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A variety of high-energy events can take place in the seconds leading up to a binary neutron-star merger. Mechanisms involving tidal resonances, electrodynamic interactions, or shocks in mass-loaded wakes have been proposed as instigators of these precursors. With a view of gravitational-wave and multimessenger astrophysics more broadly, premerger observations and theory are reviewed emphasising how gamma-ray precursors and dynamical tides can constrain the neutron-star equation of state, thermodynamic microphysics, and evolutionary pathways. Connections to post-merger phenomena, notably gamma-ray bursts, are discussed together with how magnetic fields, spin and misalignment, crustal elasticity, and stratification gradients impact observables., Comment: 50 pages, 22 figures, 4 tables. REVTeX style review article. Comments welcome. V2: improved figure resolution and some discussion

Mature neutron stars are thought to be sufficiently cold that nuclei in the outer layers freeze, solidifying a crust. Crustal elasticity allows the star to support a set of seismic modes, such as torsional oscillations. These axial-parity modes can couple to the polar sector in a number of ways, for example via rotation or a magnetic field. Even in a static, spherically-symmetric star however these modes can couple at non-linear order. In this study, such couplings in the crust are examined for the first time: we derive the axisymmetric perturbation equations for second-order axial eigenfunctions, which are sourced by axial-polar couplings at first-order, and solve the resulting equations in the time domain. Through our studies, we find that the second-order spectrum contains additional oscillation modes, not predicted by the linear analysis with either axial or polar perturbations, which can be excited to relatively large amplitudes., Comment: Accepted for publication in PRD

Tidal resonances in the final seconds of a binary neutron-star inspiral can excite oscillation modes in one or both of the constituents to large amplitudes. Under favorable circumstances, resonant pulsations can overstrain the stellar crust and unleash a torrent of magnetoelastic energy that manifests as a gamma-ray ``precursor flare.'' We show that for realistic, stratified stars rotating with a spin frequency of $\gtrsim30\,$Hz, the fundamental $g$ or its first overtone can also execute a differential rotation in the crust such that a magnetic field of strength $\gtrsim10^{13}\,$G is generated via magnetorotational instabilities. This may help to explain observed precursor rates and their luminosities. Premerger magnetic growth would also provide seed magnetic energy for the postmerger remnant., Comment: 9 pages, 5 figures, 1 table. Minor changes to match journal style

Symmetries and conservation laws associated with the ideal Einstein-Euler system, for stationary and axisymmetric stars, can be utilized to define a set of flow constants. These quantities are conserved along flow lines in the sense that their gradients are orthogonal to the four-velocity. They are also conserved along surfaces of constant magnetic flux, making them powerful tools to identify general features of neutron star equilibria. One important corollary of their existence is that mixed poloidal-toroidal fields are inconsistent with the absence of meridional flows except in some singular sense, a surprising but powerful result first proven by Bekenstein and Oron. In this work, we revisit the flow constant formalism to rederive this result together with several new ones concerning both nonlinear and perturbative magnetic equilibria. Our investigation is supplemented by some numerical solutions for multipolar magnetic fields on top of a Tolman-VII background, where strict power-counting of the flow constants is used to ensure a self-consistent treatment., Comment: 20 pages, 6 figures. Minor changes to match published version

Gamma-ray bursts resulting from binary neutron-star mergers are sometimes preceded by precursor flares. These harbingers may be ignited by quasi-normal modes, excited by orbital resonances, shattering the stellar crust of one of the inspiralling stars up to $\gtrsim10$ seconds before coalescence. In the rare case that a system displays two precursors, successive overtones of either interface- or $g$-modes may be responsible for the overstrainings. Since the free-mode frequencies of these overtones have an almost constant ratio, and the inertial-frame frequencies for rotating stars are shifted relative to static ones, the spin frequency of the flaring component can be constrained as a function of the equation of state, the binary mass ratio, the mode quantum numbers, and the spin-orbit misalignment angle. As a demonstration of the method, we find that the precursors of GRB090510 hint at a spin frequency range of $2 \lesssim \nu_{\star}/\text{Hz} \lesssim 20$ for the shattering star if we allow for an arbitrary misalignment angle, assuming $\ell=2$ $g$-modes account for the events., Comment: 11 pages, 6 figures, 2 tables with an appendix containing 1 figure. Accepted for publication in A&A

A short X-ray burst was observed from the radio-loud magnetar 1E 1547.0-5408 in 2022 April. Unusually however, the source stopped showing radio pulsations $\gtrsim 3\,$weeks prior to the burst. After recovery, radio timing revealed that the object had also undergone a modest glitch. A model for the overall event is constructed where an initially mild perturbation adjusts the magnetic geometry near the polar caps, leading to shallow fractures. Crustal ejecta or particles leaking from a pair-plasma fireball pollute the magnetospheric gaps, shutting off the pulsar mechanism, but the energy release is not yet large enough to noticeably enhance the X-ray flux. This perturbation gradually ramps, eventuating in a large-scale energy redistribution which fuels the burst. The star's mass quadrupole moment changes in tandem, issuing a glitch. Some quantitative estimates for the magnetic reconfiguration under this interpretation are provided, based on a quasi-static model where the fluid evolves through a sequence of hydromagnetic equilibria., Comment: 8 pages, 4 figures. Minor changes to match published version. Accepted for publication in MNRAS

