Super Quantum Discord and Inferior “Geometric Discord” Based on Weak Measurement in Noninertial Frames

Instead of projective measurement, we use weak measurement to define quantum and geometric discords, and compare them with the normal quantum and geometric discords based on the projective measurement in noninertial frames. We find that using weak measurement to define quantum discord we can capture more quantum correlations compared with the projective measurement, so calling it super quantum discord. However, we note that the geometric discord based on the weak measurements becomes smaller, so we name it inferior “geometric discord”. We also show that, although both the super quantum discord and the inferior “geometric discord” decrease with the increase of observer’s acceleration, the super quantum discord/inferior “geometric discord” increases/decreases as the measurements become weak. These differences reveal that the definitions of the quantum and geometric discords are not too concordant with each other.

Dependence of Entanglement on Initial States under Amplitude Damping Channel in Non-Inertial Frames

Under amplitude damping channel, the dependence of the entanglement on the initial states and , which reduce to four orthogonal Bell states if we take the parameter of states are investigated. We find that the entanglements for different initial states will decay along different curves even with the same acceleration and parame-ter of the states. We note that, in an inertial frame, the sudden death of the entanglement for will occur if , while it will not take place for for any α. We also show that the possible range of the sudden death of the entanglement for is larger than that for . There exist two groups of Bell state here we can’t distinguish only by concurrence.

Quantum Teleportation with an Accelerated Partner in Open System

We investigate the teleportation between two relatively accelerating partners undergoing the phase flip, bit flip and bit-phase flip channels. We find that: 1) the fidelity decreases by increasing the acceleration of accelerated observer;2) the dynamic evolution of the fidelity is different for various channels if the acceleration is fixed;and 3) the fidelity is always symmetric about β2=1/2 where βis a parameter of the transmission state.

Entanglement dynamics in κ-deformed spacetime

We treat two identical and mutually independent two-level atoms that are coupled to a quantum field as an open quantum system.The master equation that governs their evolution is derived by tracing over the degree of freedom of the field.With this,we compare the entanglement dynamics of the two atoms moving with different trajectories inκ-deformed and Minkowski spacetimes.Notably,when the environment-induced interatomic interaction does not exist,the entanglement dynamics of two static atoms inκ-deformed spacetime are reduced to that in Minkowski spacetime in the case that the spacetime deformation parameterκis sufficiently large as theoretically predicted.However,if the atoms undergo relativistic motion,regardless of whether inertial or non-inertial,their entanglement dynamics inκ-deformed spacetime behave differently from that in Minkowski spacetime even whenκis large.We investigate various types of entanglement behavior,such as decay and generation,and discuss how different relativistic motions,such as uniform motion in a straight line and circular motion,amplify the differences in the entanglement dynamics between theκ-deformed and Minkowski spacetime cases.In addition,when the environment-induced interatomic interaction is considered,we find that it may also enhance the differences in the entanglement dynamics between these two spacetimes.Thus,in principle,one can tell whether she/he is inκ-deformed or Minkowski spacetime by checking the entanglement behavior between two atoms in certain circumstances.

Gravitational wave fluxes on generic orbits in near-extreme Kerr spacetime:Higher spin and large eccentricity

To accurately obtain the waveform template of gravitational waves, substantial computational resources and extremely high precision are often required. In a previous study, we employed the confluent Heun function to obtain an exact solution to the Teukolsky equation. This approach allowed us to efficiently and accurately calculate the gravitational wave flux for a particle in circular orbits around a Schwarzschild black hole. Building on this method, we now extend its application to calculate the asymptotic gravitational wave fluxes from a particle in generic orbits around a near-extreme Kerr black hole. Our extended method proves particularly effective in handling computational challenges associated with large eccentricities(e = 0.9), higher spins(a = 0.999), higher harmonic modes, and strong-field regions. The results we obtained significantly outperform those derived from the numerical integration method based on the Mano-Suzuki-Takasugi method.

