arXiv subjects

Bofeng Wu

Publications and source records attributed to Bofeng Wu.

16 recordsLinked to original sources

arXiv2026

Shadows and photon spheres of static black holes embedded in a Dehnen-(1,4,5/2)-type dark matter halo with a quintessential field

This paper investigates the appearance characteristics of static black holes embedded in Dehnen-(1,4,5/2)-type dark matter halos with a quintessential field, focusing on how the dark matter halo and dark energy affect the black hole images. We first derive the event horizon radius and the photon effective potential of the black hole, and then calculate critical quantities such as the critical photon sphere radius and critical impact parameter under different parameter sets. Trajectories of photons are subsequently plotted. The study reveals that as the parameters of the dark matter halo (the central density of the dark matter halo $\rho_s$ and the scale radius of the central halo $r_s$) and the quintessential field (the normalization factor $c$ and the equation of state parameter of dark energy $w_q$) increase, the aforementioned physical quantities generally exhibit an increasing trend. Based on the derived general expressions for the redshift factor and integrated intensity, we further explore the optical effects of the spherical accretion and the thin-disk accretion models. The results indicate that dark energy exerts an influence on the black hole shadow that is strongly dependent on the observer's position, whereas the influence exerted by dark matter exhibits no such conspicuous dependence. Furthermore, dark matter and dark energy have distinct effects on both the intensity and the radius of the black hole shadow. In particular, the intensity exhibits a greater sensitivity to dark energy, whereas the radius is more responsive to dark matter. This distinction offers a potential observational criterion for identifying, through black hole images, whether the dominant interacting component near the black hole is dark matter or dark energy, and provides an important basis for constraining the equation-of-state parameter $w_q$.

gr-qc↗

arXiv2025

Motion of extended fluid bodies in the Newtonian limit of $f(R)$ gravity

In the Newtonian limit of $f(R)$ gravity, for an isolated self-gravitating system consisting of $N$ extended fluid bodies, the inter-body dynamics are studied by applying the symmetric and trace-free formalism in terms of irreducible Cartesian tensors. The multipole expansion of each body's center-of-mass acceleration is derived, and the expansion comprises the Coulomb-type part and the Yukawa-type part, where the former, identical to that in General Relativity, is encoded by the products of the mass multipole moments of the body with those of other bodies, and the latter, as the modification introduced by $f(R)$ gravity, is encoded by the products of the scalar multipole moments of the body with those of other bodies. Due to the finite range of the massive scalar mode, the scalar multipole terms in the Yukawa part do not decay systematically with increasing order. As an essential component of the system's orbital dynamics, the multipole expansion for the total gravitational potential energy is provided, and the expression for the total conserved energy in terms of the mass and scalar multipole moments of the bodies is offered. To investigate the system's spin dynamics, the equation of motion for each body's spin angular momentum is further deduced and presented in the form of multipole expansion. These findings constitute the main content of the coarse-grained description of inter-body dynamics for the system within the framework of the Newtonian limit of $f(R)$ gravity. As a by-product, for a two-body system, the effective one-body equation governing the relative motion between the two bodies and the total energy of this system are achieved.

gr-qc↗

arXiv2025

Shadow and Optical Imaging in Einstein-Maxwell-Dilaton Black Hole

This paper investigates photon motion in black hole of Einstein-Maxwell-dilaton theory, exploring black hole shadows and observational characteristics under various accretion models. We first give the relation of the event horizon, photon sphere, and critical impact parameter in terms of the magnetic charge $q$. We then use the Event Horizon Telescope data to constrain $q$. For the two spherical accretion models, the infalling scenario yields a darker shadow due to the Doppler effect. However, the shadow radius remains unchanged for different models. In the case of an optically thin, geometrically thin disk accretion model, the observed brightness is predominantly determined by direct emission. The lensing ring provides a secondary contribution to the intensity, whereas the photon ring's emission is negligible. The widths of the lensing and photon rings exhibit a positive correlation with the magnetic charge $q$. Additionally, within the disk model framework, the black hole shadow radius is found to depend on the specific emission model.

gr-qc↗

arXiv2025

The shadows and photon rings of two minimal deformations of Schwarzschild black holes