The radio pulsar GLEAM-X J162759.5-523504.3 has an extremely long spin period ($P = 1091.17\, \mbox{s}$), and yet seemingly continues to spin down rapidly ($\dot{P} < 1.2 \times 10^{-9}\, \mbox{ss}^{-1}$). The magnetic field strength that is implied, if the source is a neutron star undergoing magnetic dipole braking, could exceed $10^{16}\,\mbox{G}$. This object may therefore be the most magnetised neutron star observed to date. In this paper, a critical analysis of a magnetar interpretation for the source is provided. (i) A minimum polar magnetic field strength of $B \sim 5 \times 10^{15}\,\mbox{G}$ appears to be necessary for the star to activate as a radio pulsar, based on conventional `death valley' assumptions. (ii) Back-extrapolation from magnetic braking and Hall-plastic-Ohm decay suggests that a large angular momentum reservoir was available at birth to support intense field amplification. (iii) The observational absence of X-rays constrains the star's field strength and age, as the competition between heating from field decay and Urca cooling implies a surface luminosity as a function of time. If the object is an isolated, young ($\sim 10\, \mbox{kyr}$) magnetar with a present-day field strength of $B \gtrsim 10^{16}\,\mbox{G}$, the upper limit ($\approx 10^{30}\, \mbox{erg s}^{-1}$) set on its thermal luminosity suggests it is cooling via a direct Urca mechanism., Comment: 12 pages, 6 figures. Accepted for publication in MNRAS

The high-mass X-ray binary LS I +61{\deg}303 is also cataloged as a gamma-ray binary as a result of frequent outbursts at TeV photon energies. The system has released two soft-gamma flares in the past, suggesting a magnetar interpretation for the compact primary. This inference has recently gained significant traction following the discovery of transient radio pulses, detected in some orbital phases from the system, as the measured rotation and tentative spin-down rates imply a polar magnetic field strength of $B_p \gtrsim 10^{14}\,\mbox{G}$ if the star is decelerating via magnetic dipole braking. In this paper, we scrutinize magnetic field estimates for the primary in LS I +61{\deg}303 by analyzing the compatibility of available data with the system's accretion dynamics, spin evolution, age limits, gamma-ray emissions, and radio pulsar activation. We find that the neutron star's age and spin evolution are theoretically difficult to reconcile unless a strong propeller torque is in operation. This torque could be responsible for the bulk of even the maximum allowed spin-down, potentially weakening the inferred magnetic field by more than an order of magnitude., Comment: 12 pages, 5 figures. Minor changes to title and abstract to match published version

GRB 211211A was accompanied by a kilonova, implying a merger origin for the event. A precursor flare, modulated by quasi-periodic oscillations at $\approx 22\, \mbox{Hz}$, was also seen $\approx 1\, \mbox{s}$ prior to the main emission. It is suggested here that the precursor resulted from the resonant shattering of one star's crust prior to coalescence. Seismic aftershocks and low-frequency torsional modes may emanate from the rupture site in this case, explaining the underlying oscillations. This interpretation is directly analogous to proposals for giant flares from soft gamma repeaters, where oscillations at similar frequencies have been observed, involving starquakes followed by crustal vibrations. Torsional mode properties were computed for sequences of slowly rotating, magnetised neutron stars in general relativity. The $\approx 22\, \mbox{Hz}$ modulations in the precursor matches that of nodeless, $\ell =2$ torsional modes for a wide variety of stellar parameters. Global or discrete Alfv\'en modes are also viable candidates., Comment: 7 pages, 2 figures, 1 table. Matches published version

Buoyancy-restored modes inside neutron stars depend sensitively on both the microphysical (e.g., composition and entropy gradients) and macrophysical (e.g., stellar mass and radius) properties of the star. Asteroseismology efforts for $g$-modes are therefore particularly promising avenues for recovering information concerning the nuclear equation of state. In this work it is shown that the overall low-temperature $g$-space consists of multiple groups corresponding to different classes of equation of state (e.g., hadronic vs. hybrid). This is in contrast to the case of pressure-driven modes, for example, which tend to follow a universal relation regardless of microphysical considerations. Using a wide library of currently-viable equations of state, perturbations of static, stratified stars are calculated in general relativity to demonstrate in particular how $g$-space groupings can be classified according to the mean mass density, temperature, central speed of sound, and tidal deformability. Considering present and future observations regarding gravitational waves, accretion outbursts, quasi-periodic oscillations, and precursor flashes from gamma-ray bursts, it is shown how one might determine which group the $g$-modes belong to., Comment: 14 pages, 10 figures, 1 table; accepted by MNRAS; typos in equation (10) corrected

