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James M. Nester - One of the best experts on this subject based on the ideXlab platform.
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Quasi-local energy from a Minkowski reference
General Relativity and Gravitation, 2018Co-Authors: Chiang-mei Chen, Jian-liang Liu, James M. NesterAbstract:The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his Pseudotensor. It is now understood that energy-momentum is quasi-local (associated with a closed 2-surface). Here we consider quasi-local proposals (including Pseudotensors) in the Lagrangian–Noether–Hamiltonian formulations. There are two ambiguities: (1) there are many possible expressions, (2) they depend on some non-dynamical structure, e.g., a reference frame. The Hamiltonian approach gives a handle on both problems. The Hamiltonian perspective helped us to make a remarkable discovery: with an isometric Minkowski reference a large class of expressions—namely all those that agree with the Einstein Pseudotensor’s Freud superpotential to linear order—give a common quasi-local energy value. Moreover, with a best-matched reference on the boundary this is the Wang–Yau mass value.
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Quasi-local energy from a Minkowski reference
arXiv: General Relativity and Quantum Cosmology, 2018Co-Authors: Chiang-mei Chen, Jian-liang Liu, James M. NesterAbstract:The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his Pseudotensor. It is now understood that energy-momentum is \emph{quasi-local} (associated with a closed 2-surface). Here we consider quasi-local proposals (including Pseudotensors) in the Lagrangian-Noether-Hamiltonian formulations. There are two ambiguities: (i) there are many possible expressions, (ii) they depend on some non-dynamical structure, e.g., a reference frame. The Hamiltonian approach gives a handle on both problems. The Hamiltonian perspective helped us to make a remarkable discovery: with an isometric Minkowski reference a large class of expressions---namely all those that agree with the Einstein Pseudotensor's Freud superpotential to linear order---give a common quasi-local energy value. Moreover, with a best-matched reference on the boundary this is the Wang-Yau mass value.
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Positive small-vacuum-region gravitational-energy expressions
Physical Review D, 2009Co-Authors: James M. NesterAbstract:We construct an infinite number of new holonomic quasilocal gravitational-energy-momentum density Pseudotensors with good limits asymptotically and in small regions, both materially and in vacuum. For small vacuum regions they are all a positive multiple of the Bel-Robinson tensor and consequently have positive energy.
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Energy-momentum density in small regions: the classical Pseudotensors
Classical and Quantum Gravity, 2009Co-Authors: James M. Nester, Hsin ChenAbstract:The values for the gravitational energy-momentum density, given by the famous classical Pseudotensors: Einstein, Papapetrou, Landau-Lifshitz, Bergmann-Thompson, Goldberg, M{\o}ller, and Weinberg, in the small region limit are found to lowest non-vanishing order in normal coordinates. All except M{\o}ller's have the zeroth order material limit required by the equivalence principle. However for small vacuum regions we find that {\it none} of these classical holonomic Pseudotensors satisfies the criterion of being proportional to the Bel-Robinson tensor. Generalizing an earlier work which had identified one case, we found another independent linear combination satisfying this requirement--and hence a one parameter set of linear combinations of the classical Pseudotensors with this desirable property.
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Classical pseudotenors and positivity in small regions
arXiv: General Relativity and Quantum Cosmology, 2006Co-Authors: James M. Nester, Hsin ChenAbstract:We have studied the famous classical Pseudotensors in the small region limit, both inside matter and in vacuum. A recent work [Deser et al.1999 CQG 16, 2815] had found one combination of the Einstein and Landau-Lifshitz expressions which yields the Bel-Robinson tensor in vacuum. Using similar methods we found another independent combination of the Bergmann-Thomson, Papapetrou and Weinberg Pseudotensors with the same desired property. Moreover we have constructed an infinite number of additional new holonomic Pseudotensors satisfying this important positive energy requirement, all seem quite artificial. On the other hand we found that Moller's 1961 tetrad-teleparallel energy-momentum expression naturally has this Bel-Robinson property.
Chiang-mei Chen - One of the best experts on this subject based on the ideXlab platform.
