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
From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-O particle moving in de Sifter spacefime is conservative, by which its fimelike geodesics can be labeled completely and uniqu...From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-O particle moving in de Sifter spacefime is conservative, by which its fimelike geodesics can be labeled completely and uniquely. Based on that observation and working in Belframi coordinate for de Sifter spacefime, solutions and their asymptotic behavior to the Belframi-de Sifter-Klein-Gordon equation are given.展开更多
Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 k...Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.展开更多
We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positiv...We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positive energy theorem for such spacetimes,following Witten’s original argumentsfor the positive energy theorem in asymptotically flat spacetimes.展开更多
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The project supported by National Natural Science Foundation of China under Grant No.10547002
文摘From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-O particle moving in de Sifter spacefime is conservative, by which its fimelike geodesics can be labeled completely and uniquely. Based on that observation and working in Belframi coordinate for de Sifter spacefime, solutions and their asymptotic behavior to the Belframi-de Sifter-Klein-Gordon equation are given.
文摘Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.
基金supported by National Natural Science Foundation of China(Grant No.11171328)Fundamental Research Funds for the Central Universities of China(Grant No.210274087)
文摘We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positive energy theorem for such spacetimes,following Witten’s original argumentsfor the positive energy theorem in asymptotically flat spacetimes.
