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Massive stars end their life as core-collapse supernovae, amongst which some extremes are Type Ic broad-lined supernovae associated with long-duration gamma-ray bursts (LGRBs) having powerful relativistic jets. Their less-extreme brethren make unsuccessful jets that are choked inside the stars, appearing as X-ray flashes or low-luminosity GRBs. On the other hand, there exists a population of extragalactic fast X-ray transients (EFXTs) with timescales ranging from seconds to thousands of seconds, whose origins remain obscure. Known sources that contribute to the observed EFXT population include the softer analogs of LGRBs, shock breakouts of supernovae, or unsuccessful jets. Here, we report the discovery of the bright X-ray transient EP240414a detected by the Einstein Probe (EP), which is associated with the Type Ic supernova SN 2024gsa at a redshift of 0.401. The X-ray emission evolution is characterised by a very soft energy spectrum peaking at < 1.3 keV, which makes it distinct from known LGRBs, X-ray flashes, or low-luminosity GRBs. Follow-up observations at optical and radio bands revealed the existence of a weak relativistic jet that interacts with an extended shell surrounding the progenitor star. Located on the outskirts of a massive galaxy, this event reveals a new population of explosions of Wolf-Rayet stars characterised by a less powerful engine that drives a successful but weak jet, possibly owing to a progenitor star with a smaller core angular momentum than in traditional LGRB progenitors., Comment: 43 pages, 9 figures, 4 tables, submitted. Comments are welcome

Intense highly charged ion beam production is essential for high-power heavy ion accelerators. A novel movable Vlasov launcher for superconducting high charge state Electron Cyclotron Resonance (ECR) ion source has been devised that can affect the microwave power effectiveness by a factor of about 4 in terms of highly charged ion beam production. This approach based on a dedicated microwave launching system instead of the traditional coupling scheme has led to new insight on microwave-plasma interaction. With this new understanding, the world record highly charged xenon ion beam currents have been enhanced by up to a factor of 2, which could directly and significantly enhance the performance of heavy ion accelerators and provide many new research opportunities in nuclear physics, atomic physics and other disciplines.

The discrepancy between the observed value of the cosmological constant (CC) and its expected value from quantum field theoretical considerations motivates the search for a theory in which the CC is decoupled from the vacuum energy. In this article, we consider the viability of theories in which the Einstein equations are recovered (without additional constraints) and in which the CC is regarded as an integration constant. These theories include trace-free Einstein gravity, theories constructed from the Codazzi equation (which includes Cotton gravity and a gauge-gravity inspired theory), and conformal Killing gravity. We remark on a recent debate regarding Cotton gravity and find that while the Codazzi equation of that theory is indeed underdetermined, the solutions of the Codazzi equation trivialize to $\lambda g_{ab}$ on generic backgrounds, and that in principle, one can close the system with the divergence-free condition and an appropriate choice of initial data. We also propose a full variational principle (full in the sense that variations in all variables are considered) for each of the aforementioned theories that can incorporate the matter sector; in this manner, we can obtain the trace-free Einstein equations without a unimodular constraint. The resulting actions require additional (auxiliary) fields and are therefore only expected to be effective, but they may provide a useful starting point in bottom up approaches to constructing more fundamental theories., Comment: 8 pages. Matches published version

In this note, I argue that tidal effects generically limit the kinetic energy of a single massive elementary particle in the vicinity of a compact object. As the kinetic energy is increased, the differences in the tidal potential over a Compton wavelength will at some point exceed the rest mass of the particle. Above the threshold, one expects tidal effects to disrupt single-particle states, and in turn, one might expect an incident particle scattering off a compact object with an energy significantly exceeding the threshold to result in a shower of lower energy particles. A calculation reveals that the threshold for neutrinos scattering off a $10 M_\odot$ black hole within three Schwarzschild radii is roughly $1~\text{GeV}$., Comment: 2 pages. v2: Major changes. Calculations unchanged, major improvements to discussion regarding interpretation, and a strong assumption was relaxed. Conclusions changed accordingly

Quantum black holes (BHs), thought of as an excited multilevel system, can be effectively modelled by replacing an event horizon with a partially reflective membrane. This emergent feature affects their interaction with hosting environments, with the most pronounced effects happening for particles with mass~$m_{\rm p}\lesssim (10 M_{\odot}/M)\,10^{-11}\mathrm{\,eV}$, where~$M$ is the BH mass. We show that ultra-light bosons -- a viable dark matter candidate -- can be used to probe the quantum nature of BHs. We derive analytical expressions for the accretion rate and dynamical friction acting on exotic compact objects moving through an ultra-light scalar field, finding that while the accretion rate is sensitive to the quantum BH's reflectivity, the dynamical friction is the same as for classical BHs. We then use these expressions to estimate the orbital dephasing in the inspiralling of different binaries in the Laser Interferometer Space Antenna (LISA) band. Our results indicate that LISA may be able to discriminate quantum from classical BHs through their different accretion rates., Comment: v3, published version, 16 pages, 2 pictures

