We perform simulations of general relativistic rotating stellar core collapse and compute the gravitational waves (GWs) emitted in the core bounce phase of three representative models via multiple techniques. The simplest technique, the quadrupole formula (QF), estimates the GW content in the spacetime from the mass quadrupole tensor. It is strictly valid only in the weak-field and slow-motion approximation. For the first time, we apply GW extraction methods in core collapse that are fully curvature-based and valid for strongly radiating and highly relativistic sources. We employ three extraction methods computing (i) the Newman-Penrose (NP) scalar Psi_4, (ii) Regge-Wheeler-Zerilli-Moncrief (RWZM) master functions, and (iii) Cauchy-Characteristic Extraction (CCE) allowing for the extraction of GWs at future null infinity, where the spacetime is asymptotically flat and the GW content is unambiguously defined. The latter technique is the only one not suffering from residual gauge and finite-radius effects. All curvature-based methods suffer from strong non-linear drifts. We employ the fixed-frequency integration technique as a high-pass waveform filter. Using the CCE results as a benchmark, we find that finite-radius NP extraction yields results that agree nearly perfectly in phase, but differ in amplitude by ~1-7% at core bounce, depending on the model. RWZM waveforms, while in general agreeing in phase, contain spurious high-frequency noise of comparable amplitudes to those of the relatively weak GWs emitted in core collapse. We also find remarkably good agreement of the waveforms obtained from the QF with those obtained from CCE. They agree very well in phase but systematically underpredict peak amplitudes by ~5-11% which is comparable to the NP results and is within the uncertainties associated with core collapse physics. (abridged)
We revisit secular stability against quasi-radial collapse for rigidly rotating supermassive stars (SMSs) in general relativity. We suppose that the SMSs are in a nuclear-burning phase and can be modeled by polytropic equations of state with the polytropic index $n_p$ slightly smaller than $3$. The stability is determined in terms of the turning-point method. We find a fitting formula of the stability condition for the plausible range of $n_p$ ($2.95 \alt n_p \alt 3$) for SMSs. This condition reconfirms that, while non-rotating SMSs with mass $\sim 10^5M_\odot$--$10^6M_\odot$ may undergo a gen…
The properties of the ergosphere and energy extraction by Penrose process in a rotating non-Kerr black hole are investigated. It is shown that the ergosphere is sensitive to the deformation parameter $ε$ and the shape of the ergosphere becomes thick with increase of the parameter $ε$. It is of interest to note that, comparing with the Kerr black hole, the deformation parameter $ε$ can enhance the maximum efficiency of the energy extraction process greatly. Especially, for the case of $a>M$, the non-Kerr metric describes a superspinning compact object and the maximum efficiency can exceed 60%, …
Presented in this paper is a technique that we propose for extracting the physical parameters of a rotating stellar core collapse from the observation of the associated gravitational wave signal from the collapse and core bounce. Data from interferometric gravitational wave detectors can be used to provide information on the mass of the progenitor model, precollapse rotation and the nuclear equation of state. We use waveform libraries provided by the latest numerical simulations of rotating stellar core collapse models in general relativity, and from them create an orthogonal set of eigenvecto…
We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentum J/M^2, where J and M are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with J/M^2<1, i.e., "sub-Kerr" models, we were able to find models that are dynamically unstable and that collapse promptly to a rotating black hole. Both the dynamics of the collapse and the consequent emission of gravitational waves rese…
We present results from a new set of 3D general-relativistic hydrodynamic simulations of rotating iron core collapse. We assume octant symmetry and focus on axisymmetric collapse, bounce, the early postbounce evolution, and the associated gravitational wave (GW) and neutrino signals. We employ a finite-temperature nuclear equation of state, parameterized electron capture in the collapse phase, and a multi-species neutrino leakage scheme after bounce. The latter captures the important effects of deleptonization, neutrino cooling and heating and enables approximate predictions for the neutrino l…
We present a new multivariate regression model for analysis and parameter estimation of gravitational waves observed from well but not perfectly modeled sources such as core-collapse supernovae. Our approach is based on a principal component decomposition of simulated waveform catalogs. Instead of reconstructing waveforms by direct linear combination of physically meaningless principal components, we solve via least squares for the relationship that encodes the connection between chosen physical parameters and the principal component basis. Although our approach is linear, the waveforms' param…
Solutions describing the gravitational collapse of asymptotically flat cylindrical and prolate shells of (null) dust are shown to admit globally naked singularities.