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Quasi-local energy from a Minkowski reference
General Relativity and Gravitation, 2018Co-Authors: Chiang-mei Chen, Jian-liang Liu, James M. NesterAbstract:The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his Pseudotensor. It is now understood that energy-momentum is quasi-local (associated with a closed 2-surface). Here we consider quasi-local proposals (including Pseudotensors) in the Lagrangian–Noether–Hamiltonian formulations. There are two ambiguities: (1) there are many possible expressions, (2) they depend on some non-dynamical structure, e.g., a reference frame. The Hamiltonian approach gives a handle on both problems. The Hamiltonian perspective helped us to make a remarkable discovery: with an isometric Minkowski reference a large class of expressions—namely all those that agree with the Einstein Pseudotensor’s Freud superpotential to linear order—give a common quasi-local energy value. Moreover, with a best-matched reference on the boundary this is the Wang–Yau mass value.
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Quasi-local energy from a Minkowski reference
arXiv: General Relativity and Quantum Cosmology, 2018Co-Authors: Chiang-mei Chen, Jian-liang Liu, James M. NesterAbstract:The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his Pseudotensor. It is now understood that energy-momentum is \emph{quasi-local} (associated with a closed 2-surface). Here we consider quasi-local proposals (including Pseudotensors) in the Lagrangian-Noether-Hamiltonian formulations. There are two ambiguities: (i) there are many possible expressions, (ii) they depend on some non-dynamical structure, e.g., a reference frame. The Hamiltonian approach gives a handle on both problems. The Hamiltonian perspective helped us to make a remarkable discovery: with an isometric Minkowski reference a large class of expressions---namely all those that agree with the Einstein Pseudotensor's Freud superpotential to linear order---give a common quasi-local energy value. Moreover, with a best-matched reference on the boundary this is the Wang-Yau mass value.
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A Symplectic Hamiltonian Derivation of Quasilocal Energy-Momentum for GR
arXiv: General Relativity and Quantum Cosmology, 2000Co-Authors: Chiang-mei Chen, James M. NesterAbstract:The various roles of boundary terms in the gravitational Lagrangian and Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is ideally suited for a large class of quasilocal energy-momentum expressions for general relativity. This approach provides a physical interpretation for many of the well-known gravitational energy-momentum expressions including all of the Pseudotensors, associating each with unique boundary conditions. From this perspective we find that the Pseudotensors of Einstein and M{\o}ller (which is closely related to Komar's superpotential) are especially natural, but the latter has certain shortcomings. Among the infinite possibilities, we found that there are really only two Hamiltonian-boundary-term quasilocal expressions which correspond to {\em covariant} boundary conditions; they are respectively of the Dirichlet or Neumann type. Our Dirichlet expression coincides with the expression recently obtained by Katz and coworkers using Noether arguments and a fixed background. A modification of their argument yields our Neumann expression.
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Energy-Momentum (Quasi-)Localization for Gravitating Systems
arXiv: General Relativity and Quantum Cosmology, 1999Co-Authors: Chia-chen Chang, James M. Nester, Chiang-mei ChenAbstract:Traditional approaches to energy-momentum localization led to reference frame dependent Pseudotensors. The more modern idea is quasilocal energy-momentum. We take a Hamiltonian approach. The Hamiltonian boundary term gives not only the quasilocal values but also boundary conditions via the Hamiltonian variation boundary principle. Selecting a Hamiltonian boundary term involves several choices. We found that superpotentials can serve as Hamiltonian boundary terms, consequently Pseudotensors are actually quasilocal and legitimate. Various Hamiltonian boundary term quasilocal expressions are considered including some famous Pseudotensors, M{\o}ller's tetrad-teleparallel ``tensor'', Chen's covariant expressions, the expressions of Katz & coworkers, the expression of Brown & York, and some spinor expressions. We emphasize the need for identifying criteria for a good choice.
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Pseudotensors and quasilocal energy-momentum
Physical Review Letters, 1999Co-Authors: Chia-chen Chang, James M. Nester, Chiang-mei ChenAbstract:Early energy-momentum investigations for gravitating systems gave reference frame dependent Pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also identifies the variables to be held fixed on the boundary. We show that a Pseudotensor corresponds to a Hamiltonian boundary term. Hence they are quasilocal and acceptable; each is the energy-momentum density for a definite physical situation with certain boundary conditions. These conditions are identified for well-known Pseudotensors.
So, Lau Loi - One of the best experts on this subject based on the ideXlab platform.