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

Many classes of extended scalar-tensor theories predict that dynamical instabilities can take place at high energies, leading to the formation of scalarized neutron stars. Depending on the theory parameters, stars in a scalarized state can form a solution-space branch that shares a lot of similarities with the so-called mass twins in general relativity appearing for equations of state containing first-order phase transitions. Members of this scalarized branch have a lower maximum mass and central energy density compared to Einstein ones. In such cases, a scalarized star could potentially over-accrete beyond the critical mass limit, thus triggering a gravitational phase transition where the star sheds its scalar hair and migrates over to its non-scalarized counterpart. Such an event resembles, though is distinct from, a nuclear or thermodynamic phase transition. We dynamically track a gravitational transition by first constructing hydrostatic, scalarized equilibria for realistic equations of state, and then allowing additional material to fall onto the stellar surface. The resulting bursts of monopolar radiation are dispersively-stretched to form a quasi-continuous signal that persists for decades, carrying strains of order $\gtrsim10^{-22} (\text{kpc}/L)^{3/2} \text{ Hz}^{-1/2}$ at frequencies of $\lesssim300 \text{ Hz}$, detectable with the existing interferometer network out to distances of $L\lesssim10 \text{ kpc}$, and out to a few hundred kpc with the inclusion of the Einstein Telescope. Electromagnetic signatures of such events, involving gamma-ray and neutrino bursts, are also considered., Comment: 11 pages, 9 figures, 1 table. Accepted for publication in Physical Review Letters

Rapidly rotating neutron stars are promising sources for existing and upcoming gravitational-wave interferometers. While relatively dim, these systems are expected to emit continuously, allowing for signal to be accumulated through persistent monitoring over year-long timescales. If, at some point during the observational window, the source comes to lie behind a dense collection of stars, transient gravitational lensing may occur. Such events, though rare, would modulate the waveform, induce phase drifts, and ultimately affect parameter inferences concerning the nuclear equation of state and/or magnetic field structure of the neutron star. Importantly, the radiation wavelength will typically exceed the Schwarzschild radius of the individual perturbers in this scenario, implying that (micro-)lensing occurs in the diffractive regime where geometric optics does not apply. In this paper, we make use of numerical tools that borrow from Picard-Lefschetz theory to efficiently evaluate the relevant Fresnel-Kirchhoff integrals for $n \gtrsim 10^{2}$ microlenses. Modulated strain profiles are constructed both in general and for particular neutron star trajectories relative to some simulated macrolenses., Comment: 14 pages, 10 figures. Accepted for publication in the Astrophysical Journal

It is commonly believed that neutron stars exceeding the maximum mass limit for stability could be formed in the aftermath of binary neutron star mergers, enjoying a short life of metastability before losing centrifugal support and collapsing to a black hole. It is suggested here that a similar scenario could take place when the remnant's excess mass is supported by an ultra-strong $(\gtrsim 10^{17}\,\mbox{G})$ magnetic field that could be generated during, and shortly after, coalescence. We show that such 'magnetically supramassive' neutron stars could stave off collapse and survive for a few years before their magnetic energy is sufficiently dissipated due to ambipolar diffusion. In addition, we speculate on multi-messenger signatures of such objects and discuss the robustness of our results against limitations placed by neutron superfluidity and magneto-thermal evolution., Comment: 5 pages, 3 figures. Accepted for publication as a Letter in Phys. Rev. D

Accreting millisecond X-ray pulsars are known to provide a wealth of physical information during their successive states of outburst and quiescence. Based on the observed spin-up and spin-down rates of these objects it is possible, among other things, to infer the stellar magnetic field strength and test models of accretion disc flow. In this paper we consider the three accreting X-ray pulsars (XTE J1751-305, IGR J00291+5934, and SAX J1808.4-3658) with the best available timing data, and model their observed spin-up rates with the help of a collection of standard torque models that describe a magnetically-threaded accretion disc truncated at the magnetospheric radius. Whilst none of these models are able to explain the observational data, we find that the inclusion of the physically motivated phenomenological parameter $\xi$, which controls the uncertainty in the location of the magnetospheric radius, leads to an enhanced disc-integrated accretion torque. These 'new' torque models are compatible with the observed spin-up rates as well as the inferred magnetic fields of these objects provided that $\xi \approx 0.1-0.5$. Our results are supplemented with a discussion of the relevance of additional physics effects that include the presence of a multipolar magnetic field and general-relativistic gravity., Comment: 15 pages, 9 figures. Accepted for publication in MNRAS