We present the first systematic study of the gravitational collapse of rotating and magnetised neutron stars to charged and rotating (Kerr-Newman) black holes. In particular, we consider the collapse of magnetised and rotating neutron stars assuming that no pair-creation takes place and that the charge density in the magnetosphere is so low that the stellar exterior can be described as an electrovacuum. Under these assumptions, which are rather reasonable for a pulsar that has crossed the 'death line', we show that when the star is rotating, it acquires a net initial electrical charge, which i…
We present two-dimensional hydrodynamic simulations of the accretion-induced collapse (AIC) of rotating white dwarfs admixed with an extended component of dark matter (DM) comprising of sub-GeV degenerate fermionic DM particles. We find that the DM component would follow the collapse of the normal matter (NM) component to become a bound DM core. Thus, we demonstrate how a DM-admixed neutron star could form through DM-admixed AIC (DMAIC) for the first time, with the dynamics of DM taken into account. The gravitational-wave (GW) signature from the DMAIC shows distinctive features. In the diffusi…
We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) tha…
Gravitational waves from core collapse of rotating very-massive stars: 3D numerical relativity computation
The Pennsylvania State University（宾夕法尼亚州立大学）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理学研究所（阿尔伯特·爱因斯坦研究所））；Kyoto University（京都大学）；Tohoku University（东北大学）
We study the gravitational collapse of a rotating cylindrical null shell with flat interior and the metric of a spinning cosmic string as the exterior. We see that there is a critical radius, where the energy density of the shell vanishes and beyond which it would be negative, thereby signaling that the matching would be unphysical.
We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.
A binary neutron star merger produces a rapidly and differentially rotating compact remnant whose lifespan heavily affects the electromagnetic and gravitational emissions. Its stability depends on both the equation of state (EOS) and the rotation law and it is usually investigated through numerical simulations. Nevertheless, by means of a sufficient criterion for secular instability, equilibrium sequences can be used as a computationally inexpensive way to estimate the onset of dynamical instability, which, in general, is close to the secular one. This method works well for uniform rotation an…
Numerical evidence is presented that the Poisson-Israel mass inflation instability at the inner horizon of an accreting, rotating black hole is generically followed by Belinskii-Khalatnikov-Lifshitz oscillatory collapse to a spacelike singularity. The computation involves following all 6 degrees of freedom of the gravitational field. To simplify the problem, the computation takes as initial conditions the conformally separable solutions of arXiv:1010.1269, arXiv:1010.1271 just above the inner horizon of a slowly accreting, rotating black hole, and integrates the equations inward along single l…
In this paper, we show that a rigidly rotating string can extract the rotational energy from a rotating black hole. We consider Nambu-Goto strings stationary with respect to a corotating Killing vector with an uniform angular velocity $ω$ in the Kerr spacetime. We show that a necessary condition of the energy-extraction process is that an effective horizon on the string world sheet, which corresponds to the inner light surface, is inside the ergosphere of the Kerr black hole and the angular velocity $ω$ is less than that of the black hole $Ω_\mathrm{h}$. Furthermore, we discuss global configur…
Using predictions from three-dimensional (3D) hydrodynamics simulations of core-collapse supernovae (CCSNe), we present a coherent network analysis to detection, reconstruction, and the source localization of the gravitational-wave (GW) signals. We use the {\tt RIDGE} pipeline for the analysis, in which the network of LIGO Hanford, LIGO Livingston, VIRGO, and KAGRA is considered. By combining with a GW spectrogram analysis, we show that several important hydrodynamics features in the original waveforms persist in the waveforms of the reconstructed signals. The characteristic excess in the spec…
We reexamine the gravitational collapse of rotating neutron stars to black holes by new 3+1 numerical relativity simulations employing the Z4c formulation of Einstein equations, the moving puncture gauge conditions, and a conservative mesh refinement scheme for the general relativistic hydrodynamics. The end state of the collapse is compared to the vacuum spacetime resulting from the evolution of spinning puncture initial data. Using a local analysis for the metric fields, we demonstrate that the two spacetimes actually agree. Gravitational waveforms are analyzed in some detail. We connect the…
