Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang Mills equation on AdS space with this metric is considered and a static solution is obtained in...Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang Mills fields.展开更多
Through the gauge field theory, we obtain the solution of the DBI-AdS black hole, In the meantime, according to the relations between the action and the grand partition function, we obtain the grand partition function...Through the gauge field theory, we obtain the solution of the DBI-AdS black hole, In the meantime, according to the relations between the action and the grand partition function, we obtain the grand partition function in the DBI-AdS black hole. The temperature and the potential of the DBI-AdS black hole are gained from differential of the grand partition function. With the thermodynamic relations, other thermodynamics are also obtained. The solution and the thermodynamics of the DBI-AdS black hole are turned out that they can reduce to the case of a charged black hole in four-dimensional spacetimes.展开更多
In this paper,the extremals of curvature energy actions on non-null Frenet curves in 3-dimensional Anti-de Sitter space are studied.We completely solve the Euler-Lagrange equation by quadratures.By using the Killing f...In this paper,the extremals of curvature energy actions on non-null Frenet curves in 3-dimensional Anti-de Sitter space are studied.We completely solve the Euler-Lagrange equation by quadratures.By using the Killing fields,we obtain existence for closed general-ized elastica fully immersed in Anti-de Sitter space H_1~3.展开更多
A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its ...A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13.展开更多
The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch(2022)and for the non-spin case by Chu and Zhu(2024).In this paper,we generalize the positive energy theorem f...The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch(2022)and for the non-spin case by Chu and Zhu(2024).In this paper,we generalize the positive energy theorem for 3-dimensional asymptotically anti-de Sitter initial data sets to weighted asymptotically antide Sitter initial data sets assuming that the weighted dominant energy condition holds.展开更多
We introduce null surfaces(or nullcone fronts)of pseudo-spherical spacelike framed curves in the three-dimensional anti-de Sitter space.These surfaces are formed by the light rays emitted from points on anti-de Sitter...We introduce null surfaces(or nullcone fronts)of pseudo-spherical spacelike framed curves in the three-dimensional anti-de Sitter space.These surfaces are formed by the light rays emitted from points on anti-de Sitter spacelike framed curves.We then classify singularities of the nullcone front of a pseudo-spherical spacelike framed curve and show how these singularities are related to the singularities of the associated framed curve.We also define a family of functions called the Anti-de Sitter distance-squared functions to explain the nullcone front of a pseudo-spherical spacelike framed curve as a wavefront from the viewpoint of the Legendrian singularity theory.We finally provide some examples to illustrate the results of this paper.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
基金Supported by National Key Basic Research Program of China under Grant No. 2004CB31800；National Natural Science Foundation of China under Grant No. 10375087；CUMT Foundation for Youth under Grant No. 2008A034, Qihang Project and Innovation Project of CUMT
文摘Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang Mills fields.
文摘Through the gauge field theory, we obtain the solution of the DBI-AdS black hole, In the meantime, according to the relations between the action and the grand partition function, we obtain the grand partition function in the DBI-AdS black hole. The temperature and the potential of the DBI-AdS black hole are gained from differential of the grand partition function. With the thermodynamic relations, other thermodynamics are also obtained. The solution and the thermodynamics of the DBI-AdS black hole are turned out that they can reduce to the case of a charged black hole in four-dimensional spacetimes.
基金Supported by the NSF of China(10671066,10971066)Supported by the Shanghai Leading Academic Discipline Project(B407)
文摘In this paper,the extremals of curvature energy actions on non-null Frenet curves in 3-dimensional Anti-de Sitter space are studied.We completely solve the Euler-Lagrange equation by quadratures.By using the Killing fields,we obtain existence for closed general-ized elastica fully immersed in Anti-de Sitter space H_1~3.
文摘A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13.
基金supported by National Natural Science Foundation of China(Grant No.12326602)the special foundation for Guangxi Ba Gui Scholars and Junwu Scholars。
文摘The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch(2022)and for the non-spin case by Chu and Zhu(2024).In this paper,we generalize the positive energy theorem for 3-dimensional asymptotically anti-de Sitter initial data sets to weighted asymptotically antide Sitter initial data sets assuming that the weighted dominant energy condition holds.
文摘We introduce null surfaces(or nullcone fronts)of pseudo-spherical spacelike framed curves in the three-dimensional anti-de Sitter space.These surfaces are formed by the light rays emitted from points on anti-de Sitter spacelike framed curves.We then classify singularities of the nullcone front of a pseudo-spherical spacelike framed curve and show how these singularities are related to the singularities of the associated framed curve.We also define a family of functions called the Anti-de Sitter distance-squared functions to explain the nullcone front of a pseudo-spherical spacelike framed curve as a wavefront from the viewpoint of the Legendrian singularity theory.We finally provide some examples to illustrate the results of this paper.
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.