The ring-shaped shadow of a rotating naked singularity with a complete photon sphere

We investigate the shadows of the Konoplya-Zhidenko naked singularity.In the spacetime of the Konoplya-Zhidenko naked singularity,not only an unstable retrograde light ring(LR)but also an unstable prograde LR exists,leading to the formation of a complete photon sphere(PS).Due to the absence of an event horizon,a dark discshaped shadow does not appear;instead,a ring-shaped shadow is observed.The ring-shaped shadow appears as an infinite number of relativistic Einstein rings in the image of the naked singularity.For some parameter values,only the unstable retrograde LR exists,resulting in an incomplete unstable PS and thus giving rise to an arc-shaped shadow for the Konoplya-Zhidenko naked singularity.The shadow of the Konoplya-Zhidenko naked singularity gradually shifts to the right as the rotation parameter a increases and gradually becomes smaller as the deformation parameter |η| increases.Moreover,stable LRs and stable photon spherical orbits can exist in the Konoplya-Zhidenko naked singularity spacetime,but they have no effect on the image of the naked singularity.This study demonstrates that a rotating naked singularity can exhibit not only an arc-shaped shadow but also a ring-shaped shadow.

Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory

We extend our research on the energy flux and waveform characteristics of gravitational waves generated by merging nonspinning binary black holes through self-consistent effective one-body theory to include binary systems with slowly spinning black holes.Initially,we decompose the equation for the null tetrad component of the gravitationally perturbed Weyl tensorψ_4~B into radial and angular parts,leveraging the second-order approximation of the rotation parameter a.Subsequently,we derive an analytical solution for the radial equation and observe that our results are contingent upon the parameters a_(2),a_(3),and a,which represent the second-and third-order correction parameters,respectively.Ultimately,we calculate the energy flux,the radiation-reaction force and the waveform for the“plus”and“cross”modes of the gravitational waves generated by merging slowly spinning binary black holes.

Energy flux and waveforms by coalescing spinless binary system in effective one-body theory

We present a study on the energy radiation rate and waveforms of the gravitational wave generated by coalescing spinless binary systems up to the third post-Minkowskian approximation in the effective one-body theory.To derive an analytical expansion of the null tetrad components of the gravitational perturbed Weyl tensorΨ4in the effective spacetime,we utilize the method proposed by Sasaki et al.During this investigation,we discover more general integral formulas that provide a theoretical framework for computing the results in any order.Subsequently,we successfully compute the energy radiation rate and waveforms of the gravitational wave,which include the results of the Schwarzschild case and the correction terms resulting from the dimensionless parameters a2and a3in the effective metric.

Kerr black hole shadows cast by extraordinary light rays with Weyl corrections

We investigate the equation of motion for photons with Weyl corrections in a Kerr black hole spacetime in a small coupling case.Our results show that Weyl corrections yield phenomena of birefringence.The light rays propagating in the spacetime are separated into the ordinary rays and the extraordinary rays,and the propagation of the latter depends on the corrections.We probe the effects of Weyl corrections on the Kerr black hole shadows casted by the extraordinary rays and find that such corrections result in a weak stretching or squeezing in the vertical direction for the black hole shadows.Finally,we also study the change of the length of the Near-Horizon Extremal Kerr line(NHEK line)with Weyl corrections.These features could help us to understand the electrodynamics with Weyl corrections from black hole shadows.

Lorentz violation induces isospectrality breaking in Einstein-bumblebee gravity theory

In this study,we investigate the quasinormal modes(QNMs)of a Lorentz-violating spacetime,factoring in a cosmological constant,within the framework of Einstein-bumblebee gravity.Our findings reveal that the interaction of spacetime with an anisotropic bumblebee field imparts distinct contributions to the axial and polar sectors of the vector perturbations.This subsequently breaks the isospectrality typically observed in vector modes.Numerical evidence strongly indicates isospectral breaking in the vector modes of Einstein-bumblebee black holes:a pronounced breakage in the real part of the frequencies,while the imaginary component seems less affected.This isospectral breaking indicates the existence of two different waveforms in the Ringdown phase of the black hole,which provides a potential signal of quantum gravity observable in current experiments.

