arXiv subjects

Nigel T. Bishop

Publications and source records attributed to Nigel T. Bishop.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational wave interactions with matter: beyond quadrupolar perturbations

Previous work has developed the theory of linearized gravitational wave (GW) interactions with matter using the Bondi-Sachs formalism, but with the perturbations restricted to be quadrupolar, i.e., the angular dependence is spherical harmonic with $\ell=2$. Here, the theory is extended to the case of GWs on a Minkowski background with general $\ell$. Formulas for the GW damping and heating effects are obtained for arbitrary $\ell\ge 2$. It is found that the effects are, generally, enhanced, and this suggests that it is unlikely that higher $\ell$-modes will be seen in GW observations of the post-merger signal of a binary neutron star merger, or of a core collapse supernova.

gr-qc↗

arXiv2026

Gravitational Wave Propagation through Viscous Matter

It has been known that gravitational waves (GWs) transfer energy to viscous matter through which they propagate, but the effect is too weak to be astrophysically significant. Using linearized perturbations about a Minkowski background, we previously showed that the interaction can become important when the distance between matter and source is smaller than the GW wavelength. Here, we review extensions to more realistic backgrounds, namely Schwarzschild spacetime and a static spherically symmetric setting. We find that GW damping and the associated heating of the viscous fluid are enhanced, and can lead to substantial attenuation or even gamma-ray bursts. We investigate astrophysical scenarios where these effects may be relevant, including core-collapse supernovae, binary neutron star mergers, and accretion onto binary black hole mergers.

gr-qc↗

arXiv2026

Gravitational wave interactions with a viscous fluid: Core collapse supernova, binary neutron star merger, and accretion around a black hole merger

The interaction of gravitational waves (GWs) with matter is normally treated as being insignificant. However, recent work has shown that the interaction with a viscous fluid may be astrophysically important when the distance between the matter and GW source is somewhat smaller than the GW wavelength. Previous work has mainly considered perturbations on a Minkowski background, and here these results are extended to the case that the background is a general, non-vacuum, static, spherically symmetric spacetime. Expressions are obtained for GW damping and the consequent heating of the fluid, and implemented in computer code. The results are applied to astrophysical scenarios: Core collapse supernovae, the post-merger signal from a binary neutron star merger, and matter accreting at a binary black hole merger. It is found that, compared to the Minkowski case, the damping and heating effects increase, in some cases by several orders of magnitude. It is possible for a GW signal to be completely damped, and for the heating to be such that a gamma-ray burst occurs.

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arXiv2025

Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework

Studies of quasinormal modes (QNMs) of black holes have a long and well established history. Predominantly, much research in this area has customarily focused on the equations given by Regge, Wheeler and Zerilli. In this work we study linearized perturbations of a Schwarzschild black hole using the Characteristic formulation of numerical relativity, with an emphasis on the computation of QNMs. Within this formalism, the master equation describing gravitational perturbations is known to satisfy a fourth order differential equation. We analyse the singular points of this master equation, and obtain series solutions whose coefficients are given by three term recurrence relations, from which Leaver's continued fraction method can be applied. Using this technique, we recover the standard Schwarzschild quasinormal modes. In addition, we find that imposing purely outgoing boundary conditions, a natural feature of the Bondi-Sachs framework, leads to the recovery of the algebraically special mode.

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arXiv2024

The interaction of gravitational waves with matter

It is well-known that gravitational waves undergo no absorption or dissipation when traversing through a perfect fluid. However, in the presence of a viscous fluid, GWs transfer energy to the fluid medium. In this paper, we present a review of our recent series of results regarding the interaction between gravitational waves and surrounding matter. Additionally, we examine the impact of a viscous fluid shell on gravitational wave propagation, focusing particularly on GW damping and GW heating. Furthermore, we explore the significance of these effects in various astrophysical scenarios such as core-collapse Supernovae and primordial gravitational waves.