In some short gamma-ray bursts, precursor flares occurring $\sim$ seconds prior to the main episode have been observed. These flares may then be associated with the last few cycles of the inspiral when the orbital frequency is a few hundred Hz. During these final cycles, tidal forces can resonantly excite quasi-normal modes in the inspiralling stars, leading to a rapid increase in their amplitude. It has been shown that these modes can exert sufficiently strong strains onto the neutron star crust to instigate yieldings. Due to the typical frequencies of $g$-modes being $\sim 100\text{ Hz}$, their resonances with the orbital frequency match the precursor timings and warrant further investigation. Adopting realistic equations of state and solving the general-relativistic pulsation equations, we study $g$-mode resonances in coalescing quasi-circular binaries, where we consider various stellar rotation rates, degrees of stratification, and magnetic field structures. We show that for some combination of stellar parameters, the resonantly excited $g_1$- and $g_2$-modes may lead to crustal failure and trigger precursor flares., Comment: 15 pages, 8 figures, 2 tables. Accepted for publication in MNRAS

During the final stages of a neutron-star binary coalescence, stellar quasi-normal modes can become resonantly excited by tidal fields. If the strain exerted by the excited modes exceeds the extent to which the crust can respond linearly, localised crustal failures may occur. In this work, we re-examine resonant $g$-mode excitations of relativistic neutron stars in the last $\sim$ 10 seconds of an inspiral. We adopt realistic equations of state that pass constraints from GW170817, include 3rd order post-Newtonian terms for the conservation orbital motion, and employ a 2.5 post-Newtonian scheme for gravitational back-reaction. Frequency modulations of the modes due to tidal fields, Lorentz forces, and (slow) rotation are also considered to investigate the maximal strain achievable by resonantly-excited $g$-modes. Depending on the equation of state, degree of stratification, and stellar magnetic field, we find that certain $g$-modes excitations may be able to break the crust some seconds prior to coalescence., Comment: 15 pages, 11 figures, 2 tables. Matches published version in MNRAS

By virtue of their sub-hour orbital periods, ultra-compact X-ray binaries are promising sources for the space-borne gravitational-wave interferometers LISA, Taiji, and TianQin. Some of these systems contain a neutron star primary, whose spin period can be measured directly via pulse timing, or indirectly through rotational modulations of burst phenomena. It is pointed out here that since actively accreting stars, with spin frequencies in the hundreds of Hz, may continuously emit appreciable gravitational waves due to the presence of accretion-built mountains, toroidal magnetic fields, and/or $r$-mode oscillations, such binaries are also candidate sources for ground-based interferometers. Two Galactic systems (4U 1728-34 and 4U 1820-30) are identified as being potentially detectable by both LISA and aLIGO simultaneously: a dual-line detection of this sort could provide percent-level constraints on the mass, radius, and internal magnetic field strength of the neutron star. With the Einstein Telescope, we find that at least four of the known ultra-compact binaries become dual-line visible., Comment: 10 pages, 3 figures, 2 tables. Matches published version in MNRAS

The Kerr geometry admits the Carter symmetry, which ensures that the geodesic equations are integrable. It is shown that gravitational waveforms associated with extreme-mass-ratio inspirals involving a non-integrable compact object display `glitch' phenomena, where the frequencies of gravitational waves increase abruptly, when the orbit crosses certain spacetime regions known as Birkhoff islands. The presence or absence of these features in data from upcoming space-borne detectors will therefore allow not only for tests of general relativity, but also of fundamental spacetime symmetries., Comment: 5 pages, 2 figures, accepted for publication in Physical Review Letters, matches published version

A covariant, scalar-tensor gravity is constructed such that the static, spherically symmetric Rezzolla-Zhidenko metric is an exact solution to the theory. The equations describing gravitational perturbations of this spacetime, which represents a generic black hole possessing an arbitrary number of hairs, can then be derived. This allows for a self-consistent study of the associated quasinormal modes. It is shown that mode spectra are tied to not only the non-Einstein parameters in the metric but also to those that appear at the level of the action, and that different branches of the exact theory can, in some cases, predict significantly different oscillation frequencies and damping times. For choices which make the theory appear more like general relativity in some precise sense, we find that a nontrivial Rezzolla-Zhidenko parameter space is permissible under current constraints on fundamental ringdown modes observed by Advanced LIGO., Comment: 11 pages, 4 figures, 2 tables. Minor updates to match PRD version

Short gamma-ray bursts that are followed by long-duration X-ray plateaus may be powered by the birth, and hydrodynamic evolution, of magnetars from compact binary coalescence events. If the rotation and magnetic axes of the system are not orthogonal to each other, the star will undergo free precession, leading to fluctuations in the luminosity of the source. In some cases, precession-induced modulations in the spin-down power may be discernible in the X-ray flux of the plateau. In this work, 25 X-ray light curves associated with bursts exhibiting a plateau are fitted to luminosity profiles appropriate for precessing, oblique rotators. Based on the Akaike Information Criterion, 16 (64 per cent) of the magnetars within the sample display either moderate or strong evidence for precession. Additionally, since the precession period of the star is directly tied to its quadrupolar ellipticity, the fits allow for an independent measure of the extent to which the star is deformed by internal stresses. Assuming these deformations arise due to a mixed poloidal-toroidal magnetic field, we find that the distribution of magnetic-energy ratios is bimodal, with data points clustering around energetically equal and toroidally dominated partitions. Implications of this result for gravitational-wave emission and dynamo activity in newborn magnetars are discussed., Comment: 15 pages, 6 figures, 4 tables. Matches published version in MNRAS