We have investigated the properties of the ergosphere and the energy extraction by Penrose process in a Konoplya-Zhidenko rotating non-Kerr black hole spacetime. We find that the ergosphere becomes thin and the maximum efficiency of energy extraction decreases as the deformation parameter increases. For the case with $a<M$, the positive deformation parameter yields that the maximum efficiency is lower than that in the Kerr black hole with the same rotation parameter. However, for the superspinning case with $a>M$, we find that the maximum efficiency can reach so high that it is almost unlimite…
We present an analytic study of the mode-coupling phenomena for a scalar field propagating on a rotating Kerr background. Physically, this phenomena is caused by the dragging of reference frames, due to the black-hole (or star's) rotation. We find that different modes become mixed during the evolution and the asymptotic late-time tails are dominated by a mode which, in general, has an angular distribution different from the original one. We show that a rotating Kerr black hole becomes `bald' slower than a spherically-symmetric Schwarzschild black hole.
We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $Γ= 2$ and focus on uniformly rotating stars. We find that the onset of dynamical instability along mass-shedding sequences nearly coincides with the onset of secular instability. Unstable stars collapse to rotating black holes within about one rotation period. We also study the collapse of stable stars which have been destabilized by pressure depletion (e.g. via a pha…
We follow the collapse in axisymmetry of a uniformly rotating, supermassive star (SMS) to a supermassive black hole (SMBH) in full general relativity. The initial SMS of arbitrary mass $M$ is marginally unstable to radial collapse and rotates at the mass-shedding limit. The collapse proceeds homologously early on and results in the appearance of an apparent horizon at the center. Although our integration terminates before final equilibrium is achieved, we determine that the final black hole will contain about 90% of the total mass of the system and have a spin parameter $J/M^2 \sim 0.75$. The …
In this paper, we seek to answer the question "given a rotating core collapse gravitational wave signal, can we determine its nuclear equation of state?". To answer this question, we employ deep convolutional neural networks to learn visual and temporal patterns embedded within rotating core collapse gravitational wave (GW) signals in order to predict the nuclear equation of state (EOS). Using the 1824 rotating core collapse GW simulations by Richers et al. (2017), which has 18 different nuclear EOS, we consider this to be a classic multi-class image classification and sequence classification …
The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles, which emits both gravitational waves and massless particles when it is expanding or collapsing, is studied. It is found that when the models represent a collapsing shell, in some cases the angular momentum of the dust particles is strong enough to halt the collapse, so that a spacetime singularity is prevented from forming, while in other cases it is not, and a …
The discovery of quasars at increasingly large cosmological redshifts may favor "direct collapse" as the most promising evolutionary route to the formation of supermassive black holes. In this scenario, supermassive black holes form when their progenitors - supermassive stars - become unstable to gravitational collapse. For uniformly rotating stars supported by pure radiation pressure and spinning at the mass-shedding limit, the critical configuration at the onset of collapse is characterized by universal values of the dimensionless spin and radius parameters $J/M^2$ and $R/M$, independent of …
We provide details and present additional results on the numerical study of the gravitational-wave emission from the collapse of neutron stars to rotating black holes in three dimensions. More specifically, we concentrate on the advantages and disadvantages of the use of the excision technique and on how alternative approaches to that of excision can be successfully employed. Furthermore, as a first step towards source-characterization, we present a systematic discussion of the influence that rotation and different perturbations have on the waveforms and hence on the energy emitted in gravitat…
Explosions from Rotating Very Massive Star Collapses to Black Holes: Effects of Nuclear Burning
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（东北大学前沿交叉科学研究院）；Astronomical Institute, Graduate School of Science, Tohoku University（东北大学理学研究科天文学研究所）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Institute for Gravitation and the Cosmos, The Pennsylvania State University（宾夕法尼亚州立大学引力与宇宙研究中心）；Department of Physics, The Pennsylvania State University（宾夕法尼亚州立大学物理系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）；Department of Physics, Toho University（东邦大学物理系）