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arXiv2024

The interaction between gravitational waves and a viscous fluid shell on a Schwarzschild background

Previous work has shown that the interaction between gravitational waves (GWs) and a shell of viscous matter leads to damping of the GWs and heating of the matter, and that these effects may be astrophysically significant. This result was derived using the theory of linear perturbations about a Minkowki background, and in this work the model is extended to be more physically realistic by allowing the background geometry to be Schwarzschild. It is found that the difference between using a Schwarzschild or Minkowski background is minimal when either $r\gg M$ or $λ< M$, where $r$ is the radius of the shell, $λ$ is the GW wavelength and $M$ is the mass of the system in geometric units (so that $1M_\odot=1.48$km). However, when $r\sim 6M$ and $λ\sim 25M$, then the damping and heating effects are about 9 times larger on a Schwarzschild background than on Minkowski, and such situations occur astrophysically.

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arXiv2024

Astrophysical and cosmological scenarios for gravitational wave heating

Gravitational waves (GWs) passing through a viscous shell of matter are expected to be damped resulting in an increase in the temperature of the fluid as energy is transferred to it from the GWs. In previous work we constructed a model for this process, obtaining an expression for the temperature distribution inside the shell, and it was shown that the temperature increase can be astrophysically significant. In this paper we extend the analysis to GW heating and damping following a binary neutron star merger, GW heating during a core-collapse supernova, and primordial gravitational waves.

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arXiv2024

Gravitational Wave Heating

It was shown in previous work that when a gravitational wave (GW) passes through a viscous shell of matter the magnitude of the GW will be damped and there are astrohysical circumstances in which the damping is almost complete. The energy transfer from the GWs to the fluid will increase its temperature. We construct a model for this process and obtain an expression for the temperature distribution inside the shell in terms of spherical harmonics. Further, it is shown that this effect is astrophysically significant: a model problem is constructed for which the temperature increase is of order $10^6{}^\circ$K.

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arXiv2023

Numerical convergence of model Cauchy-characteristic extraction and matching

Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers. Cauchy-characteristic extraction and matching are methods to compute gravitational waves at null infinity, a mathematical idealization of detector location, from numerical relativity simulations. Both methods can in principle contribute to modeling by providing highly accurate gravitational waveforms. An underappreciated subtlety in realizing this potential is posed by the (mere) weak hyperbolicity of the particular PDE systems solved in the characteristic formulation of the Einstein field equations. This shortcoming results from the popular choice of Bondi-like coordinates. So motivated, we construct toy models that capture that PDE structure and study Cauchy-characteristic extraction and matching with them. Where possible we provide energy estimates for their solutions and perform careful numerical norm convergence tests to demonstrate the effect of weak hyperbolicity on Cauchy-characteristic extraction and matching. Our findings strongly indicate that, as currently formulated, Cauchy-characteristic matching for the Einstein field equations would provide solutions that are, at best, convergent at an order lower than expected for the numerical method, and may be unstable. In contrast, under certain conditions, the extraction method can provide properly convergent solutions. Establishing however that these conditions hold for the aforementioned characteristic formulations is still an open problem.

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arXiv2022

Effect of a viscous fluid shell on the propagation of gravitational waves

In this paper we show that there are circumstances in which the damping of gravitational waves (GWs) propagating through a viscous fluid can be highly significant; in particular, this applies to Core Collapse Supernovae (CCSNe). In previous work, we used linearized perturbations on a fixed background within the Bondi-Sachs formalism, to determine the effect of a dust shell on GW propagation. Here, we start with the (previously found) velocity field of the matter, and use it to determine the shear tensor of the fluid flow. Then, for a viscous fluid, the energy dissipated is calculated, leading to an equation for GW damping. It is found that the damping effect agrees with previous results when the wavelength $λ$ is much smaller than the radius $r_i$ of the matter shell; but if $λ\gg r_i$, then the damping effect is greatly increased. Next, the paper discusses an astrophysical application, CCSNe. There are several different physical processes that generate GWs, and many models have been presented in the literature. The damping effect thus needs to be evaluated with each of the parameters $λ,r_i$ and the coefficient of shear viscosity $η$, having a range of values. It is found that in most cases there will be significant damping, and in some cases that it is almost complete. We also consider the effect of viscous damping on primordial gravitational waves (pGWs) generated during inflation in the early Universe. Two cases are investigated where the wavelength is either much shorter than the shell radii or much longer; we find that there are conditions that will produce significant damping, to the extent that the waves would not be detectable.