Many millisecond pulsars are thought to be old neutron stars spun up (`recycled') during an earlier accretion phase. They typically have relatively weak ($\lesssim 10^{9} \text{ G}$) dipole field strengths, consistent with accretion-induced magnetic burial. Recent data from the Neutron Star Interior Composition Explorer indicate that hot spots atop the recycled pulsar PSR J0030$+$0451 are not antipodal, so that the magnetic field cannot be that of a centered dipole. In this paper it is shown that multipolarity is naturally expected in the burial scenario because of equatorial field line compression. Grad-Shafranov equilibria are constructed to show how magnetic multipole moments can be calculated in terms of various properties, such as the amount of accreted mass and the crustal equation of state., Comment: 14 pages, 14 figures. Accepted for publication in MNRAS

One of the primary aims of upcoming space-borne gravitational wave detectors is to measure radiation in the mHz range from extreme-mass-ratio inspirals. Such a detection would place strong constraints on hypothetical departures from a Kerr description for astrophysically stable black holes. The Kerr geometry, which is unique in general relativity, admits a higher-order symmetry in the form of a Carter constant, which implies that the equations of motion describing test particle motion in a Kerr background are Liouville-integrable. In this article, we investigate whether the Carter symmetry itself is discernible from a generic deformation of the Kerr metric in the gravitational waveforms for such inspirals. We build on previous studies by constructing a new metric which respects current observational constraints, describes a black hole, and contains two non-Kerr parameters, one of which controls the presence or absence of the Carter symmetry, thereby controlling the existence of chaotic orbits, and another which serves as a generic deformation parameter. We find that these two parameters introduce fundamentally distinct features into the orbital dynamics, and evince themselves in the gravitational waveforms through a significant dephasing. Although only explored in the quadrupole approximation, this, together with a Fisher metric analysis, suggests that gravitational wave data analysis may be able to test, in addition to the governing theory of gravity, the underlying symmetries of spacetime., Comment: 14 pages, 7 figures, matches published version

In general relativity without a cosmological constant, a classical theorem due to Hawking states that stationary black holes must be topologically spherical. This result is one of the several ingredients that collectively imply the uniqueness of the Kerr metric. If, however, general relativity describes gravity inexactly at high energies or over cosmological scales, Hawking's result may not apply, and black holes with non-trivial topology may be, at least mathematically, permissible. While tests involving electromagnetic and gravitational-wave data have been used to place tight constraints on various theoretical departures from a Kerr description of astrophysical black holes, relatively little attention has been paid to topological alternatives. In this paper, we derive a new exact solution in an $f(R)$ theory of gravity which admits topologically non-trivial black holes, and calculate observables like fluorescent K$\alpha$ iron-line profiles and black hole images from hypothetical astrophysical systems which house these objects, to provide a theoretical basis for new tests of black hole nature. On the basis of qualitative comparisons, we show that topologically non-trivial objects would leave a strong imprint on electromagnetic observables and can be easily distinguished from general-relativistic black holes in nearly all cases., Comment: 15 pages, 9 figures. Comments welcome

A method is presented to construct a particular, non-minimally coupled scalar-tensor theory such that a given metric is an exact vacuum solution in that theory. In contrast to the standard approach in studies of gravitational dynamics, where one begins with an action and then solves the equations of motion, this approach allows for an explicit theory to be built around some pre-specified geometry. Starting from a parameterized black hole spacetime with generic, non-Kerr hairs, it is shown how an overarching family of theories can be designed to fit the metric exactly., Comment: 5 pages, 1 figure, substantially revised. Accepted for publication in Gen. Rel. Grav. Lett

The set of all metrics that can be placed on a given manifold defines an infinite-dimensional `superspace' that can itself be imbued with the structure of a Riemannian manifold. Geodesic distances between points on Met$(M)$ measure how close two different metrics over $M$ are to one another. Restricting our attention to only those metrics that describe physical black holes, these distances may therefore be thought of as measuring the level of geometric similarity between different black hole structures. This allows for a systematic quantification of the extent to which a black hole, possibly arising as an exact solution to a theory of gravity extending general relativity in some way, might be `non-Kerr'. In this paper, a detailed construction of a superspace for stationary black holes with an arbitrary number of hairs is carried out. As an example application, we are able to strengthen a recent claim made by Konoplya and Zhidenko about which deviation parameters describing a hypothetical, non-Schwarzschild black hole are likely to be most relevant for astrophysical observables., Comment: 17 pages, 4 figures. Accepted for publication in Class. Quant. Grav. (Minor typos corrected)