This paper primarily investigates the optical characteristics of two minimal Schwarzschild black hole deformations, the Kazakov-Solodukhin and Ghosh-Kumar black holes, under different accretion models. The event horizon, photon sphere, and critical impact parameter of the former increase compared with the Schwarzschild black hole, but those of the latter decrease. The data from the Event Horizon Telescope Collaboration are used to constrain the parameter ranges of the two black holes. In the case of spherical accretion, the quantum correction of Kazakov-Solodukhin black hole leads to the increase of black hole shadow size and the decrease of integrated intensity, while the shadow size of magnetically charged Ghosh-Kumar black hole decreases and the integrated intensity increases. The shadow radius of the black hole is independent of the spherical accretion models. For an optically and geometrically thin accretion disk, the integrated intensity is mainly contributed by direct emission, and the contributions of photon rings and lensed rings are very small. In addition, the photon rings and lensed rings of Kazakov-Solodukhin black hole are narrower, while those of Ghosh-Kumar black hole are wider. Whereas the Kazakov-Solodukhin black hole exhibits higher brightness, the Ghosh-Kumar black hole shows lower brightness. Additionally, a disk closer to the black hole correlates with a smaller shadow radius. This paper proposes a method to distinguish different black holes in a specific thin disk model.

gr-qc↗

arXiv2024

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

In the static and infalling spherical-shell models of optically thin accretion on Schwarzschild black hole, the formulas for the integrated intensities observed by a distant observer are derived, and by taking the monochromatic emission pattern with a $1/r^{2}$ radial profile as example, the black hole images for the spherical shell with different boundaries are plotted. For these BH images, the geometric and luminosity features are summarized, and the qualitative explanations of the luminosity variations between the static and infalling spherical-shell models are provided. A notable feature of the black hole image in the infalling spherical-shell model is that when the inner boundary of the spherical shell is far from the bound photon orbit, the observed luminosity near the exterior of the shadow is enhanced. The circular-annulus models of optically and geometrically thin accretion on Schwarzschild black hole are further explored. For a lightlike geodesic, the analytical forms of the transfer functions working for all impact parameter values are first given, and the redshift factors in the static, infalling, and rotating circular-annulus models are then deduced. With these results, in the three situations, the formulas for the integrated intensities observed by a distant observer viewing the circular annulus at an inclination angle are derived, and the corresponding black hole images for each emission pattern provided in Phys. Rev. D \textbf{100} (2019) 024018 are plotted. Finally, for the BH images of arbitrary order, the geometric and luminosity features are also summarized, and the qualitative explanations of the luminosity variations between different CA models are also given.

gr-qc↗

arXiv2023

The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity

By applying the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, the metric for the external gravitational field of a spatially compact stationary source is provided in $F(X,Y,Z)$ gravity, a generic fourth-order theory of gravity, where $X:=R$ is Ricci scalar, $Y:=R_{μν}R^{μν}$ is Ricci square, and $Z:=R_{μνρσ}R^{μνρσ}$ is Riemann square. A new type of gauge condition is proposed so that the linearized gravitational field equations of $F(X,Y,Z)$ gravity are greatly simplified, and then, the stationary metric in the region exterior to the source is derived. In the process of applying the result, integrations are performed only over the domain occupied by the source. The multipole expansion of the metric potential in $F(X,Y,Z)$ gravity for a spatially compact stationary source is also presented. In the expansion, the corrections of $F(X,Y,Z)$ gravity to General Relativity are Yukawa-like ones, dependent on two characteristic lengths. Two additional sets of mass-type source multipole moments appear in the corrections and the salient feature characterizing them is that the integrations in their expressions are always modulated by a common radial factor related to the source distribution.

gr-qc↗

arXiv2023

Multipole expansion of the gravitational field in a general class of fourth-order theories of gravity and the application in gyroscopic precession

A viable weak-field and slow-motion approximation method is constructed in $F(R,R_{\mu\nu}R^{\mu\nu}, R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma})$ gravity, a general class of fourth-order theories of gravity. By applying this method, the metric, presented in the form of the multipole expansion, outside a spatially compact source up to $1/c^3$ order is provided, and the closed-form expressions for the source multipole moments are all presented explicitly. The metric consists of the massless tensor part, the massive scalar part, and the massive tensor part, where the former is exactly the metric in General Relativity, and the latter two are the corrections to it. It is shown that the corrections bear the Yukawa-like dependence on the two massive parameters and predict the appearance of six additional sets of source multipole moments, which indicates that up to $1/c^3$ order, there exist six degrees of freedom beyond General Relativity within $F(R,R_{\mu\nu}R^{\mu\nu}, R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma})$ gravity. By means of the metric, for a gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of the Thomas precession, the geodetic precession, and the Lense-Thirring precession are derived, and from them, the corrections to the angular velocities of the three types of precession in General Relativity can be read off. These results indicate that differently from $f(R)$ or $f(R,\mathcal{G})$ gravity, the most salient feature of the general $F(R,R_{\mu\nu}R^{\mu\nu}, R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma})$ gravity is that it gives the nonvanishing correction to the gyroscopic spin's angular velocity of the Lense-Thirring precession in General Relativity.