We consider a class of quasiregular singularities characterized by points possessing two future-directed light cones and two past-directed light cones. Such singularities appear in the $1+1$ trousers spacetime and the Deutsch-Politzer spacetime. We argue that these singularities are relevant for describing the end point of an evaporating black hole, and show that a class of emergent Lorentz signature theories can provide a microscopic description for these singularities., Comment: 12 pages, 7 figures. Added and corrected a reference, minor formatting changes. Matches published version

An efficient numerical code FP3D has been developed to calculate particle orbits and evaluate particle confinement in 3D magnetic fields including stellarators and tokamaks with 3D fields. The magnetic field is either calculated from coils directly or obtained from equilibrium codes. FP3D has been verified with the 3D equilibrium code VMEC (S. P. Hirshman, Phys. Fluids 26, 3553 (1983)) for magnetic field calculation and with the drift-kinetic code SFINCS (M. Landreman, Physics of Plasmas 21 (4) (2014)) for neoclassical transport. The code has been applied successfully to the NCSX stellarator (B. Nelson, Fusion Engineering and design 66 (2003)) for the calculation of neoclassical transport coefficient with the 3D magnetic field obtained directly from coils. FP3D is also used to calculate ripple losses in the tokamak EAST (W. Yuanxi, Plasma Science Technology 8 (3) (2006))., Comment: 13 pages, 19 figures, submitted to Physics of Plasmas

In this note, I consider a class of metric tensors with smooth components that naively appear to describe dynamical wormholes with vanishing spacetime curvature. I point out that the smoothness of the metric tensor components is deceptive, and that in general relativity, such metrics must be sourced by exotic thin shells., Comment: 2 pages, fixed typo

We describe a shielding mechanism for a charged black hole immersed in a background involving charged matter fields, solely arising from the Einstein-Maxwell field equations. In particular, we consider a charged generalization of the Einstein cluster, that is a charged black hole surrounded by an effective fluid model for a partially charged dust cloud. We show that the shielding mechanism, arising thereof, is generic and appears in a different parametrization of the problem as well. In this process, we provide the most general electrovacuum solution in a spacetime region devoid of charges, but in the presence of a static and spherically symmetric charge distribution elsewhere. Side by side, we also introduce a convenient parametrization, providing the global solution of the Einstein-Maxwell's field equations in the presence of a charged black hole within the environment of charged fluid. We also comment on the nature of the photon sphere, shadow radius and the eikonal quasi-normal modes in the Einstein-Maxwell cluster., Comment: 12 pages, 9 figures, 1 table

The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise to logarithmically divergent terms that would result in irregular variables and equations on the compactified domain, which would in turn prevent accurate numerical approximation. It has been shown, however, that a suitable choice of gauge and constraint addition can be used to prevent their appearance. Presently we give a first order symmetric hyperbolic reduction of general relativity in GHG on compactified hyperboloidal slices that exploits this knowledge and eradicates these log-terms at leading orders. Because of their effect on the asymptotic solution space, specific formally singular terms are systematically chosen to remain. Such formally singular terms have been successfully treated numerically in toy models and result in a formulation with the desirable property that unphysical radiation content near infinity is suppressed., Comment: 20 pages

It is shown that a large class of systems of non-linear wave equations, based on the good-bad-ugly model, admit formal solutions with polyhomogeneous expansions near null infinity. A particular set of variables is introduced which allows us to write the Einstein field equations in generalized harmonic gauge as a good-bad-ugly system and the functional form of the first few orders in such an expansion is found by applying the aforementioned result. Exploiting these formal expansions of the metric components, the peeling property of the Weyl tensor is revisited. The question addressed is whether or not the use of generalized harmonic gauge, by itself, causes a violation of peeling. Working in harmonic gauge, it is found that log-terms that prevent the Weyl tensor from peeling do appear. The impact of gauge source functions and constraint additions on the peeling property is then considered. Finally, the special interplay between gauge and constraint addition, as well as its influence on the asymptotic system and the decay of each of the metric components, is exploited to find a particular gauge which suppresses this specific type of log-term to arbitrarily high order., Comment: 18 pages