Many gamma-ray bursts are followed by periods of extended emission. At least in some cases, the burst afterglow may be powered by a rapidly rotating, highly-magnetised neutron star, which spins down due to electromagnetic and gravitational wave emission. Such a remnant is likely to strongly precess in the early stages of its life, which would lead to modulations in the X-ray luminosity as the triaxiality of the system evolves over time. Using a radiation profile appropriate for a precessing, oblique rotator, we find that Swift-XRT data of a long (080602) and a short (090510) burst matches the model with significantly higher accuracy (mean-square residuals dropping by $\gtrsim 200 \%$ in the early stages of the extended emission) than for an orthogonal rotator. We interpret this as evidence for precession in newborn magnetars., Comment: 6 pages, 4 figures, 1 table. Accepted for publication in ApJL

As evidenced by the coincident detections of GW170817 and GRB 170817A, short gamma-ray bursts are likely associated with neutron star-neutron star merger events. Although rare, some bursts display episodes of early emission, with precursor flares being observed up to $\sim 10$ seconds prior to the main burst. As the stars inspiral due to gravitational wave emission, the exertion of mutual tidal forces leads to the excitation of stellar oscillation modes, which may come into resonance with the orbital motion. Mode amplitudes increase substantially during a period of resonance as tidal energy is deposited into the star. The neutron star crust experiences shear stress due to the oscillations and, if the resonant amplitudes are large enough, may become over-strained. This over-straining can lead to fractures or quakes which release energy, thereby fueling precursor activity prior to the merger. Using some simple Maclaurin spheroid models, we investigate the influence of magnetic fields and rapid rotation on tidally-forced $f$- and $r$- modes, and connect the associated eigenfrequencies with the orbital frequencies corresponding to precursor events seen in, for example, GRB 090510., Comment: 16 pages, 8 figures, 1 table. Added a few references. Accepted for publication in Phys. Rev. D

In general relativity, the Kerr metric uniquely represents the geometry surrounding an isolated, rotating black hole. An identification of significant non-Kerr features in some astrophysical source would then provide a `smoking-gun' for the break-down of general relativity in the strong-field regime. On the other hand, Kerr black holes are common to many other theories of gravity, and thus a validation of the Kerr metric does not necessarily favour general relativity amongst all possibilities. The nature of gravitational perturbations will however differ between different theories of gravity. Future precision tests involving gravitational waves from oscillating black holes, such as identifications of the quasi-normal mode spectrum from ring-down, will thus be able to probe the underlying theory, even if the object is Kerr. Here, we write down the equations governing metric perturbations of a Kerr black hole in $f(R)$ gravity in a form that is more conducive to numerical study., Comment: 8 pages. To appear in the proceedings of the 6th Conference of the Polish Society on Relativity

Some pairs of neutron star models can intuitively be thought of as being `closer' together than others, in the sense that more precise observations might be required to distinguish between them than would be necessary for other pairs. In this paper, borrowing ideas from the study of geometrodynamics, we introduce a mathematical formalism to define a geometric distance between stellar models, to provide a quantitative meaning to this notion of closeness. In particular, it is known that the set of all metrics on a Riemannian manifold itself admits the structure of a Riemannian manifold (`configuration manifold'), which comes equipped with a canonical metric. By thinking of a stationary star as being a particular $3+1$ metric, the structure of which is determined through the Tolman-Oppenheimer-Volkoff relations and their generalisations, points on a suitably restricted configuration manifold can be thought of as representing different stars, and distances between these points can be computed. We develop the necessary mathematical machinery to build the configuration manifold of neutron star models, and provide some worked examples to illustrate how this space might be used in future studies of stellar structure., Comment: 6 pages, 1 figure. Accepted for publication in Classical and Quantum Gravity

Fast radio bursts are millisecond-duration radio pulses of extragalactic origin. A recent statistical analysis has found that the burst energetics of the repeating source FRB 121102 follow a power-law, with an exponent that is curiously consistent with the Gutenberg-Richter law for earthquakes. This hints that repeat-bursters may be compact objects undergoing violent tectonic activity. For young magnetars, possessing crustal magnetic fields which are both strong ($B \gtrsim 10^{15}$ G) and highly multipolar, Hall drift can instigate significant field rearrangements even on $\lesssim$ century long timescales. This reconfiguration generates zones of magnetic stress throughout the outer layers of the star, potentially strong enough to facilitate frequent crustal failures. In this paper, assuming a quake scenario, we show how the crustal field evolution, which determines the resulting fracture geometries, can be tied to burst properties. Highly anisotropic stresses are generated by the rapid evolution of multipolar fields, implying that small, localised cracks can occur sporadically throughout the crust during the Hall evolution. Each of these shallow fractures may release bursts of energy, consistent in magnitude with those seen in the repeating sources FRB 121102 and FRB 180814.J0422+73., Comment: 13 pages, 7 figures. Several references added. Matches published version in MNRAS

Modified theories of gravity are often built such that they contain general relativity as a limiting case. This inclusion property implies that the Kerr metric is common to many families of theories. For example, all analytic $f(R)$ theories with vanishing constant term admit the Kerr solution. In any given theory, however, the response of the gravitational field to astrophysical disturbances is tied to the structure of the field equations. As such, even if black holes are Kerr, the underlying theory can, in principle, be probed through gravitational distortions. In this paper, we study linear perturbations of a Kerr black hole in $f(R)$ gravity using the Newman-Penrose formalism. We show that, as in general relativity, the equations governing the perturbed metric, which depend on the quadratic term of the function $f$, completely decouple., Comment: 8 pages. Accepted for publication in Phys. Rev. D

