關於消失質量的問題，在 1930 年代開始被討論與研究,但直到 1980 左右，維拉·魯賓（ Vera Rubin）發現了 螺旋星系中的平坦的旋轉曲線(Flat rotation curve)，這樣的研究結果，讓我們重新思考關於宇宙組成的重大問題。 在當時大部分的人確信牛頓力學是完全正確的，因此他去尋找一種物質，它有質量但不與相互作用，他們稱之暗物質。 暗物質的假設已經被許多人所接受， 也絕了許多問題，更是現代宇宙學當中重要的一環。 但暗物質仍被一些人存疑，有許多人提出了新的看法，這當中最被認可的便是”修改牛頓力學(Modified Newtonian Dynamics, MOND)”。 MOND 的主要想法是在小加速度時，重力會超出牛頓力學的想像，因此他們認為牛頓力學必須修改。事實上， MOND 在解釋螺旋星系
中的平坦的旋轉曲線(Flat rotation curve)是非常成功的。而最近有更多的研究致力於橢圓星系的研究。 我們也對相對論當中的重力透鏡(Gravitational lensing)，在橢圓星系中會如何表現很感興趣。因此我們再 MOND 基礎下，建立了一個輕微變形的球面系統，並針對強重力透鏡(Strong gravitational lensing)的圖像去進行分析。 然後我們利用數值分析寫成一個程式碼，使我們可以解決在 Bekenstein 方程式下(一種常被使用關於 MOND 的插值函數)圖像的位置。比較數值分析與現有的分析方式結果相當吻合。我們對大部分的參數進行大量的分析，包括強重力透鏡中，來源的位置、透鏡平面上質量分布略為的改變，配合上不同程度 MOND 的影響程度。我們的目標是提供一個類似書庫的系統並且未來能對實際的現象做更深入的研究。

The missing mass problem was first discussed in the 1930s. However, not until the 1970s and 1980s that the flat rotation curve of spiral galaxies was confirmed in quite a number of galaxies before the astronomy community realized that the missing mass problem is a genuine problem. The mainstream idea is Newtonian dynamics is intact and there is some form of matter which possesses mass but does not interact electromagnetically. It is usually called the dark matter model (or dark matter paradigm). Besides successful in resolving the missing mass problem, dark matter is also an important ingredient in modern cosmology. Nonetheless, it still faces some challenging problems. On the other hand, there is no lack of non-mainstream ideas tossing around. Particularly satisfactory is modified Newtonian dynamics (MOND), which maintains that gravity is stronger than Newtonian when the acceleration is small. It is very successful in explaining the flat rotation curve of spiral galaxies. Many studies of MOND were devoted to spiral galaxies. Recently, some more attentions are paid to elliptical galaxies. We are interested in the relativistic phenomenon gravitational lensing by elliptical galaxies. Base on a recent analysis on slightly deformed spherical systems in the framework of MOND, we investigate their strong lensing images. We develop a numerical code to solve for the image positions under the Bekenstein form (one commonly used MOND interpolation function). The numerical results agree well with the available analytical results. We do an extensive parameter space survey which includes the source position, the lens ellipticity and its orientation, and the degree of MOND. Our aim is to provide a library of cases and a systematic way to study real observations.

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