagnetic and gravitational field perturbations. We then use these $\ell$-modes to calculate, in the gravitational case, the retarded Green function minus its direct part: this is a better representation in practise of the retarded Green function for points near coincidence.

gr-qc↗

arXiv2026

Green functions of the Regge-Wheeler and Teukolsky equations in Schwarzschild spacetime

We present a calculation of the full retarded Green functions of the Regge-Wheeler and Teukolsky equations obeyed by gravitational field perturbations of Schwarzschild spacetime. We perform the calculations for spacetime points along: (i) a timelike circular geodesic (where null-separated points are not at caustics); and (ii) a static worldline (where null-separated points are at caustics). These Green functions show a 4-fold singularity structure away from caustics, and 2-fold at caustics (similarly to the case of scalar field perturbations, which we also reproduce). Physical oscillations near the singularities appear in the gravitational case, which were not present in the scalar case. We obtain our results by developing various numerical and analytical methods.

gr-qc↗

arXiv2023

Hadamard Tail from Initial Data on the Light Cone

Field perturbations of a curved background spacetime generally propagate not only at the speed of light but also at all smaller velocities. This so-called $Hadamard\,tail$ contribution to wave propagation is relevant in various settings, from classical self-force calculations to communication between quantum particle detectors. One method for calculating this tail contribution is by integrating the homogeneous wave equation using Characteristic Initial Data on the light cone. However, to the best of our knowledge, this method has never been implemented before except in flat or conformally-flat spacetimes, where null geodesics emanating from a point do not cross. In this work, we implement this method on the black hole toy model Plebański-Hacyan spacetime, $\mathbb{M}_2\times\mathbb{S}^2$. We obtain new results in this spacetime by calculating the Hadamard tail of a scalar field everywhere where it is defined (namely, in the maximal normal neighbourhood of an arbitrary point) and investigate how it varies for various values of the coupling constant. This serves as a proof-of-concept for the Characteristic Initial Data method on spacetimes where null geodesics emanating from a point $do$ cross.

gr-qc↗

arXiv2020

Communication through quantum fields near a black hole

We study the quantum channel between two localized first-quantized systems that communicate in 3+1 dimensional Schwarzschild spacetime via a quantum field. We analyze the information carrying capacity of direct and black hole-orbiting null geodesics as well as of the timelike contributions that arise because the strong Huygens principle does not hold on the Schwarzschild background. We find, in particular, that the non-direct-null and timelike contributions, which do not possess an analog on Minkowski spacetime, can dominate over the direct null contributions. We cover the cases of both geodesic and accelerated emitters. Technically, we apply tools previously designed for the study of wave propagation in curved spacetimes to a relativistic quantum information communication setup, first for generic spacetimes, and then for the case of Schwarzschild spacetime in particular.

quant-ph↗

arXiv2018

Analogue gravity and radial fluid flows: The case of AdS and its deformations

An analogue model for the $\text{AdS}_2$ spacetime has been recently introduced by Mosna, Pitelli and Richartz [Phys. Rev. D 94, 104065 (2016)] by considering sound waves propagating on a fluid with an ill-defined velocity profile at its source/sink. The wave propagation is then uniquely defined only when one imposes an extra boundary condition at the source/sink (which corresponds to the spatial infinity of $\text{AdS}_2$). Here we show that, once this velocity profile is smoothed out at the source/sink, the need for extra boundary conditions disappears. This, in turn, corresponds to deformations of the $\text{AdS}_2$ spacetime near its spatial infinity. We also examine how this regularization of the velocity profile picks up a specific boundary condition for the idealized system, so that both models agree in the long wavelength limit.

gr-qc↗