A magnetically confined mountain on the surface of an accreting neutron star simultaneously reduces the global magnetic dipole moment through magnetic burial and generates a mass quadrupole moment, which emits gravitational radiation. Previous mountain models have been calculated for idealized isothermal and adiabatic equations of state. Here these models are generalised to include non-zero, finite thermal conduction. Grad-Shafranov equilibria for three representative, polytropic equations of state are evolved over many conduction time-scales with the magnetohydrodynamic solver PLUTO. It is shown that conduction facilitates the flow of matter towards the pole. Consequently the buried magnetic field is partially resurrected starting from an initially polytropic Grad-Shafranov equilibrium. The poleward mass current makes the star more prolate, marginally increasing its detectability as a gravitational wave source, though to an extent which is likely to be subordinate to other mountain physics. Thermal currents also generate filamentary hot spots $(\gtrsim 10^{8} \text{ K})$ in the mountain, especially near the pole where the heat flux is largest, with implications for type I X-ray bursts., Comment: 23 pages,17 figures, 3 tables. Accepted for publication in MNRAS

In problems of parameter estimation from sensor data, the Fisher Information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the measurements. From the geometric viewpoint, it is a Riemannian metric on the manifold of parameters of the observed system. In this paper we consider the case of parameterized sensors and answer the question, "How best to reconfigure a sensor (vary the parameters of the sensor) to optimize the information collected?" A change in the sensor parameters results in a corresponding change to the metric. We show that the change in information due to reconfiguration exactly corresponds to the natural metric on the infinite dimensional space of Riemannian metrics on the parameter manifold, restricted to finite-dimensional sub-manifold determined by the sensor parameters. The distance measure on this configuration manifold is shown to provide optimal, dynamic sensor reconfiguration based on an information criterion. Geodesics on the configuration manifold are shown to optimize the information gain but only if the change is made at a certain rate. An example of configuring two bearings-only sensors to optimally locate a target is developed in detail to illustrate the mathematical machinery, with Fast-Marching methods employed to efficiently calculate the geodesics and illustrate the practicality of using this approach., Comment: submitted to Information Geometry 2018-11-02

Some modified theories of gravity are known to predict monopolar, in addition to the usual quadrupolar and beyond, gravitational radiation in the form of `breathing' modes. For the same reason that octupole and higher-multipole terms often contribute negligibly to the overall wave strain, monopole terms tend to dominate. We investigate both monopolar and quadrupolar continuous gravitational radiation from neutron stars deformed through internal magnetic stresses. We adopt the Parameterised-Post-Newtonian formalism to write down equations describing the leading-order stellar properties in a theory-independent way, and derive some exact solutions for stars with mixed poloidal-toroidal magnetic fields. We then turn to the specific case of scalar-tensor theories to demonstrate how observational upper limits on the gravitational-wave luminosity of certain neutron stars may be used to place constraints on modified gravity parameters, most notably the Eddington parameter $\gamma$. For conservative, purely poloidal models with characteristic field strength given by the spindown minimum, upper limits for the Vela pulsar yield $1-\gamma \lesssim 4.2 \times 10^{-3}$. For models containing a strong toroidal field housing $\sim 99\%$ of the internal magnetic energy, we obtain the bound $1- \gamma \lesssim 8.0 \times 10^{-7}$. This latter bound is an order of magnitude tighter than those obtained from current Solar system experiments, though applies to the strong-field regime., Comment: 13 pages, 6 figures, 1 table. Accepted for publication in Phys. Rev. D

The oscillation spectrum of a perturbed neutron star is intimately related to the physical properties of the star, such as the equation of state. Observing pulsating neutron stars therefore allows one to place constraints on these physical properties. However, it is not obvious exactly how much can be learnt from such measurements. If we observe for long enough, and precisely enough, is it possible to learn everything about the star? A classical result in the theory of spectral geometry states that one cannot uniquely `hear the shape of a drum'. More formally, it is known that an eigenfrequency spectrum may not uniquely correspond to a particular geometry; some `drums' may be indistinguishable from a normal-mode perspective. In contrast, we show that the drum result does not extend to perturbations of simple neutron stars within general relativity -- in the case of axial (toroidal) perturbations of static, perfect fluid stars, a quasi-normal mode spectrum uniquely corresponds to a stellar profile. We show in this paper that it is not possible for two neutron stars, with distinct fluid profiles, to oscillate in an identical manner. This result has the information-theoretic consequence that gravitational waves completely encode the properties of any given oscillating star: unique identifications are possible in the limit of perfect measurement., Comment: 6 pages, 1 figure, Accepted for publication in MNRAS