We study the gravitational collapse of a magnetized neutron star using a novel numerical approach able to capture both the dynamics of the star and the behavior of the surrounding plasma. In this approach, a fully general relativistic magnetohydrodynamics implementation models the collapse of the star and provides appropriate boundary conditions to a force-free model which describes the stellar exterior. We validate this strategy by comparing with known results for the rotating monopole and aligned rotator solutions and then apply it to study both rotating and non-rotating stellar collapse sce…
We present results from the first 2D and 3D simulations of the collapse of rotating stellar iron cores in general relativity employing a finite-temperature equation of state and an approximate treatment of deleptonization during collapse. We compare fully nonlinear and conformally flat spacetime evolution methods and find that the conformally flat treatment is sufficiently accurate for the core-collapse supernova problem. We focus on the gravitational wave (GW) emission from rotating collapse, core bounce, and early postbounce phases. Our results indicate that the GW signature of these phases …
We investigate the gravitational collapse of rapidly rotating relativistic supermassive stars by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity. We study the evolution of differentially rotating supermassive stars of $q \equiv J/M^{2} \sim 1$ ($J$ is the angular momentum and $M$ is the gravitational mass of the star) from the onset of radial instability at $R/M \sim 65$ ($R$ is the circumferential radius of the star) to the point where the conformally flat approximation breaks down. We find that the collapse of the star of $q \gtrsim 1$, a radiall…
Energy extraction from a rotating Buchdahl star via magnetic reconnection
New Uzbekistan University（新乌兹别克斯坦大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究大学TIIAME基础与应用研究所）；Tashkent University of Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
We study the final state of the gravitational collapse of uniformly rotating supramassive neutron stars by axisymmetric simulations in full general relativity. The rotating stars provided as the initial condition are marginally stable against quasiradial gravitational collapse and its equatorial radius rotates with the Kepler velocity (i.e., the star is at the mass-shedding limit). To model the neutron stars, we adopt the polytropic equations of state for a wide range of the polytropic index as $n=2/3$, 4/5, 1, 3/2 and 2. We follow the formation and evolution of the black holes, and show that …
We present results from the first 2+1 and 3+1 simulations of the collapse of rotating stellar iron cores in general relativity employing a finite-temperature equation of state and an approximate treatment of deleptonization during collapse. We compare full 3+1 and conformally-flat spacetime evolution methods and find that the conformally-flat treatment is sufficiently accurate for the core-collapse supernova problem. We focus on the gravitational wave (GW) emission from rotating collapse, core bounce, and early postbounce phases. Our results indicate that the GW signature of these phases is mu…
We investigate the collapse of differentially rotating supermassive stars (SMSs) by means of 3+1 hydrodynamic simulations in general relativity. We particularly focus on the onset of collapse to understand the final outcome of collapsing SMSs. We find that the estimated ratio of the mass between the black hole (BH) and the surrounding disk from the equilibrium star is roughly the same as the results from numerical simulation. This suggests that the picture of axisymmetric collapse is adequate, in the absence of nonaxisymmetric instabilities, to illustrate the final state of the collapse. We al…
Force-Free Electrodynamics for black holes in Anti de Sitter is considered. We present new, energy extracting solutions of Force-Free Electrodynamics in Anti de Sitter - Near Horizon Extremal Kerr and Super-Entropic Near Horizon Extremal Kerr geometries. The relevant equations of motion are derived from an action for force-free plasma surrounding spinning black holes with generic asymptotics. We consider the energy flux of electrodynamic fields in rotating frames to argue that the correct measure for energy extraction is the energy flux measured by a rotating observer in the near horizon regio…
We present results from the first fully relativistic simulations of the critical collapse of rotating radiation fluids. We observe critical scaling both in subcritical evolutions, in which case the fluid disperses to infinity and leaves behind flat space, and in supercritical evolutions that lead to the formation of black holes. We measure the mass and angular momentum of these black holes, and find that both show critical scaling with critical exponents that are consistent with perturbative results. The critical exponents are universal; they are not affected by angular momentum, and are indep…
