| 摘要: | 我們計畫持續我們的時空幾何動力學的研究路線，特別是基於局部時空對稱性的重力規範理論 (獨立的度規和聯絡，包括Poincare 規範理論(PGT)、度規仿射(MA)理論、 teleparallel 理論和Einstein 的廣義相對論)。我們的興趣著重在引力的能量。主要的方法是透過我們的協變哈密頓數學形式。我們主要的工具有微分幾何、變分原理、正則 Hamiltonian 分析、旋量技巧、我們的特殊標架規範條件、符號和數值的電腦計算。我們預期有更多新的結果包括，可傳播模式的動力學、拘束條件、規範(特別是非線性的效應)、引力的能量-動量(也包括角動量和質心矩)準局域性、能量的正定性和長距離的效應。我們正在探尋替代的引力理論，該理論能夠說明銀河尺度的觀測而不用大量的暗物質，且/或解釋宇宙的加速膨脹而不用暗能量。我們最近的研究還包含了宇稱破缺效應。我們希望更進一步發展一般協變正則分析和準局域能動的表示式、檢驗準則、和別人的結果比較，並且應用到黑洞熱力學上，除此之外，探索更多他們與膺張量和參考系及邊界值的關係，我們將更進一步探討Bondi 極限、協變性、準局域角動量、物質的質心和能量流，以及旋量形式的限制和應用範圍。我們正在發展協變正則表示式，並更進一步研究尚未被廣泛重視但卻有希望決定出好的引力能量表達式的小範圍極限。我們主要考慮的為引力系統的適恰能量表示。近來我們驚訝地發現許多宇宙學模型具有負能量，與我們對正能量的期望產生強烈的對比。 We plan to continue our dynamic spacetime geometry investigations, especially for gauge theories of gravity based on local spacetime symmetry (independent metric & connection, including the Poincare Gauge Theory (PGT), the metric-affine (MA) theory, and teleparallel theories as well as Einstein's GR). Our major interest is quasi-local gravitational energy. The main approach is via our covariant Hamiltonian formalism. The principal tools are differential geometry, the variational principle, the canonical Hamiltonian analysis, spinor techniques, our special orthonormal frame gauge conditions, symbolic and numerical computer calculations. We expect some new results re propagating mode dynamics, gravitational energy-momentum (also angular momentum & center-of-mass) and its quasi-localization, energy positivity, and long range effects. We are exploring alternate gravity theories which can account for the galactic scale observations without large amounts of “dark matter” a/o account for the accelerating universe and “dark energy”. Our latest investigations include parity violating effects. We hope to further develop our general covariant canonical analysis and our quasi-local energy-momentum expressions, examining criteria, comparing with other expressions, refining their application to black hole thermodynamics, probing more their relationship with pseudotensors and the choice of boundary and reference values. We will look deeper into the Bondi limit, covariance,quasi-local angular momentum, center-of mass, energy flux and the scope and limitations of spinor formulations. We are developing a manifestly covariant canonical formalism and will further refine our study of the under-appreciated small region limit. Our main concern is the proper formulation of energy for gravitating systems. Recently we found, surprisingly, that many cosmological models have negative energy, in sharp contrast with our positivity expectations. 研究期間：10008 ~ 10107 |