Black hole images:A review

In recent years,unprecedented progress has been achieved regarding black holes’observation through the electromagnetic channel.The images of the supermassive black holes M87*and Sgr A*released by the Event Horizon Telescope(EHT)Collaboration provided direct visual evidence for their existence,which has stimulated further studies on various aspects of the compact celestial objects.Moreover,the information stored in these images provides a new way to understand the pertinent physical processes that occurred near the black holes,to test alternative theories of gravity,and to furnish insight into fundamental physics.In this review,we briefiy summarize the recent developments on the topic.In particular,we elaborate on the features and formation mechanism of black hole shadows,the properties of black hole images illuminated by the surrounding thin accretion disk,and the corresponding polarization patterns.The potential applications of the relevant studies are also addressed.

Determination of the spin parameter and the inclination angle from the primary and secondary images caused by gravitational lensing

We study the primary images(PIs)and secondary images(SIs)caused by strong gravitational lensing around a Kerr black hole shadow,which carry some essential signatures related to the black hole space-time.We define a new celestial coordinate,whose origin is the center of the black hole shadow,to locate the PIs and SIs of luminous celestial objects.Based on the dragging effect caused by the rotating black hole and the inclination angle of the observer,the relative positions between the PIs and SIs are different for different values of the Kerr spin parameter a and the observer's inclination angle i;hence,it can be used to determine the values of a and i.We propose a specific approach to measure a and i using the PIs and SIs.The time delays between the PIs and SIs are different for different values of a and i.The time delays,in conjunction with the relative positions between the PIs and SIs,can enable us to measure a and i more precisely.These PIs and SIs around the black hole shadow act as unique fingerprints for the black hole space-time,using which we can further determine other parameters of different types of compact objects and verify various theories of gravity.Our results provide a new method to implement parameter estimation in the study of black hole physics and astrophysics.

Direct characteristic-function tomography of the quantum states of quantum fields

Herein,we propose a novel strategy for implementing a direct readout of the symmetric characteristic function of the quantum states of quantum fields without the involvement of idealized measurements,an aspect that has always been deemed ill-defined in quantum field theory.This proposed scheme relies on the quantum control and measurements of an auxiliary qubit locally coupled to the quantum fields.By mapping the expectation values of both the real and imaginary parts of the field displacement operator to the qubit states,the qubit's readout provides complete information regarding the symmetric characteristic function.We characterize our technique by applying it to the Kubo-Martin-Schwinger(thermal)and squeezed states of a quantum scalar field.In addition,we have discussed general applications of this approach to analogue-gravity systems,such as Bose-Einstein condensates,within the scope of state-of-the-art experimental capabilities.This proposed strategy may serve as an essential in understanding and optimizing the control of quantum fields for relativistic quantum information applications,particularly in exploring the interplay between gravity and quantum,for example,the relation to locality,causality,and information.

Quasinormal modes and late time tails of perturbation fields on a Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory

In this paper we complete a systematic study on quasinormal modes(QNMs) and late time tails for scalar,Dirac and Maxwell fields on a spherically symmetric Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory.To look for QNMs,we solve the equations of motion for all perturbation fields considered herein numerically,by employing both the matrix and the WKB methods,and find good agreements for numeric data obtained by these two techniques in the regime when both are valid.The impact of the bumblebee parameter c,the monopole parameter η^(2),and the multipole number l on the fundamental quasinormal frequency are analyzed in detail.Our results are shown in terms of the quasinormal frequency measured by √1+c M ,where M is a black hole mass parameter.We observe,by increasing the parameter c(η^(2)) with fixed first few l,that the real part of QNMs increases for all spin fields;while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields.By increasing the multipole numberlwith fixed other parameters,we disclose that the real part of QNMs for all spin fields increases while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields.In the eikonal limit(l>>n),QNMs for all spin fields coincide with each other and the real part scale linearly with l.In particular,the asymptotic QNMs approach the corresponding results given by the first order WKB formula,and only the real part of QNMs is dependent on the bumblebee and monopole parameters.In addition,it is shown that the late time behavior is determined not only by the multipole number but also by the bumblebee and monopole parameters,and is distinct for bosonic and fermonic fields.Moreover,the presence of the bumblebee(monopole) field makes the spin fields decay faster.Our results indicate,both in the context of QNMs and late time tails,that the bumblebee field and the monopole field play the same role in determining the dynamic evolution of perturbation fields.

Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation

This study extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation(Sci.China-Phys.Mech.Astron.65,100411(2022))to the case of a binary system for the spinning black holes.An effective rotating metric and an improved Hamiltonian for the spinning black hole binaries are constructed.The decoupled equation for the null tetrad component of the gravitational perturbed Weyl tensorψ4B in the effective rotating spacetime is found with the help of the gauge transform characteristics of the Weyl tensors.The decoupled equation is then separated between radial and angular variables in the slowly rotating background spacetime,and a formal solution of ψ_(4)^(B) is obtained.On this basis,the formal expressions of the radiation reaction force and the waveform for the“plus”and“cross”modes of the gravitational wave are presented.These results,obtained in the same effective spacetime,constitute a self-consistent effective-one-body theory for the spinning black hole binaries based on the post-Minkowskian approximation.

Thick accretion disk configurations around a compact object in the brane-world scenario

We have studied the equipotential surfaces of a thick accretion disk around a Casadio-Fabbri-Mazzacurati compact object in the brane-world scenario,which possesses a mass parameter together with a parameterized post-Newtonian(PPN)parameter.With the increase in the PPN parameter,the size of the thick accretion disk decreases,but the corresponding Roche lobe size increases.Thus,the larger PPN parameter yields the larger region of existing bound disk structures,where the fluid is not accreted into the central wormhole.Moreover,with the increase in the PPN parameter,the position of the Roche lobe gradually moves away from the central compact object,and the thickness of the region enclosed by the Roche lobe decreases near the compact object but increases in the region far from the compact object.Our results also show that the pressure gradient in the disk decreases with the PPN parameter.These effects of the PPN parameter on the thick accretion disk could help one to further understand compact objects in the brane-world scenario.

Gauge invariant perturbations of general spherically symmetric spacetimes

In this paper,the gauge choices in general spherically symmetric spacetimes are explored.In particular,we construct the gauge invariant variables and the master equations for both the Detweiler easy gauge and the Regge-Wheeler gauge,respectively.The particular cases for l=0,1 are also investigated.Our results provide analytical calculations of metric perturbations in general spherically symmetric spacetimes,which can be applied to various cases,including the effective-one-body problem.A simple example is presented to show how the metric perturbation components are related to the source perturbation terms.

Strong gravitational lensing of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory

The strong gravitational lensing of a regular and rotating magnetic black hole in non-minimally coupled Einstein-Yang-Mills theory is studied.We find that,with the increase of any characteristic parameters of this black hole,such as the rotating parameter a,magnetic charge q and EYM parameterλ,the angular image positionθ∞and relative magnification rm decrease while deflection angleα(θ)and image separation s increase.The results will degenerate to that of the Kerr case,RN case with magnetic charge and Schwarzschild case when we take some specific values for the black hole parameters.The results also show that,due to the small influence of magnetic charge and EYM parameters,it is difficult for current astronomical instruments to tell this black hole apart from a General Relativity one.

Genuine tripartite entanglement and geometric quantum discord in entangled three-body Unruh-DeWitt detector system

We studied the quantum correlations of a three-body Unruh-DeWitt detector system using genuine tripartite entanglement(GTE)and geometric quantum discord(GQD).We considered two representative three-body initial entangled states,namely the GHZ state and the W state.We demonstrated that the quantum correlations of the tripartite system are completely destroyed at the limit of infinite acceleration.In particular,it is found that the GQD of the two initial states exhibits“sudden change”behavior with increasing acceleration.It is shown that the quantum correlations of the W state are more sensitive than those of the GHZ state under the effect of Unruh thermal noise.The GQD is a more robust quantum resource than the GTE,and we can achieve robustness in discord-type quantum correlations by selecting the smaller energy gap in the detector.These findings provide guidance for selecting appropriate quantum states and resources for quantum information processing tasks in a relativistic setting.

Generalized gravitomagnetic field and gravitational waves

Synge was the first to derive the geodesic deviation entirely mathematically (1)Only later did people realize its importance [2] for describing the physical behavior of curved spacetime [3], particularly that it can unambiguously manifest gravitational waves (4, 5)The geodesic deviation relates purely to the 'electric' part of a curved spacetime, while the complementary 'magnetic' part is related to the way gyroscopes adapt to geodesics. For Ricci flat spacetimes.