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Black hole's tidal heating and angular momentum
2019Co-Authors: So, Lau LoiAbstract:In 1985 Thorne and Hartle used the Landau-Lifshitz Pseudotensor to demonstrate the tidal heating and angular momentum flux for a black hole. Later in 2004, Poisson used the gravitational perturbation method to study a black hole and obtained the same result. Poisson proposed a new idea, that the mass quardupole moment and current quadrupole moment can be written as the rate of change of the tidal gravitational field. Inspired by these two papers, we use the method of Thorne and Hartle to study other classical Pseudotensors: Einstein, Bergmann-Thomson, Papapetrou and Weinberg. Moreover, we also constructed a general expression Pseudotensor. We find that for (i) tidal heating: other classical Pseudotensors give the same result as the Landau-Lifshitz contribution. (ii) angular momentum flux: except for the Einstein Pseudotensor, all of them give the same value as the Landau-Lifshitz Pseudotensor.Comment: 7 pages, 1 Tabl
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General relativistic tidal heating for the Moller Pseudotensor
2017Co-Authors: So, Lau LoiAbstract:In his study of tidal stabilization of fully relativistic neutron stars Thorne showed that the fully relativistic expression for tidal heating is the same as in non-relativistic Newtonian theory. Furthermore, Thorne also noted that the tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Purdue and Favata calculated the tidal heating for a number of classical gravitational Pseudotensors including that of Moller, and obtained the result that all of them produced the same (Newtonian) value. However, in a re-examination of the calculation using the Moller Pseudotensor we find that there is no tidal heating. This leads us to the conclusion that Thorne's assertion needs a minor modification: the relativistic tidal heating is Pseudotensor independent only if the Pseudotensor is derived from a Freud type superpotential.Comment: 10 pages, a major revision of arXiv:1509.0920
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General relativistic tidal work for Papapetrou, Weinberg and Goldberg Pseudotensors
2015Co-Authors: So, Lau LoiAbstract:In 1998 Thorne claimed that all Pseudotensors give the same tidal work as the Newtonian theory. In 1999, Purdue used the Landau-Lifshitz Pseudotensor to calculate the tidal heating and the result matched with the Newtonian gravity. Soon after in 2001, Favata employed the same method to examine the Einstein, Bergmann-Thomson and M{\o}ller Pseudotensors, all of them give the same result as Purdue did. Inspired by the work of Purdue and Favata, for the completeness, here we manipulate the tidal work for Papapetrou, Weinberg and Goldberg Pseudotensors. We obtained the same tidal work as Purdue achieved. In addition, we emphasize that a suitable gravitational energy-momentum Pseudotensor requires fulfill the inside matter condition and all of the classical Pseudotensors pass this test except M$\o$ller. Moreover, we constructed a general pseudotesnor which is modified by 13 linear artificial higher order terms combination with Einstein Pseudotensor. We find that the result agrees with Thorne's prediction, i.e., relativistic tidal work is Pseudotensor independent.Comment: 6 page
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General relativistic tidal heating for Moller Pseudotensor
2015Co-Authors: So, Lau LoiAbstract:Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain formula. Purdue and Favata calculated the tidal heating for different classical Pseudotensors including Moller and obtained the results all matched with the Newtonian perspective. After re-examined this Moller Pseudotensor, we find that there does not exist any tidal heating value. Thus we claim that the relativistic tidal heating is Pseudotensor independent under the condition that if the peusdotensor is a Freud typed superpotential.Comment: 4 page
Paul A. Cahill - One of the best experts on this subject based on the ideXlab platform.
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Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules
Journal of the Optical Society of America B, 1998Co-Authors: S. F. Hubbard, Rolfe G. Petschek, Kenneth D. Singer, Liang-chy Chien, N. D'sidocky, C. Hudson, Craig C. Henderson, Paul A. CahillAbstract:We have designed a hyper-Rayleigh scattering scheme to measure six scalar invariants of the squared hyperpolarizability tensor β2. Our theoretical approach expresses the rotational invariants of the irreducible β components as scalars, which eliminates the need for difficult frame transformations. We applied our scheme to several conjugated chiral molecules and found that there are significant Kleinman-disallowed Pseudotensor contributions to their hyperpolarizability. These components, along with a large optical rotation and the results of quantum-chemical calculations, indicate a handed nonplanar delocalization of the charge-transfer system in such molecules as predicted by quantum-chemical calculations and are expected to lead to macroscopic second-harmonic generation in axially aligned polymer materials. Pseudotensor contributions to the hyperpolarizability in chiral molecules were found to be as large as the vector contribution in p-nitroaniline. We qualitatively investigated the dispersion in the Kleinman-disallowed components and confirmed that these components are smaller at longer wavelengths.