An astrophysically realistic model of wave dynamics in black-hole spacetimes must involve a non-spherical background geometry with angular momentum. We consider the evolution of gravitational (and electromagnetic) perturbations in rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes `bald' slower than the corresponding spherically-symmetric Schwarzschild black hole. Moreover, our results turn over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal. In particular, we show that …
Motivated by a recent paper by the Potsdam numerical relativity group, we have constructed a new numerical code for hydrodynamic simulation of axisymmetric systems in full general relativity. In this code, we solve the Einstein field equation using Cartesian coordinates with appropriate boundary conditions. On the other hand, the hydrodynamic equations are solved in cylindrical coordinates. Using this code, we perform simulations to study axisymmetric collapse of rotating stars, which thereby become black holes or new compact stars, in full general relativity. To investigate the effects of rot…
We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an osc…
Penrose process on rotational energy extraction of the black hole (BH) in the original non-projectable Hořava-Lifshitz gravity is studied. The strong dependence of the extracted energy from the special range of parameters of the Hořava-Lifshitz gravity, such as parameter $Λ_W$ and specific angular momentum $a$ has been found. Particle acceleration near the rotating BH in Hořava-Lifshitz gravity has been studied. It is shown that the fundamental parameter of the Hořava-Lifshitz gravity can impose limitation on the the energy of the accelerating particles preventing them from the infinite value.
This paper explores the circular geodesics of neutral test particles on an equatorial plane around a rotating black hole. After using equations of motion of scalar-tensor-vector gravity with the circular geodesics of null-like particles, we find the equation of photon orbit. With the help of an effective potential form, we have examined the stable regimes of photons orbits. The Lyapunov exponent, as well as the effective force acting on photons, is also investigated. We examine the energy extraction from a black hole via Penrose process. Furthermore, we discuss the negative energy state and th…
Gravitational collapse of matter in the presence of rotation is a mostly unexplored topic but it might have important implications for cosmic censorship. Recently a convenient setup was identified to address this problem, by considering thin matter shells at the interface between two equal angular momenta Myers-Perry spacetimes in five dimensions. This note provides more details about the matching of such cohomogeneity-1 spacetimes and extends the results obtained therein to arbitrary higher odd dimensions. It is also pointed out that oscillatory orbits for shells in asymptotically flat spacet…
We study the gravitational collapse of a rotating supermassive star (SMS) by means of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approxi- mation of general relativity. This problem is particularly challenging because of the vast dynamical range in space which must be covered in the course of col- lapse. We evolve a uniformly rotating SMS from the onset of radial instability at R_{p}/M=411, where R_{p} is the proper polar radius of the star and M is the total mass-energy, to the point at which the PN approximation breaks down. We introduce a scale factor and a "comoving" coordin…
The thin shell collapse leading to the formation of charged rotating black holes in three dimensions is analyzed in the light of a recently developed Hamiltonian formalism for these systems. It is proposed to demand, as a way to reconcile the properties of an infinitely extended solenoid in flat space with a magnetic black hole in three dimensions, that the magnetic field should vanish just outside the shell. The adoption of this boundary condition results in an exterior solution with a magnetic field different from zero at a finite distance from the shell. The interior solution is also found …
High-energy collisions can occur for radially moving charged test particles in the extremal Reissner-Nordström spacetime if one of the particles is fine-tuned and the collision point is taken close to the horizon. This is an analogy of the Banados-Silk-West (BSW) effect, first described for extremal Kerr black holes. However, it differs significantly in terms of energy extraction: unlike for the original BSW process, no unconditional upper bounds on mass and energy of an escaping test particle produced in the collision were found for the charged version. We show that these results can be repli…
Extracting Energy from a Non-Kerr Rotating Spacetime with an Anomalous Quadrupole Moment via Magnetic Reconnection
School of Material Science and Engineering, Chongqing Jiaotong University（重庆交通大学材料科学与工程学院）；College of Physics and Optoelectronic Engineering, Chongqing Normal University（重庆师范大学物理与光电工程学院）