In this article, we develop the formalism for singular hypersurfaces and junction conditions in generalized coupling theories using a variational approach. We then employ this formalism to examine the behavior of sharp matter density gradients in generalized coupling theories. We find that such gradients do not necessarily lead to the pathologies present in other theories of gravity with auxiliary fields. A detailed example, based on a simple instance of a generalized coupling theory called the MEMe model, is also provided. In the static case, we show that sharp boundaries do not generate singularities in the dynamical frame despite the presence of an auxiliary field. Instead, in the case of a collapsing spherical density distribution with a general profile an additional force compresses over-densities and expands underdensities. These results can also be used to deduce additional constraints on the parameter of this model., Comment: 17 pages, 7 figures

In this article, we describe and numerically implement a method for relativistic location in slightly curved but otherwise generic spacetimes. For terrestrial positioning in the context of Global Navigation Satellite Systems, our algorithm incorporates gravitational as well as tropospheric and ionospheric effects modeled by the Gordon metric. The algorithm is implemented in the \textsc{squirrel.jl} code, which employs a quasi-Newton Broyden algorithm in conjunction with automatic differentiation of numerical geodesics. Our work provides a practical solution to the relativistic location problem in a generic spacetime and consolidates relativistic and atmospheric effects in a single framework. Though optimization is not our primary focus, our implementation is already fast enough for practical use, establishing a position from five emission points in $< 1~{\rm s}$ on a desktop computer for reasonably simple spacetime geometries. In vacuum, our implementation can achieve submillimeter accuracy considering the Kerr metric with terrestrial parameters and submeter accuracy including tropospheric and ionospheric effects., Comment: 19 pages, 16 figures, 1 table

To maximize the light yield of the liquid scintillator (LS) for the Jiangmen Underground Neutrino Observatory (JUNO), a 20 t LS sample was produced in a pilot plant at Daya Bay. The optical properties of the new LS in various compositions were studied by replacing the gadolinium-loaded LS in one antineutrino detector. The concentrations of the fluor, PPO, and the wavelength shifter, bis-MSB, were increased in 12 steps from 0.5 g/L and <0.01 mg/L to 4 g/L and 13 mg/L, respectively. The numbers of total detected photoelectrons suggest that, with the optically purified solvent, the bis-MSB concentration does not need to be more than 4 mg/L. To bridge the one order of magnitude in the detector size difference between Daya Bay and JUNO, the Daya Bay data were used to tune the parameters of a newly developed optical model. Then, the model and tuned parameters were used in the JUNO simulation. This enabled to determine the optimal composition for the JUNO LS: purified solvent LAB with 2.5 g/L PPO, and 1 to 4 mg/L bis-MSB., Comment: 13 pages, 8 figures

We introduce a population-age-time (PAT) model which describes the temporal evolution of the population distribution in age. The surprising result is that the qualitative nature of the population distribution dynamics is robust with respect to the birth rate and death rate distributions in age, and initial conditions. When the number of children born per woman is 2, the population distribution approaches an asymptotically steady state of a kink shape; thus the total population approaches a constant. When the number of children born per woman is greater than 2, the total population increases without bound; and when the number of children born per woman is less than 2, the total population decreases to zero.

The Weiss variation of the Einstein-Hilbert action with an appropriate boundary term has been studied for general boundary surfaces; the boundary surfaces can be spacelike, timelike, or null. To achieve this we introduce an auxiliary reference connection and find that the resulting Weiss variation yields the Einstein equations as expected, with additional boundary contributions. Among these boundary contributions, we obtain the dynamical variable and the associated conjugate momentum, irrespective of the spacelike, timelike or, null nature of the boundary surface. We also arrive at the generally non-vanishing covariant generalization of the Einstein energy-momentum pseudotensor. We study this tensor in the Schwarzschild geometry and find that the pseudotensorial ambiguities translate into ambiguities in the choice of coordinates on the reference geometry. Moreover, we show that from the Weiss variation, one can formally derive a gravitational Schr{\"o}dinger equation, which may, despite ambiguities in the definition of the Hamiltonian, be useful as a tool for studying the problem of time in quantum general relativity. Implications have been discussed., Comment: v2, Published in the GERG memorial volume for Prof. T. Padmanabhan, 25 pages, 1 figure

Multi-wavelength simultaneous observations are essential to the constraints on the origin of fast radio bursts (FRBs). However, it is a significant observational challenge due to the nature of FRBs as transients with a radio millisecond duration, which occur randomly in the sky regardless of time and position. Here, we report the search for short-time fast optical bursts in the GWAC archived data associated with FRB 20181130B, which were detected by the Five Hundred Meter Spherical Radio Telescope (FAST) and recently reported. No new credible sources were detected in all single GWAC images with an exposure time of 10 s, including image with coverage of the expected arrival time in optical wavelength by taking the high dispersion measurements into account. Our results provide a limiting magnitude of 15.43$\pm0.04$ mag in R band, corresponding to a flux density of 1.66 Jy or 8.35 mag in AB system by assuming that the duration of the optical band is similar to that of the radio band of about 10 ms. This limiting magnitude makes the spectral index of $\alpha<0.367$ from optical to radio wavelength. The possible existence of longer duration optical emission was also investigated with an upper limits of 0.33 Jy (10.10 mag), 1.74 mJy (15.80 mag) and 0.16 mJy (18.39 mag) for the duration of 50 ms, 10 s and 6060 s, respectively. This undetected scenario could be partially attributed to the shallow detection capability, as well as the high inferred distance of FRB 20181130B and the low fluence in radio wavelength. The future detectability of optical flashes associated with nearby and bright FRBs are also discussed in this paper., Comment: Accepted by ApJ

