| 摘要: | 我們現在正處在引力波天體物理學和宇宙學的新時代。我對研究彎曲時空中波浪的因果結構感興趣。具體來說，在彎曲的時空和奇數維的平面時空中，無質量的粒子（例如光子和引力子）不再嚴格在零錐上傳播-但它們會形成尾巴，即在光錐內傳播。這種尾巴現象會對在這種時空中運動的物體產生自力，因為它們的時態軌跡現在可能會接收到自己過去的信號。這種情況發生在極端質量比吸入系統中，在該系統中，緊湊的太陽質量物體繞著超大質量黑洞運行，天文學家告訴我們它們位於許多（如果不是全部）星系的核心。這激勵了我追求一個定量程序，以研究彎曲時空中引力波的因果結構和其他相關特性。儘管數學比黑洞時空更簡單，但與真空情況相比，它具有一些新穎的功能：由於公制和流體自由度的混合，可能存在聲重力輻射。例如，在輻射主導的宇宙中移動的宇宙弦或一對原始黑洞的聲輻射特徵是什麼？在理想的流體驅動的宇宙中，平坦的時空四極子公式將如何推廣？同樣，在這樣的宇宙學背景下，引力動力學將與平坦的對應物中的開普勒斯動力學有所不同-我也希望更仔細地理解這種差異。與宇宙萬有引力波密切相關的問題是如何“繼續”我們在大多數宇宙解的解析和數值相對論計算中獲得的漸近平坦解。在牛頓後系統中，尾巴誘發的自力可能使我們能夠探測雙星系統中恆星的內部結構。這是因為（按先導順序）它是從給定物體發出的空信號產生的，該信號在返回以聲明自力之前先反射了另一個物體的質量密度和牛頓勢。我和我的合作者計劃量化重力自力及其對有限尺寸效應的敏感性。最近，在Sohyun Park實驗室，我發現了一種特殊的非局部引力理論模型的引力能量動量通量中的一種潛在病理。我打算將此分析擴展到市場上的其他非本地模型。探索的其他主題包括：擾動的de Sitter時空中的晚期尾巴，建立/記錄我的張量微積分TensoriaCalc，以及量子場論中的初值問題（其技術可能與自力問題有關）。 ;We are now firmly in the new era of gravitational-wave astrophysics and cosmology. I am interested in studying the causal structure of waves in curved spacetimes. Specifically, in curved spacetimes and in odd dimensional flat spacetimes, massless particles such as photons and gravitons no longer travel strictly on the null cone -- but they develop tails, i.e., propagating inside the light cone. This tail phenomenon produces a self-force on objects moving about in such spacetimes, since their timelike trajectories now may receive signals from their own past. Such a situation occurs in Extreme-Mass-Ratio inspiral systems, where compact solar mass objects orbit around the supermassive black holes astronomers tell us reside at the core of many (if not all) galaxies. This has motivated me to pursue a quantitative program to study the causal structure and other related properties of gravitational waves in curved spacetimes. Even though the math is simpler than in black hole spacetimes, there are novel features compared to the vacuum case: the potential existence of acoustic-gravitational radiation, due to the mixing of metric and fluid degree-of-freedom. What are these acoustic radiation signatures for, say, a cosmic string or a pair of primordial black holes moving about in a radiation dominated universe? How would the flat spacetime quadrupole formula generalize to, in a perfect fluid driven universe? Along the same lines, the gravitational dynamics in such a cosmological background will defer from the Keplerian one in the flat counterpart -- I too wish to understand this difference more carefully. Closely related to cosmological gravitational waves is the issue of how to `continue' the asymptotically flat solutions we obtain in most analytical and numerical relativity calculations to cosmological solutions.Within a post-Newtonian system, the tail induced self-force may allow us to probe the interior structure of stars in binary systems. This is because (at leading order) it arises from the null signal emitted from a given body, reflecting off the other body's mass density and Newtonian potential, before returning to assert a self-force. My collaborators and I plan to quantify the gravitational self-force and its sensitivity to finite size effects.With Sohyun Park, I recently discovered a potential pathology in the energy-momentum flux of gravitational energy of a particular nonlocal model of gravity theories. I am planning to extend this analysis to other nonlocal models on the market.Other topics of exploration include: late time tails in perturbed de Sitter spacetime, building/documenting my tensor calculus packpage TensoriaCalc, and the initial value problem in quantum field theory (whose techniques could be relevant for the self-force problem). |