gr-qc↗

arXiv2022

Gauge structure of the Einstein field equations in Bondi-like coordinates

The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype formulations of this type are only weakly hyperbolic. Presently we examine the root cause of this result. In a linear analysis we identify the gauge, constraint and physical blocks in the principal part of the Einstein field equations in such a gauge, and show that the subsystem related to the gauge variables is only weakly hyperbolic. Weak hyperbolicity of the full system follows as a consequence in many cases. We demonstrate this explicitly in specific examples, and thus argue that Bondi-like gauges result in weakly hyperbolic free evolution systems under quite general conditions. Consequently the characteristic initial (boundary) value problem of GR in these gauges is rendered ill-posed in the simplest norms one would like to employ. The possibility of finding good alternative norms, in which well-posedness is achieved, is discussed. So motivated, we present numerical convergence tests with an implementation of full GR which demonstrate the effect of weak hyperbolicity in practice.

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arXiv2021

Introduction to gravitational wave astronomy

This chapter provides an overview of gravitational wave (GW) astronomy, providing background material that underpins the other, more specialized chapters in this handbook. It starts with a brief historical review of the development of GW astronomy, from Einstein's prediction of GWs in 1916 to the first direct detection in 2015. It presents the theory of linearized perturbations about Minkowski spacetime of Einstein's equations, and shows how gauge transformations reduce the problem to the standard wave equation with two degrees of freedom, or polarizations, $h_+,h_\times$. We derive the quadrupole formula, which relates the motion of matter in a source region to the far GW field. It is shown that GWs carry energy, as well as linear and angular momentum, away from a source. The GW field of an orbiting circular binary is found; and properties of the evolution of the binary including rate of inspiral and time to coalescence, are calculated. A brief review is given of existing and proposed GW detectors, and of how to estimate source parameters in LIGO or Virgo data of a GW event. The contributions that GW observations have already made to physics, astrophysics and cosmology are discussed.

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arXiv2020

Effect of a low density dust shell on the propagation of gravitational waves

Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust.

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arXiv2017

Testing the Copernican principle with future radio-astronomy observations

We use a direct observational approach to investigate the possibility of testing the Copernican principle with data from upcoming radio surveys. In particular we illustrate the importance of measuring derivatives transverse to the past light-cone when prior knowledge of the value of the cosmological constant is not available.

astro-ph.CO↗

arXiv2016

Extraction of Gravitational Waves in Numerical Relativity

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.

gr-qc↗

arXiv2016

Gravitational waves in a de Sitter universe

The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers, but that it can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic.

gr-qc↗

arXiv2016

Numerically reconstructing the geometry of the Universe from data

We give an outline of an algorithm designed to reconstruct the background cosmological metric within the class of spherically symmetric dust universes that may include a cosmological constant. Luminosity and age data are used to derive constraints on the geometry of the universe up to a redshift of $z = 1.75$. It is shown that simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time Universe cannot be ruled out by these data alone.

astro-ph.CO↗

arXiv2015

Towards the geometry of the universe from data

We present a new algorithm that can reconstruct the full distributions of metric components within the class of spherically symmetric dust universes that may include a cosmological constant. The algorithm is capable of confronting this class of solutions with arbitrary data and opens a new observational window to determine the value of the cosmological constant. In this work we use luminosity and age data to constrain the geometry of the universe up to a redshift of $z = 1.75$. We show that, although current data are perfectly compatible with homogeneous models of the universe, simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time universe cannot yet be ruled out. In doing so we reconstruct the density of cold dark matter out to $z = 1.75$ and derive constraints on the metric components when the universe was 10.5 Gyr old within a comoving volume of approximately 1 Gpc$^{3}$.

astro-ph.CO↗