We consider the self-collision of portals in classical general relativity. Portals are wormholes supported by a single loop of negative mass cosmic string, and being wormholes, portals have a nontrivial topology. Portals can be constructed so that the curvature is zero everywhere outside the cosmic string, with vanishing ADM mass. The conical singularities of these wormholes can be smoothed, yielding a spatial topology of $S^2 \times S^1$ with a point corresponding to spatial infinity removed. If one attempts to collide the mouths of a smoothed portal to induce self-annihilation, one naively might think that a Euclidean topology is recovered, which would violate the classical no topology change theorems. We consider a particular limit of smoothed portals supported by an anisotropic fluid, and find that while the portal mouths do not experience an acceleration as they are brought close together, a curvature singularity forms in the limit that the separation distance vanishes. We find that in general relativity, the interaction between portal mouths is not primarily gravitational in nature, but depends critically on matter interactions., Comment: 12 pages, 8 figures

In this paper, we report the detection and follow-ups of a super stellar flare GWAC\,181229A with an amplitude of $\Delta R\sim$9.5 mag on a M9 type star by $\text{SVOM/GWAC}$ and the dedicated follow-up telescopes. The estimated bolometric energy $E_{bol}$ is $(5.56-9.25)\times10^{34}$ ergs, which places the event to be one of the most powerful flares on ultracool stars. The magnetic strength is inferred to be (3.6-4.7) kG. Thanks to the sampling with a cadence of 15 seconds, a new component near the peak time with a very steep decay is detected in the $R$-band light curve, followed by the two-component flare template given by Davenport et al. (2014). An effective temperature of $5340\pm40$ K is measured by a blackbody shape fitting to the spectrum at the shallower phase during the flare. The filling factors of the flare are estimated to be $\sim$30\% and 19\% at the peak time and at 54 min after the first detection. The detection of the particular event with large amplitude, huge-emitted energy and a new component demonstrates that a high cadence sky monitoring cooperating with fast follow-up observations is very essential for understanding the violent magnetic activity., Comment: 14 pages, 12 figures, 4 tables, accepted by ApJ

Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might expect Killing symmetries to exist only in an approximate sense due to perturbations from external matter fields. In this work, we consider the generalized notion of Killing vectors provided by the almost Killing equation, and study the perturbations induced by a perturbation of a background spacetime satisfying exact Killing symmetry. To first order, we demonstrate that for nonradiative metric perturbations (that is, metric perturbations with nonvanishing trace) of symmetric vacuum spacetimes, the perturbed almost Killing equation avoids the problem of an unbounded Hamiltonian for hyperbolic parameter choices. For traceless metric perturbations, we obtain similar results for the second-order perturbation of the almost Killing equation, with some additional caveats. Thermodynamical implications are also explored., Comment: 21 pages. Matches published version

We examine the post-Newtonian limit of the minimal exponential measure (MEMe) model presented in [J. C. Feng, S. Carloni, Phys. Rev. D 101, 064002 (2020)] using an extension of the parameterized post-Newtonian (PPN) formalism which is also suitable for other type-I minimally modified Gravity theories. The new PPN expansion is then used to calculate the monopole term of the post-Newtonian gravitational potential and to perform an analysis of circular orbits within spherically symmetric matter distributions. The latter shows that the behavior does not differ significantly from that of general relativity for realistic values of the MEMe model parameter $q$. Instead the former shows that one can use precision measurements of Newton's constant $G$ to improve the constraint on $q$ by up to $10$ orders of magnitude., Comment: 14 pages, 3 figures. Matches published version

We introduced a more general predator-prey model to analyze the paradox of enrichment. We hope the results obtained for the model can guide us on identifying real field paradox of enrichment.