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of $a_{2}$. Anisotropic solutions are found, whose wave-fronts trace out time- or space-like hypersurfaces with complicated geometric properties. We show that the solutions exist in $f(R)$ theories that are consistent with Solar System and pulsar timing experiments., Comment: 8 pages, 3 figures, 1 table. Accepted for publication in PRD

The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. As a worked example, we apply the generalised Ernst equations to derive a $f(R)$ generalisation of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in $f(R)$ gravity in the context of soliton-like solutions that display shock-wave behaviour across the causal boundary., Comment: 12 pages, zero figures. Accepted for publication in PRD

A precondition for the radio emission of pulsars is the existence of strong, small-scale magnetic field structures (`magnetic spots') in the polar cap region. Their creation can proceed via crustal Hall drift out of two qualitatively and quantitatively different initial magnetic field configurations: a field confined completely to the crust and another which penetrates the whole star. The aim of this study is to explore whether these magnetic structures in the crust can deform the star sufficiently to make it an observable source of gravitational waves. We model the evolution of these field configurations, which can develop, within $\sim 10^4$ -- $10^5$ yr, magnetic spots with local surface field strengths $\sim 10^{14}$ G maintained over $\gtrsim 10^6$ yr. Deformations caused by the magnetic forces are calculated. We show that, under favourable initial conditions, a star undergoing crustal Hall drift can have ellipticity $\epsilon\sim 10^{-6}$, even with sub-magnetar polar field strengths, after $\sim 10^5$ yr. A pulsar rotating at $\sim 10^2$ Hz with such $\epsilon$ is a promising gravitational-wave source candidate. Since such large deformations can be caused only by a particular magnetic field configuration that penetrates the whole star and whose maximum magnetic energy is concentrated in the outer core region, gravitational wave emission observed from radio pulsars can thus inform us about the internal field structures of young neutron stars., Comment: 14 pages, 6 figures, 5 tables. Accepted for publication in MNRAS

We construct multipole moments for stationary, asymptotically flat, spacetime solutions to higher-order curvature theories of gravity. The moments are defined using $3+1$ techniques involving timelike Killing vector constructions as in the classic papers by Geroch and Hansen. Using the fact that the Kerr-Newman metric is a vacuum solution to a particular class of $f(R)$ theories of gravity, we compute all its moments, and find that they admit recurrence relations similar to those for the Kerr solution in general relativity. It has been proposed previously that modelling the measured frequencies of quasi-periodic oscillations from galactic microquasars enables experimental tests of the no-hair theorem. We explore the possibility that, even if the no-hair relation is found to break down in the context of general relativity, there may be an $f(R)$ counterpart that is preserved. We apply the results to the microquasars GRS $1915$+$105$ and GRO J$1655$-$40$ using the diskoseismology and kinematic resonance models, and constrain the spins and `charges' [which are not really electric charges in the $f(R)$ context] of their black holes., Comment: 14 pages, 5 figures; Accepted for publication in PRD

The sudden spin-down event ('anti-glitch') observed in AXP 1E 2259+586 on 2012 April 21 was arguably caused by a decay of its internal toroidal magnetic field component, which turns a stable prolate configuration into an unstable one. We refine previous models of this process by modelling the star's magnetic field self-consistently as a 'twisted torus' configuration in non-barotropic equilibrium (which allows us to explore a greater range of equilibrium configurations). It is shown that, if the star's magnetic field is purely dipolar, the change in the toroidal field strength required to produce an anti-glitch of the observed size can be ~ 10 times larger than previously calculated. If the star has a quadrupolar magnetic field component, then an anti-glitch of similar magnitude can be produced via a decay of the quadrupole component, in addition to a decay of the toroidal component. We show that, if the quadrupole component decays, the minimum initial toroidal field strength and the change in toroidal field strength needed to produce the observed anti-glitch are lower than in the pure dipole twisted torus. In addition, we predict the maximum anti-glitch sizes, assuming that they are caused by a change in ellipticity, in four glitching magnetars and discuss the implications for energetics of accompanying X-ray bursts., Comment: 12 pages, 4 figures

A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic-field-aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalises previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g., spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin downs, and are not purely dipolar., Comment: 14 pages, 6 figures, 1 table. Accepted for publication in the Monthly Notices of the Royal Astronomical Society

We present some results regarding metric perturbations in general relativity and other metric theories of gravity. In particular, using the Newman Penrose variables, we write down and discuss the equations which govern tensor field perturbations of ranks $0, \pm 1$ and $\pm 2$ (scalar,vector,tensor bosonic perturbations) over certain space-times that admit specific background metrics expressible in isotropic coordinates. Armed with these equations, we are able to develop the Hadamard series which can be associated with the fundamental solution of the equations, wherein we introduce an inhomogeneous singularity at the physical space-time point of the perturbing particle. The Hadamard series is then used to generate closed form solutions by making choices for an appropriate ansatz solution. In particular, we solve for the spin-weighted electrostatic potential for the Reissner-Nordstrom black hole and for the fully dynamical potential for the Friedmann-Robertson-Walker cosmological solution., Comment: 15 pages, 0 figures