We investigate the dynamic shadows of a black hole with a self-interacting massive complex scalar hair.The complex scalar field ψ evolves with time t,and its magnitude on the apparent horizon|ψ_(h)|starts from zero,...We investigate the dynamic shadows of a black hole with a self-interacting massive complex scalar hair.The complex scalar field ψ evolves with time t,and its magnitude on the apparent horizon|ψ_(h)|starts from zero,undergoes a sharp rise followed by rapid oscillations,and eventually converges to a constant value.The variation in the photon sphere radius r_(ps) is similar to that of the magnitude|ψ_(h)|.Owing to the emergence of the complex scalar hair ψ,the apparent horizon radius r_(h) starts increasing sharply and then smoothly approaches a stable value eventually.The shadow radius R_(sh) of the black hole with an accretion disk increases with time t_(o) at the observer's position.In the absence of an accretion disk,the shadow radius R_(sh) is larger and also increases as t_(o) increases.Furthermore,we slice the dynamical spacetime into spacelike hypersurfaces for all time points t.For the case with an accretion disk,the variation in R_(sh) is similar to that in the apparent horizon r_(h),because the inner edge of the accretion disk extends to the apparent horizon.In the absence of an accretion disk,the variation in R_(sh) is similar to that in the photon sphere radius r_(ps),because the black hole shadow boundary is determined by the photon sphere.As the variation in r_(ps) is induced by ψ,it can be stated that the variation in the size of the shadow is similarly caused by the change in ψ.Regardless of the presence or absence of the accretion disk,the emergence of the complex scalar hair ψ causes the radius R_(sh) of the shadow to start changing.Moreover,we investigate the time delay Δt of light propagating from light sources to the observer.These findings not only enrich the theoretical models of dynamic black hole shadows but also provide a foundation for testing black hole spacetime dynamics.展开更多
A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is de...A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex＇s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.12105151the Shandong Provincial Natural Science Foundation of China under Grant No.ZR2020QA080partially supported by the National Natural Science Foundation of China under Grant No.12375048,11875026,11875025 and 12035005。
文摘We investigate the dynamic shadows of a black hole with a self-interacting massive complex scalar hair.The complex scalar field ψ evolves with time t,and its magnitude on the apparent horizon|ψ_(h)|starts from zero,undergoes a sharp rise followed by rapid oscillations,and eventually converges to a constant value.The variation in the photon sphere radius r_(ps) is similar to that of the magnitude|ψ_(h)|.Owing to the emergence of the complex scalar hair ψ,the apparent horizon radius r_(h) starts increasing sharply and then smoothly approaches a stable value eventually.The shadow radius R_(sh) of the black hole with an accretion disk increases with time t_(o) at the observer's position.In the absence of an accretion disk,the shadow radius R_(sh) is larger and also increases as t_(o) increases.Furthermore,we slice the dynamical spacetime into spacelike hypersurfaces for all time points t.For the case with an accretion disk,the variation in R_(sh) is similar to that in the apparent horizon r_(h),because the inner edge of the accretion disk extends to the apparent horizon.In the absence of an accretion disk,the variation in R_(sh) is similar to that in the photon sphere radius r_(ps),because the black hole shadow boundary is determined by the photon sphere.As the variation in r_(ps) is induced by ψ,it can be stated that the variation in the size of the shadow is similarly caused by the change in ψ.Regardless of the presence or absence of the accretion disk,the emergence of the complex scalar hair ψ causes the radius R_(sh) of the shadow to start changing.Moreover,we investigate the time delay Δt of light propagating from light sources to the observer.These findings not only enrich the theoretical models of dynamic black hole shadows but also provide a foundation for testing black hole spacetime dynamics.
文摘A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex＇s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.