In this article, we study Beltrami equilibria for plasmas in near the horizon of a spinning black hole, and develop a framework for constructing the magnetic field profile in the near horizon limit for Clebsch flows in the single-fluid approximation. We find that the horizon profile for the magnetic field is shown to satisfy a system of first-order coupled ODEs dependent on a boundary condition for the magnetic field. For states in which the generalized vorticity vanishes (the generalized `superconducting' plasma state), the horizon profile becomes independent of the boundary condition, and depend only on the thermal properties of the plasma. Our analysis makes use of the full form for the time-independent Ampere's law in the 3+1 formalism, generalizing earlier conclusions for the case of vanishing vorticity, namely the complete magnetic field expulsion near the equator of an axisymmetric black horizon assuming that the thermal properties of the plasma are symmetric about the equatorial plane. For the general case, we find and discuss additional conditions required for the expulsion of magnetic fields at given points on the black hole horizon. We perform a length scale analysis which indicates the emergence of two distinct length scales characterizing the magnetic field variation and strength of the Beltrami term, respectively., Comment: 11 pages

The discovery of spectral type transition of active galactic nuclei (AGNs), the so-called changing-look(CL) phenomenon, challenges the widely accepted AGN paradigm, not only in the orientation based Unified Model, but also in the standard disk model. In past decades, only a couple of nearby repeat "changing-look" active galactic nuclei (CL-AGNs) have been identified. Here we report spectroscopic observations of UGC 3223 over the course of 18 years, from 2001 onwards. Combining the spectrum taken in 1987 by Stirpe, we have witnessed its type transitions from $1.5\rightarrow2.0\rightarrow1.8$ over 32 years, and captured a long-lived (at least 10 years) thorough "turn-off" state with a spectrum typical of a Seyfert 2 galaxy. The long-term thorough "turn-off" state probably suggests a once-dormant and an awakening central engine in UGC3223. We argue the (dis)appearance of the broad Balmer emission lines can be explained by the disk-wind BLR model given the evolution of the calculated Eddington ratio of accretion of the supermassive black hole., Comment: 8 pages, 4 figures and 1 table, accepted for publication in AJ (matches accepted version). arXiv admin note: text overlap with arXiv:1910.02392

In this note, I describe an attempt to construct a phenomenological gravitational model at the boundary of the AdS manifold from the variation of boundary terms in the gravitational action. I find that for an AdS vacuum in the bulk, geometric constraints require that the energy-momentum tensor has constant trace., Comment: 3 pages. Added reference, changes to title and abstract. The author was made aware of a result that changed the conclusions

In three previous papers we presented the LARES 2 space experiment aimed at a very accurate test of frame-dragging and at other tests of fundamental physics and measurements of space geodesy and geodynamics. We presented the error sources in the LARES 2 experiment, its error budget, Monte Carlo simulations and covariance analyses confirming an accuracy of a few parts per thousand in the test of frame-dragging, and we treated the error due to the uncertainty in the de Sitter effect, a relativistic orbital perturbation. Here we discuss the impact in the error budget of the LARES 2 frame-dragging experiment of the orbital perturbation due to thermal drag or thermal thrust. We show that the thermal drag induces an uncertainty of about one part per thousand in the LARES 2 frame-dragging test, consistent with the error estimates in our previous papers., Comment: 17 pages, 9 figures

We examine the Hamiltonian formulation and hyperbolicity of the almost-Killing equation (AKE). We find that for all but one parameter choice, the Hamiltonian is unbounded, and in some cases, the AKE has ghost degrees of freedom. We also show the AKE is only strongly hyperbolic for one parameter choice, which corresponds to a case in which the AKE has ghosts. Fortunately, one finds that the AKE reduces to the homogeneous Maxwell equation in a vacuum, so that with the addition of the divergence-free constraint (a "Lorenz gauge"), one can still obtain a well-posed problem that is stable in the sense that the corresponding Hamiltonian is positive definite. An analysis of the resulting Komar currents reveals an exact Gauss law for a system of black holes in vacuum spacetimes and suggests a possible measure of matter content in asymptotically flat spacetimes., Comment: 10 pages, 3 figures. Matches published version

We propose a new class of gravity theories which are characterized by a nontrivial coupling between the gravitational metric and matter mediated by an auxiliary rank-2 tensor. The actions generating the field equations are constructed so that these theories are equivalent to general relativity in a vacuum, and only differ from general relativity theory within a matter distribution. We analyze in detail one of the simplest realizations of these generalized coupling theories. We show that in this case the propagation speed of gravitational radiation in matter is different from its value in vacuum and that this can be used to weakly constrain the (single) additional parameter of the theory. An analysis of the evolution of homogeneous and isotropic spacetimes in the same framework shows that there exist cosmic histories with both an inflationary phase and a dark era characterized by a different expansion rate., Comment: 19 pages, 1 table, 3 figures. Minor revisions, added references. Matches published version

Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{\sigma \sqrt{Re} t}$ (where $\sigma \sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential $e^{\sigma \sqrt{Re} \sqrt{t} +\sigma_1 t}$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here we conduct a large numerical verification with resolution up to $2048^3$ and Reynolds number up to $6210$. Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations serve as the mechanism for the generation, development and persistence of fully developed turbulence.

