雙黑洞系統之散射振幅描述

Spinning Amplitudes into Black Holes

鍾明志(Ming-Zhi Chung)

指導教授 ： 黃宇廷

國立臺灣大學/理學院/物理學研究所/博士(2022年)

https://doi.org/10.6342/NTU202201852

摘要

在本篇論文中, 我們討論如何使用散射振幅計算古典重力理論中的物理量, 我們使用方法是基於知名的帶質量旋量旋性法以及數個現代在殼振幅方法發展而來。

首先我們建立在殼方法中的耦合常數以及世界線有效場論中的威爾森係數的對應關係, 這有助於我們建立古典3點振幅的概念, 並可將其以在殼的方式建立2對2的散射振幅。

接著我們將這套方法用來提取任意自旋物體的$\mathcal{O}(G)$哈彌爾頓量, 我們提取的哈彌爾頓量準確到任意速度與自旋的階數, 我們也證明我們從散射振幅提取的$\mathcal{O}(G)$衝量與測地線方程式計算的$\mathcal{O}(G)$衝量是一致的。

我們更近一步研究$\mathcal{O}(G)^2$的物理量, 在$\mathcal{O}(G)^2$的計算中, 我們會需要1圈的振幅, 且古典效應源自1圈振幅中的三角係數, 在一圈振幅的計算中, 我們會需要重力的古典康普頓振幅。有了一圈振幅後, 我們將在本文中計算克爾黑洞到自旋四次方的$\mathcal{O}(G)^2$哈彌爾頓量。

最後, 我們從自旋空間中量子糾纏的角度討論三點振幅的性質, 我們發現在一個2對2的散射過程中, 當散射的粒子最簡耦合到重力子時, 糾纏熵的改變是最小的。

關鍵字

散射振幅 ； 旋量旋性法 ； 在殼方法 ； 克爾黑洞 ； 後牛頓展開 ； 後閔考斯基展開 ； 糾纏熵

並列摘要

In this thesis, we summarize the formalism of computing physical observables in classical gravity using scattering amplitudes methods. This formalism is developed based on the well-known massive spinor helicity formalism and several modern on-shell amplitude techniques.

We first establish the correspondence between coupling constants in on-shell framework and Wilson coefficients of the effective one body worldline formalism. This sets up the notion of classical 3-point amplitudes, and will later be used to construct $2\rightarrow 2$ scattering amplitudes via on-shell techniques.

Then we apply our methods to compute the Hamiltonian of general spinning bodies to all orders in spin and velocity at $\mathcal{O}(G)$. We also match the impulse at $\mathcal{O}(G)$ computed by scattering ampliutdes and that computed from solving the geodesic equations.

We further explore the dynamics at $\mathcal{O}(G)^2$, where one loop amplitudes come into play. It is well known that the classical dynamics at $\mathcal{O}(G)^2$ is completely captured by the trianlge coefficient of the one-loop amplitude. This requires us to construct the tree level classical gravitational Compton amplitude which will be embedded into the triangle coefficient computation. With the one loop ampliutde, we extract the 2PM Hamiltonian up to quartic order in spin for binary Kerr black hole.

We also study the properties of the 3 point amplitude through the entanglement in the spin space. We discover the minimization of entropy change in a $2\rightarrow 2$ scattering process when the scattered particle is minimally coupled to graviton.

並列關鍵字

Scattering amplitudes ； Spinor Helicity ； On-shell methods ； Kerr black holes ； PN expansion ； PM expansion ； entanglement

參考文獻

M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP 04 (2019) 156,[1812.08752].

M.-Z. Chung, Y.-T. Huang and J.-W. Kim, Classical potential for general spinning bodies, JHEP 09 (2020) 074, [1908.08463].

[3] M.-Z. Chung, Y.-T. Huang and J.-W. Kim, Kerr-Newman stress-tensor from minimal coupling, JHEP 12 (2020) 103, [1911.12775].

[4] M.-Z. Chung, Y.-t. Huang, J.-W. Kim and S. Lee, Complete Hamiltonian for spinning binary systems at first post-Minkowskian order, JHEP 05 (2020) 105, [2003.06600].

[5] R. Aoude, M.-Z. Chung, Y.-t. Huang, C. S. Machado and M.-K. Tam, Silence of Binary Kerr Black Holes, Phys. Rev. Lett. 125 (2020) 181602, [2007.09486].