We study the dynamics of the critical collapse of a spherically symmetric scalar field.Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained.In the central ...We study the dynamics of the critical collapse of a spherically symmetric scalar field.Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained.In the central region,owing to the boundary conditions,the equation of motion for the scalar field is reduced to the flat-spacetime form.展开更多
We study the energy issue in critical collapse.It is found that in critical collapse,the contribution from the material energy is greater than that from the gravitational energy.The quantity m/r plays an important rol...We study the energy issue in critical collapse.It is found that in critical collapse,the contribution from the material energy is greater than that from the gravitational energy.The quantity m/r plays an important role in identifying the formation of an apparent horizon in gravitational collapse,where m is the Misner-Sharp mass and r is the areal radius.We observe that in critical collapse,the maximum value of m/r fluctuates between 2/15 and 4/15.This denotes a large gap between critical collapse and black hole formation for which the criterion is m/r=1/2.展开更多
We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime.Our primary focus is on the behavior of the critical amplitude un...We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime.Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field.Through our numerical results,we obtain a formula that determines critical amplitude in terms of cosmological constantΛ:A^(*)∝(0.01360σ/v_(0)+0.001751)Λ,whereσdenotes the initial width of the scalar field and is the initial position of the scalar field.Notably,we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.展开更多
In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic ...In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic mechanics in this paper.By solving this model the deformation of water-resistant rock strata under the action of water pressure and the expression of critical water pressure for collapse pillar waterinrush have been obtained The research results indicate that：the boundary conditions and strength of water-resistant strata play important roles in influencing water-inrush of collapse pillars.The critical water-inrush pressure is determined by both relative thickness and absolute thickness of water-resistant strata.展开更多
基金JQG is Supported by the Natural Science Foundation of Shandong Province,China(ZR2019MA068)YH,PPW and CGS are Supported by the National Natural Science Foundation of China(11925503)。
文摘We study the dynamics of the critical collapse of a spherically symmetric scalar field.Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained.In the central region,owing to the boundary conditions,the equation of motion for the scalar field is reduced to the flat-spacetime form.
基金supported by the National Natural Science Foundation of China(Grant No.11925503)supported by Shandong Province Natural Science Foundation under grant No.ZR2019MA068.
文摘We study the energy issue in critical collapse.It is found that in critical collapse,the contribution from the material energy is greater than that from the gravitational energy.The quantity m/r plays an important role in identifying the formation of an apparent horizon in gravitational collapse,where m is the Misner-Sharp mass and r is the areal radius.We observe that in critical collapse,the maximum value of m/r fluctuates between 2/15 and 4/15.This denotes a large gap between critical collapse and black hole formation for which the criterion is m/r=1/2.
基金Supported by the National Natural Science Foundation of China (11925503)the Guangdong Major project of Basic and Applied Basic Research (2019B030302001).
文摘We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime.Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field.Through our numerical results,we obtain a formula that determines critical amplitude in terms of cosmological constantΛ:A^(*)∝(0.01360σ/v_(0)+0.001751)Λ,whereσdenotes the initial width of the scalar field and is the initial position of the scalar field.Notably,we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.
基金Projects are supported by the National Basic Research Program of China(No.2007CB209400)the National Natural Science Foundation of China(Nos.50974115,50904065 and 50974107)the 111 Project(No.B07028).
文摘In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic mechanics in this paper.By solving this model the deformation of water-resistant rock strata under the action of water pressure and the expression of critical water pressure for collapse pillar waterinrush have been obtained The research results indicate that：the boundary conditions and strength of water-resistant strata play important roles in influencing water-inrush of collapse pillars.The critical water-inrush pressure is determined by both relative thickness and absolute thickness of water-resistant strata.