gr-qc↗

arXiv2023

Multipole analysis on stationary massive vector and symmetric tensor fields

The multipole expansions for massive vector and symmetric tensor fields in the region outside spatially compact stationary sources are obtained by using the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, and the closed-form expressions for the source multipole moments are provided. The expansions show a Yukawa-like dependence on the massive parameters of the fields, and the integrals of the stationary source multipole moments are all modulated by a common radial factor related to the source distribution. For stationary massive vector field, there are two types of ``magnetic'' multipole moments, among which one is the generalization of that of the magnetostatic field, and another, being an additional set of multipole moments of the stationary massive vector field, can not be transformed away. As to the stationary massive symmetric tensor field, its multipole expansion is presented when the trace of its spatial part is specified, where besides the counterparts of the mass and spin multipole moments of massless symmetric tensor field, three additional sets of multipole moments also appear. The multipole expansions of the tensor field under two typical cases are discussed, where it is shown that if the spatial part of the tensor field is trace-free, the monopole and dipole moments in the corresponding expansion will vanish.

gr-qc↗

arXiv2022

A signature invariant geometric algebra framework for spacetime physics and its applications in relativistic dynamics of a massive particle and gyroscopic precession

A signature invariant geometric algebra framework for spacetime physics is formulated. By following the original idea of David Hestenes in the spacetime algebra of signature $(+,-,-,-)$, the techniques related to relative vector and spacetime split are built up in the spacetime algebra of signature $(-,+,+,+)$. The even subalgebras of the spacetime algebras of signatures $(\pm,\mp,\mp,\mp)$ share the same operation rules, so that they could be treated as one algebraic formalism, in which spacetime physics is described in a signature invariant form. Based on the two spacetime algebras and their "common" even subalgebra, rotor techniques on Lorentz transformation and relativistic dynamics of a massive particle in curved spacetime are constructed. A signature invariant treatment of the general Lorentz boost with velocity in an arbitrary direction and the general spatial rotation in an arbitrary plane is presented. For a massive particle, the spacetime splits of the velocity, acceleration, momentum, and force four-vectors with the normalized four-velocity of the fiducial observer, at rest in the coordinate system of the spacetime metric, are given, where the proper time of the fiducial observer is identified, and the contribution of the bivector connection is considered, and with these results, a three-dimensional analogue of Newton's second law for this particle in curved spacetime is achieved. Finally, as a comprehensive application of the techniques constructed in this paper, a geometric algebra approach to gyroscopic precession is provided, where for a gyroscope moving in the Lense-Thirring spacetime, the precessional angular velocity of its spin is derived in a signature invariant manner.

gr-qc↗

arXiv2021

Multipole analysis on gyroscopic precession in $f(R)$ gravity with irreducible Cartesian tensors

In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/c^3$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of General Relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a point-like or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of gravitoelectric-type precession, gravitomagnetic-type precession, $f(R)$ precession, and Thomas precession are all derived. The first two types of precession are collectively called General Relativity-like precession, and the $f(R)$ precession is the correction in $f(R)$ gravity. At the leading pole order, these expansions can recover the results for the gyroscope moving around a point-like or ball-like source. If the gyroscope has a nonzero four-acceleration, its spin's total angular velocity of precession up to $1/c^3$ order in $f(R)$ gravity is the same as that in General Relativity.

gr-qc↗

arXiv2021

Weakly Supervised Dense Video Captioning via Jointly Usage of Knowledge Distillation and Cross-modal Matching

This paper proposes an approach to Dense Video Captioning (DVC) without pairwise event-sentence annotation. First, we adopt the knowledge distilled from relevant and well solved tasks to generate high-quality event proposals. Then we incorporate contrastive loss and cycle-consistency loss typically applied to cross-modal retrieval tasks to build semantic matching between the proposals and sentences, which are eventually used to train the caption generation module. In addition, the parameters of matching module are initialized via pre-training based on annotated images to improve the matching performance. Extensive experiments on ActivityNet-Caption dataset reveal the significance of distillation-based event proposal generation and cross-modal retrieval-based semantic matching to weakly supervised DVC, and demonstrate the superiority of our method to existing state-of-the-art methods.