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Quadrupoled materials for second-order nonlinear optics
Nonlinear Optical Properties of Organic Materials X, 1997Co-Authors: S. F. Hubbard, Rolfe G. Petschek, Kenneth D. Singer, Liang-chy Chien, N. D'sidocky, C. Hudson, Craig C. Henderson, Paul A. CahillAbstract:We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This "quadrupolar" nonlinearity arises from the second rank Pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two Pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light for which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.
Kenneth D. Singer - One of the best experts on this subject based on the ideXlab platform.
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Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media
2015Co-Authors: V. Ostroverkhov, Oksana Ostroverkhova, Kenneth D. Singer, L. Sukhomlinova, R.j. Twieg, R.g. Petschek, -x. S. Wang, Liang-chy ChienAbstract:Molecular properties leading to second harmonic generation in chiral media in the electric dipole approximation for the cases of axial and biaxial symmetry are described. The components of the hyperpolarizability tensor that transform like a second-rank Pseudotensor (L=2) and a third-rank tensor (L=3) contribute. The sum-over-states quantum formula for the hyperpolarizability is used to illuminate the molecular features necessary for optimizing the second-rank Pseudotensor for dipolar molecules including orthogonal moments and high frequency. The example of C2v, appropriate for a L-shaped molecules, is examined in more detail. Results of the measurements of these components in representative molecules using hyper-Rayleigh scattering are presented. Two compounds in which the delocalized pi-system is two-dimensional, a camphorquinone derivative and crystal violet are found to exhibit sizable L=2 and L=3 components. 1
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Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media
Chemical Physics, 2000Co-Authors: V. Ostroverkhov, Oksana Ostroverkhova, Rolfe G. Petschek, Kenneth D. Singer, L. Sukhomlinova, R.j. Twieg, S. X. Wang, Liang-chy ChienAbstract:Molecular properties leading to second harmonic generation in chiral media in the electric dipole approximation for the cases of axial and biaxial symmetry are described. The components of the hyperpolarizability tensor that transform like a second-rank Pseudotensor (La 2) and a third-rank tensor (La 3) contribute. The sum-over-states quantum formula for the hyperpolarizability is used to illuminate the molecular features necessary for optimizing the secondrank Pseudotensor for dipolar molecules including orthogonal moments and high frequency. The example of C2v, appropriate for K-shaped molecules, is examined in more detail. Results of the measurements of these components in representative molecules using hyper-Rayleigh scattering are presented. Two compounds in which the delocalized pisystem is two-dimensional, a camphorquinone derivative and crystal violet are found to exhibit sizable La 2 and La 3 components. ” 2000 Elsevier Science B.V. All rights reserved.
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Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules
Journal of the Optical Society of America B, 1998Co-Authors: S. F. Hubbard, Rolfe G. Petschek, Kenneth D. Singer, Liang-chy Chien, N. D'sidocky, C. Hudson, Craig C. Henderson, Paul A. CahillAbstract:We have designed a hyper-Rayleigh scattering scheme to measure six scalar invariants of the squared hyperpolarizability tensor β2. Our theoretical approach expresses the rotational invariants of the irreducible β components as scalars, which eliminates the need for difficult frame transformations. We applied our scheme to several conjugated chiral molecules and found that there are significant Kleinman-disallowed Pseudotensor contributions to their hyperpolarizability. These components, along with a large optical rotation and the results of quantum-chemical calculations, indicate a handed nonplanar delocalization of the charge-transfer system in such molecules as predicted by quantum-chemical calculations and are expected to lead to macroscopic second-harmonic generation in axially aligned polymer materials. Pseudotensor contributions to the hyperpolarizability in chiral molecules were found to be as large as the vector contribution in p-nitroaniline. We qualitatively investigated the dispersion in the Kleinman-disallowed components and confirmed that these components are smaller at longer wavelengths.
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Quadrupoled materials for second-order nonlinear optics
Nonlinear Optical Properties of Organic Materials X, 1997Co-Authors: S. F. Hubbard, Rolfe G. Petschek, Kenneth D. Singer, Liang-chy Chien, N. D'sidocky, C. Hudson, Craig C. Henderson, Paul A. CahillAbstract:We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This "quadrupolar" nonlinearity arises from the second rank Pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two Pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light for which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.
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{open_quotes}Quadrupoled{close_quotes} materials for second-order nonlinear optics
1997Co-Authors: S. F. Hubbard, R.g. Petschek, Kenneth D. SingerAbstract:We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This {open_quotes}quadrupolar{close_quotes} nonlinearity arises from the second rank Pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two Pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light for which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.