The generalized vortical formalism provides an electrodynamic description for superconducting states---in the generalized vortical formalism, a superconducting state may be defined by the vanishing of an appropriate generalized vorticity and characterized by zero generalized helicity for incompressible fluids. In this article, we investigate these states for compressible plasmas in black hole spacetime geometries using the curved spacetime generalization of the grand generalized vortical formalism. If the magnetic field is axisymmetric and the thermodynamic properties are symmetric about the equatorial plane, the resulting states are characterized by a vanishing skin depth and a complete expulsion of the magnetic field at the equator of the black hole horizon. Moreover, if the thermodynamic properties of the plasma are uniform at the horizon, we find that the magnetic field is completely expelled from the horizon, and the plasma behaves as a perfect superconductor near the horizon. This result is independent of the spin of a black hole, holding even for a (nonrotating) Schwarzschild black hole, and demonstrates that the geometry near black hole horizons can have a significant effect on the electrodynamics of surrounding plasmas., Comment: 5 pages

The second observational campaign of gravitational waves organized by the LIGO/Virgo Collaborations has led to several breakthroughs such as the detection of gravitational wave signals from merger systems involving black holes or neutrons stars. During O2,14 gravitational wave alerts were sent to the astronomical community with sky regions covering mostly over hundreds of square degrees. Among them, 6 have been finally confirmed as real astrophysical events. Since 2013, a new set of ground-based robotic telescopes called GWAC and its pathfinder mini-GWAC have been developed to contribute to the various challenges of themulti-messenger and time domain astronomy. The GWAC system is built up in the framework of the ground-segment system of the SVOM mission that will be devoted to the study of the multi-wavelength transient sky in the next decade. During O2, only the mini-GWAC telescopenetwork was fully operational. Due to the wide field of view and fast automatic follow-up capabilities of the mini-GWAC telescopes, they were well adapted to efficiently cover the sky localization areas of the gravitational wave event candidates. In this paper, we present the mini-GWAC pipeline we have set up to respond to the GW alerts and we report our optical follow-up observations of 8 GW alerts detected during the O2 run. Our observations provided the largest coverage of the GW localization areas in a short latency made by any optical facility. We found tens of optical transient candidates in our images, but none of those could be securely associated with any confirmed black hole-black hole merger event. Based on this first experience and the near future technical improvements of our network system, we will be more competitive to detect the optical counterparts from some gravitational wave events that will be detected during the upcoming O3 run, especially those emerging from binary neutron star mergers., Comment: 17 pages, 10 figures, 11 tables

In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an identically vanishing divergence. I obtain some expressions for Komar currents constructed from some generalizations of Killing vectors which may in principle be constructed in a generic spacetime. I then present an explicit example for an outgoing Vaidya spacetime which demonstrates that the resulting Komar currents can yield conserved quantities that behave in a manner expected for the energy contained in the outgoing radiation. Finally, I describe a method for constructing another class of (non-Komar) globally conserved currents using a scalar test field that satisfies an inhomogeneous wave equation, and discuss two examples; the first example may provide a useful framework for examining the arrow of time and its relationship to energy conditions, and the second yields (with appropriate initial conditions) a globally conserved energy- and momentumlike quantity that measures the degree to which a given spacetime deviates from symmetry., Comment: 8 pages. Matches published version

In this article, I present a volume average regularization for the second functional derivative operator that appears in the metric-basis Wheeler-DeWitt equation. Naively, the second functional derivative operator in the Wheeler-DeWitt equation is infinite, since it contains terms with a factor of a delta function or derivatives of the delta function. More precisely, the second functional derivative contains terms that are only well defined as a distribution---these terms only yield meaningful results when they appear within an integral. The second functional derivative may, therefore, be regularized by performing an integral average of the distributional terms over some finite volume; I argue that such a regularization is appropriate if one regards quantum general relativity (from which the Wheeler-DeWitt equation may be derived) to be the low-energy effective field theory of a full theory of quantum gravity. I also show that a volume average regularization can be viewed as a natural generalization of the same-variable second partial derivative for an ordinary multivariable function. Using the regularized second functional derivative operator, I construct an approximate solution to the Wheeler-DeWitt equation in the low-curvature, long-distance limit., Comment: 22 pages. Revised to match published version. Note added in proof containing additional references

