Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of i...Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.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
Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ...Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective.展开更多
According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model ...According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.展开更多
We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissi...We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.展开更多
We investigate quasi-local energy distribution and thermodynamics of the Reissner-Nordstr6m black hole space-time surrounded by quintessence. We use the quasi-local energy distribution from Einstein energy-momentum co...We investigate quasi-local energy distribution and thermodynamics of the Reissner-Nordstr6m black hole space-time surrounded by quintessence. We use the quasi-local energy distribution from Einstein energy-momentum complex. We plot the variation of the energies, temperature and heat capacity with the state parameter related to the quintessence ωq. We show that due to the presence of quintessence, the total energy of the outer region as well as the temperature and heat capacity decreases with the increase of the density of quintessence, while the total energy of the black hole region increases.展开更多
Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surject...Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties： f＇（x0） is double splitting and R（f＇（x）） ∩ N（T0^＋） = {0} near x0. However, in infinite dimensional Banach spaces, f＇（x0） is not always double splitting （i.e., the generalized inverse of f（x0） does not always exist）, but its bounded outer inverse of f＇（x0） always exists. Only using the C^1 map f and the outer inverse To^# of f（x0）, the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.展开更多
基金the Preliminary Research Foundation of National Defense (No,002,2BQ) the Foundation of Fuzhou University (No.0030824649)
文摘Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.
基金partially supported by the National Natural Science Foundation of China (Grant No. 10421001)the National Key Basic Research Project of China (Grant No. 2006CB805905)the Innovation Project ofChinese Academy of Sciences
文摘We extend our previous definition of quasi-local mass to 2-spheres whose Gauss curvature is negative, and prove its positivity.
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.
文摘Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective.
文摘According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.
基金partially supported by the Natural Science Foundation of Hunan Province(Grant 2018JJ2073)partially supported by the National Natural Science Foundation of China(Grant 11671089).
文摘We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.
文摘We investigate quasi-local energy distribution and thermodynamics of the Reissner-Nordstr6m black hole space-time surrounded by quintessence. We use the quasi-local energy distribution from Einstein energy-momentum complex. We plot the variation of the energies, temperature and heat capacity with the state parameter related to the quintessence ωq. We show that due to the presence of quintessence, the total energy of the outer region as well as the temperature and heat capacity decreases with the increase of the density of quintessence, while the total energy of the black hole region increases.
基金Project supported by the National Natural Science Foundation of China (No. 10271053).
文摘Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties： f＇（x0） is double splitting and R（f＇（x）） ∩ N（T0^＋） = {0} near x0. However, in infinite dimensional Banach spaces, f＇（x0） is not always double splitting （i.e., the generalized inverse of f（x0） does not always exist）, but its bounded outer inverse of f＇（x0） always exists. Only using the C^1 map f and the outer inverse To^# of f（x0）, the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.
