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.

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.

Abstract The interaction of gravitational waves (GWs) passing through matter is normally treated as being very weak. We have re-investigated this issue using linearized perturbations within the Bondi-Sachs formalism, with a model comprising a spherical shell of matter surrounding a GW source. The background geometry at the shell is either Minkowski or Schwarzschild. Even a shell of dust causes the GWs to be modified both in magnitude and phase; and if the shell is viscous, then the shear induced in the velocity field results in an energy transfer so damping the GWs and heating the matter in the shell. The effect is very weak when the matter is far from the GW source, but can be very significant when the shell radius is less than the GW wavelength. The applications to astrophysics include supernova explosions, the quasinormal mode regime after a neutron star merger, and a binary black hole merger at which matter is present, as well as to primordial gravitational waves in cosmology.

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 ℓ=2. Here, the theory is extended to the case of GWs on a Minkowski background with general ℓ. Formulas for the GW damping and heating effects are obtained for arbitrary ℓ≥ 2. It is found that the effects are, generally, enhanced, and this suggests that it is unlikely that higher ℓ-modes will be seen in GW observations of the post-merger signal of a binary neutron star merger, or of a core collapse supernova.

Understanding viral evolution and predicting future mutations are crucial for overcoming drug resistance and developing long-lasting treatments. Previously, we established machine learning (ML) models using dynamic residue network (DRN) metric data and leveraging a vast amount of existing mutation data from the SARS-CoV-2 main protease (Mpro). Here, we sought to assess the generalizability and robustness of the current models across other SARS-CoV-2 proteins. To achieve this, for the first time, we employed a transfer learning (TL) approach, allowing us to determine the extent to which Mpro trained models could be applied to other SARS-CoV-2 proteins. The TL results were highly promising, with artificial neural network (ANN) and random forest (RF) correlation coefficients for Mpro closely matching those of NSP10, NSP16, and PLpro. The ANN |R| value for Mpro was 0.564, while NSP10, NSP16, and PLpro had values of 0.533, 0.527, and 0.464, respectively. Similarly, the RF |R| value for Mpro was 0.673, compared to 0.457, 0.460, and 0.437 for NSP10, NSP16, and PLpro, respectively. Interestingly, we did not observe a strong correlation for the spike (S) protein monomer and its domains. The low p-values that are associated with the correlation |R| values show that the linear correlations between predicted and actual mutation frequencies are statistically significant. This indicates that TL may generalize well across structurally related viral proteins using DRN-derived ML model from Mpro. Overall, we aim to develop a universal ML model for predicting missense mutation frequencies in viral proteins, and this study lays the foundation for that goal.

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 analyze 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.

Deciphering the effect of evolutionary mutations of viruses and predicting future mutations is crucial for designing long-lasting and effective drugs. While understanding the impact of current mutations on protein drug targets is feasible, predicting future mutations due to natural evolution of viruses and environmental pressures remains challenging. Here, we leveraged existing mutation data during the evolution of the SARS-CoV-2 protein drug target main protease (Mpro) to test the predictive power of dynamic residue network (DRN) analysis in identifying mutation cold and hot spots. We conducted molecular dynamics simulations on the Mpro of SARS-CoV-2 (Wuhan strain) and calculated eight DRN metrics (averaged BC, CC, DC, EC, ECC, KC, L, PR), each of which identifies a unique network feature within the protein. The sets of residues with the highest and lowest values for each metric, comprising potential cold and hot spots, were compared to published biochemical analyses and per residue mutation frequencies observed across five SARS-CoV-2 lineages, encompassing a total of 191,878 sequences. Individual DRN metrics displayed only modest power to predict the mutation frequency of individual residues. However, integrating the eight DRN metrics with additional structural and sequence-derived metrics allowed us to develop machine learning models which significantly improved the prediction of residue mutation frequency. While further refinements should enhance accuracy, we demonstrated a robust method to understand pathogen evolution. This approach can also guide the development of long-lasting drugs by targeting functional residues located in and near active site, and allosteric sites, that are less prone to mutations.

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 >> M or A < M, where r is the radius of the shell, A is the GW wavelength and M is the mass of the system in geometric units (so that 1M(circle dot) = 1.48 km). However, when r 6M and A 25M, then the damping and heating effects are about 9 times larger on a Schwarzschild background than on Minkowski, and such situations occur astrophysically.

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.

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 astrophysical 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 106 K.

It is well known that gravitational waves (GWs) 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 GWs and surrounding matter. Additionally, we examine the impact of a viscous fluid shell on GW 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 GWs.

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.

As detections of mergers of compact bodies begin to flow in, and as we enter an era of precision GW measurements, our understanding of compact bodies, their physics and that of the surrounding astrophysical environment, will continue to grow and at times even be challenged. The need to revise the mass bounds of compact bodies such as BHs and NSs and the possibility of the existence of GW echoes are just some of consequences of the first few years of GW detection. In previous work, using linearised perturbation theory, we made the novel finding that a dust shell will cause a GW to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. We extend our analysis to matter shells surrounding compact body mergers and to intervening matter in cosmology. Instead of only monochromatic GW sources, as we used in our initial investigation, we also consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable. We show that GW echoes that are claimed to be present in the LIGO data of certain events, could not have been caused by a matter shell. We do find, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity.

This paper provides a summary of the fourteen talks that were presented in the session GW4 on various aspects of numerical relativity and computation concerning gravitational waves.

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 we 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.

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 A is much smaller than the inner radius of the matter shell ri; but, if A >> ri, 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 A and ri and the coefficient of shear viscosity eta 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 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.

This dataset is the result of the runs performed for the paper "Gauge structure of the Einstein field equations in Bondi-like coordinates". The data can be used to reproduce the convergence plots, as well as to compare with the data obtained if one performs the same runs independently. To perform independently the runs that produce the data, the PITTNullCode included has to be used. More details on how to proceed with this can be found in the ancillary files of https://arxiv.org/abs/2111.14794 at the directory "anc/numerics/README".

In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these results to astrophysical scenarios. Firstly, it is shown that GW echoes that are claimed to be present in LIGO data of certain events, could not have been caused by a matter shell. However, it is also shown that there are scenarios in which matter shells could make modifications of order a few percent to a GW signal; these scenarios include binary black hole mergers, binary neutron star mergers, and core collapse supernovae.

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×. 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.

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.