We reexamine the relationship between the path integral and canonical formulation of quantum general relativity. In particular, we present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum general relativity by way of boundary variations. One feature of this approach is that it does not require an explicit 3+1 splitting of spacetime in the bulk. For spacetimes with a spatial boundary, we show that the dependence of the transition amplitudes on spatial boundary conditions is determined by a Wheeler-DeWitt equation for the spatial boundary surface. We find that variations in the induced metric at the spatial boundary can be used to describe time evolution---time evolution in quantum general relativity is therefore governed by boundary conditions on the gravitational field at the spatial boundary. We then briefly describe a formalism for computing the dependence of transition amplitudes on spatial boundary conditions. Finally, we argue that for nonsmooth boundaries, meaningful transition amplitudes must depend on boundary conditions at the joint surfaces., Comment: Revised to match published version in Phys. Rev. D

The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel geometric derivation of the Weiss variation for the gravitational action: the Einstein-Hilbert action plus the Gibbons-Hawking-York boundary term. In particular, we use the first and second variation of area formulas (we present a derivation accessible to physicists in an appendix) to interpret and vary the Gibbons-Hawking-York boundary term. The Weiss variation for the gravitational action is in principle known to the Relativity community, but the variation of area approach formalizes the derivation, and facilitates the discussion of time evolution in General Relativity. A potentially useful feature of the formalism presented in this article is that it avoids an explicit 3+1 decomposition in the bulk spacetime., Comment: 32 pages w/ 2 figures. Revised to match published version

Short term unpredictability is discovered numerically for high Reynolds number fluid flows under periodic boundary conditions. Furthermore, the abundance of the short term unpredictability is also discovered. These discoveries support our theory that fully developed turbulence is constantly driven by such short term unpredictability.

Based on the gravitational redshift, one prediction of Einstein's general relativity theory, of broad optical emission lines in active galactic nuclei (AGNs), a new method is proposed to estimate the virial factors $f$ in measuring black hole masses $M_{\rm{RM}}$ by the reverberation mapping of AGNs. The factors $f$ can be measured on the basis of two physical quantities, i.e. the gravitational redshifts $z_{\rm{g}}$ and full widths at half maxima $v_{\rm{FWHM}}$ of broad lines. In the past it has been difficult to determine the factors $f$ for individual AGNs. We apply this new method to several reverberation mapped Seyfert 1 galaxies. There is a correlation between $f$ and broad-line region (BLR) radius $r_{\rm{BLR}}$, $f=5.4 r_{\rm{BLR}}^{0.3}$, for the gravitationally redshifted broad lines He II, He I, H$\beta$ and H$\alpha$ in narrow-line Seyfert 1 galaxy (NLS1) Mrk 110. This correlation results from the radiation pressure influence of the accretion disc on the BLR clouds. The radiation pressure influence seems to be more important than usually thought in AGNs. Mrk 110 has $f \approx$ 8--16, distinctly larger than the mean $\langle f\rangle \approx 1$, usually used to estimate $M_{\rm{RM}}$ in the case of $v_{\rm{FWHM}}$. NGC 4593 and NLS1 Mrk 486 has $f\approx 3$ and $f\approx 9$, respectively. Higher $f$ values of several tens are derived for three other NLS1s. There is a correlation between $f$ and accretion rate $\mathscr{\dot M}_{f=1}$, $f=6.8\mathscr{\dot M}^{0.4}_{f=1}$ for five objects, where $\mathscr{\dot M}_{f=1}=\dot M_{\bullet}/L_{\rm{Edd}}c^{-2}$ as $f=1$ is assumed to estimate $M_{\rm{RM}}$ used in the Eddington luminosity $L_{\rm{Edd}}$, $\dot M_{\bullet}$ is the mass accretion rate, and $c$ is the speed of light. These larger $f$ values will produce higher $M_{\rm{RM}}$ values and lower Eddington ratios., Comment: 9 pages, 4 figure, 4 tables, moderate revision, version III

In this paper, we investigate the influences of two continuum radiation pressures of the central engines on the black hole mass estimates for 40 active galactic nuclei (AGNs) with high accretion rates. The two continuum radiation pressure forces, usually believed negligible or not considered, are from the free electron Thomson scattering, and the recombination and re-ionization of hydrogen ions that continue to absorb ionizing photons to compensate for the recombination. The masses counteracted by the two radiation pressures $M_{\rm{RP}}$ depend sensitively on the percent of ionized hydrogen in the clouds $\beta$, and are not ignorable compared to the black hole virial masses $M_{\rm{RM}}$, estimated from the reverberation mapping method, for these AGNs. As $\beta$ increases, $M_{\rm{RP}}$ also does. The black hole masses $M_{\rm{\bullet}}$ could be underestimated at least by a factor of 30--40 percent for some AGNs accreting around the Eddington limit, regardless of redshifts of sources $z$. Some AGNs at $z < 0.3$ and quasars at $z \ga 6.0$ have the same behaviors in the plots of $M_{\rm{RP}}$ versus $M_{\rm{RM}}$. The complete radiation pressures will be added as AGNs match $M_{\rm{RP}}\ga 0.3 M_{\rm{RM}}$ due to the two continuum radiation pressures. Compared to $M_{\rm{RM}}$, $M_{\rm{\bullet}}$ might be extremely underestimated if considering the complete radiation pressures for the AGNs accreting around the Eddington limit., Comment: 23 pages, 2 figures, 1 table