cs.CV↗

arXiv2020

Analytical analysis on the orbits of Taiji spacecrafts to infinite order of the orbital eccentricity

The dual configuration of the original one is proposed for the orbit design of Taiji spacecrafts. In terms of these two configurations of Taiji, an algorithm is devised to expand the unperturbed Keplerian orbits of spacecrafts to infinite order of $e$, the orbital eccentricity, in the heliocentric coordinate system. Further, based on the algorithm, all the kinematic indicators of Taiji triangles, say three arm-lengths and their corresponding rates of change, and three vertex angles, in both configurations are also be expanded to infinite order of $e$, and it is proved that both configurations of Taiji possess the same symmetry: At every order, three components of every kinematic indicator of Taiji triangle are identical to each other up to a phase shift of $2π/3$, which is independent on the tilt angle of Taiji plane relative to the ecliptic plane. Finally, the above algorithm is slightly modified, and with it, by adjusting the tilt angle around $π/3$ to any order of $e$, the orbits of Taiji spacecrafts in each configuration can be optimized.

gr-qc↗

arXiv2019

Analytical analysis on the orbits of Taiji spacecrafts

The unperturbed Keplerian orbits of Taiji spacecrafts are expanded to $e^3$ order in the heliocentric coordinate system, where $e$ is their orbital eccentricity. The three arm-lengths of Taiji triangle and their rates of change are also expanded to $e^3$ order, while the three vertex angles are expanded to $e^2$ order. These kinematic indicators of Taiji triangle are, further, minimized, respectively, by adjusting the tilt angle of Taiji plane relative to the ecliptic plane around $\pmπ/3$, and thus, their corresponding optimized expressions are presented. Then, under the case that the nominal trailing angle of Taiji constellation following the Earth is set to be $χ(\approx\pmπ/9)$ from the viewpoint of the Sun, the influence of the Earth perturbation on three spacecrafts is calculated according to the equations of motion in the problem of three bodies, and the perturbative solutions of the leading order and the next leading order are derived. With the perturbative solutions, the leading-order corrections to the above kinematic indicators of Taiji triangle and the expression of the above trailing angle to the order of $e^3$ are provided.

gr-qc↗

arXiv2018

Multipole analysis in the radiation field for linearized $f(R)$ gravity with irreducible Cartesian tensors

The $1/r$-expansion in the distance to the source is applied to the linearized $f(R)$ gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized $f(R)$ gravity. All of these results have two parts which are associated with the tensor part and the scalar part in the multipole expansion of linearized $f(R)$ gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom, and places an important role in distinguishing GR and $f(R)$ gravity.

gr-qc↗

arXiv2018

Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors

The field equations of $f(R)$ gravity are rewritten in the form of obvious wave equations with the stress-energy pseudotensor of the matter fields and the gravitational field as its source under the de Donder condition. The method of multipole analysis in terms of irreducible Cartesian tensors is applied to the linearized $f(R)$ gravity, and its multipole expansion is presented explicitly. In this expansion, the tensor part is symmetric and trace-free and is the same as that in General Relativity, and the scalar part predicts the appearance of monopole and dipole radiation in $f(R)$ gravity, as shown in literature. As a by-product, the multipole expansion for the massive Klein-Gordon field with an external source in terms of irreducible Cartesian tensors and its corresponding stationary results are provided.

gr-qc↗

arXiv2015

Spherically symmetric solution of $f(R,\mathcal{G})$ gravity at low energy

The weak-field and slow-motion limit of $f(R,\mathcal{G})$ gravity is developed up to $(v/c)^{4}$ order in a spherically symmetric background. Considering the Taylor expansion of a general function $f$ around vanishing values of $R$ and $\mathcal{G}$, we present general vacuum solutions up to $(v/c)^{4}$ order for the gravitational field generated by a ball-like source. The spatial behaviors at $(v/c)^{2}$ order are the same for $f(R,\mathcal{G})$ gravity and $f(R)$ gravity, and their corresponding real valued static behaviors are presented and compared with the one in general relativity. The static Yukawa-like behavior is proved to be compatible with the previous result of the most general fourth-order theory. At $(v/c)^{4}$ order, the static corrections to the Yukawa-like behavior for $f(R,\mathcal{G})$ gravity, $f(R)$ gravity, and the Starobinsky gravity are presented and compared with the one in general relativity.

gr-qc↗