We restudy the issue of cross-correlations between broad-line and jet emission variations, and aim to locate the position of radio (and gamma-ray) emitting region in jet of active galactic nuclei (AGNs). Considering the radial profiles of the radius and number density of clouds in a spherical broad-line region (BLR), we derive new formulae connecting jet emitting position $R_{\rm{jet}}$ to time lag $\tau_{\rm{ob}}$ between broad-line and jet emission variations, and BLR radius. Also, formulae are derived for a disk-like BLR and a spherical shell BLR. The model-independent FR/RSS method is used to estimate $\tau_{\rm{ob}}$. For 3C 120, positive lags of about 0.3 yr are found between the 15 GHz emission and the H$\beta$, H$\gamma$ and He II $\lambda 4686$ lines, including broad-line data in a newly published paper, indicating the line variations lead the 15 GHz ones. Each of the broad-line light curves corresponds to a radio outburst. $R_{\rm{jet}}=$1.1--1.5 parsec (pc) are obtained for 3C 120. For 3C 273, a common feature of negative time lags is found in the cross-correlation functions between light curves of radio emission and the Balmer lines, and as well Ly$\alpha \/\ \lambda 1216$ and C~{\sc iv} $\lambda 1549$ lines. $R_{\rm{jet}}=$ 1.0--2.6 pc are obtained for 3C 273. The estimated $R_{\rm{jet}}$ are comparable for 3C 120 and 3C 273, and the gamma-ray emitting positions will be within $\sim$ 1--3 pc from the central engines. Comparisons show that the cloud number density and radius radial distributions and the BLR structures only have negligible effects on $R_{\rm{jet}}$., Comment: Accepted for publication in MNRAS. 11 pages, 8 figures, 5 tables

The paradox of enrichment was observed by M. Rosenzweig in a class of predator-prey models. Two of the parameters in the models are crucial for the paradox. These two parameters are the prey's carrying capacity and prey's half-saturation for predation. Intuitively, increasing the carrying capacity due to enrichment of the prey's environment should lead to a more stable predator-prey system. Analytically, it turns out that increasing the carrying capacity always leads to an unstable predator-prey system that is susceptible to extinction from environmental random perturbations. This is the so-called paradox of enrichment. Our resolution here rests upon a closer investigation on a dimensionless number $H$ formed from the carrying capacity and the prey's half-saturation. By recasting the models into dimensionless forms, the models are in fact governed by a few dimensionless numbers including $H$. The effects of the two parameters: carrying capacity and half-saturation are incorporated into the number $H$. In fact, increasing the carrying capacity is equivalent (i.e. has the same effect on $H$) to decreasing the half-saturation which implies more aggressive predation. Since there is no paradox between more aggressive predation and instability of the predator-prey system, the paradox of enrichment is resolved. We also further explore spatially dependent models for which the phase space is infinite dimensional. The spatially independent limit cycle which is generated by a Hopf bifurcation from an unstable steady state, is linearly stable in the infinite dimensional phase space. Numerical simulations indicate that the basin of attraction of the limit cycle is riddled. This shows that spatial perturbations can sometimes (neither always nor never) remove the paradox of enrichment near the limit cycle!, Comment: submitted

Flux dynamics in an annular long Josephson junction is studied. Three main topics are covered. The first is chaotic flux dynamics and its prediction via Melnikov integrals. It turns out that DC current bias cannot induce chaotic flux dynamics, while AC current bias can. The existence of a common root to the Melnikov integrals is a necessary condition for the existence of chaotic flux dynamics. The second topic is on the components of the global attractor and the bifurcation in the perturbation parameter measuring the strength of loss, bias and irregularity of the junction. The global attractor can contain co-existing local attractors e.g. a local chaotic attractor and a local regular attractor. In the infinite dimensional phase space setting, the bifurcation is very complicated. Chaotic attractors can appear and disappear in a random fashion. Three types of attractors (chaos, breather, spatially uniform and temporally periodic attractor) are identified. The third topic is ratchet effect. Ratchet effect can be achieved by a current bias field which corresponds to an asymmetric potential, in which case the flux dynamics is ever lasting chaotic. When the current bias field corresponds to a symmetric potential, the flux dynamics is often transiently chaotic, in which case the ratchet effect disappears after sufficiently long time.