此篇論文的第一部分，我們關注至少一顆中子星參與其中的雙星合併系統內之潮汐效應。在諸多可能的現象中，我們探討中子星中低頻準正規振態---例如$g$模式與$i$模式震盪---的共振可能導致的星震現象；若該中子星的磁場達到磁星的強度，則伴隨的能量釋放可能會引起短伽馬射線脈衝的前導放射。實際上，我們發現短伽馬射線脈衝事件SGRB090510所觀測到的兩個前導脈衝可分別歸因於$g_1$與$g_2$模式共振所產生的星震。換言之，我們可以由前導放射觀測的時間脈絡得知當下雙星運動的軌道頻率，進而推算震盪模式的頻率。我們進一步發現藉由兩個（或以上）前導放射的觀測結果，可以估算中子星的自旋速度。此外，由於目前尚待實際觀測確認的候選核子狀態方程式可以藉由$g$模式震盪的頻率高低被分為三組，因此上述推得的$g$模式震盪之頻率或可對核子狀態方程式提供特定限制。另一方面，$f$模式的震盪可以有效加速併合的進程、誘發「潮汐陷落」的現象，由此產生重力波型的相位差。雖然對於自轉速度不快的中子星而言，潮汐引起的相位差大多是由星體本身形變所導致的，但若中子星快速自轉，其$f$震盪可能導致更大程度的相位差---我們在某些系統中觀察到大約100弧度的相位差。

在論文的第二部分，我們探討非愛因斯坦重力的理論中，中子星及黑洞在強重力環境下的動態行為。在多純量張量理論中，純量化(緊緻)物體的純量場在星體外會以距離平方反比的趨勢減弱（因此脈衝星的觀測數據無法限制此類理論），且穩態星體可被離散地以其拓墣性質來加以分類並以「拓墣荷」來量化描述。對於拓墣荷為零的穩態解，我們發現星體的穩定性在達到最大可能質量前都被保持，因此在某些環境下的吸積現象，可能會將穩定星體的質量增加到不穩定性的閾值，而引發非線性的動態過程---去純量化。星體在此過程中，會迅速縮小，類似於一般物質的相變過程，不過會有伴隨而生的純量重力波。我們也探討可能隨之產生的電磁指標性訊號。除吸積過程外，我們也採用純量張量理論與純量高斯-博內理論來考慮核心塌陷。前者理論中，由於無毛定理，純量化的穩態黑洞並不存在，不過在後者理論的框架下，我們透過數值模發現擬塌陷而成的黑洞在特定理論條件下可以賦有純量場。這是在相對真實的物理過程中，對純量化黑洞生成管道的第一個動態演示。

In the first part of this thesis, we investigate some tidal phenomena in the pre-merger stage of coalescing binaries with at least one neutron star (NS) involved.
Among other things, resonance of low frequency modes (e.g., $g$- and $i$-modes) may result in crustal fracture, whereby unleash the energy used to be stored in the cracked area, possibly constituting a pre-emission of short gamma-ray burst (SGRB) if the NS is highly magnetised. In particular, we find it possible to associate two pre-emissions of SGRB 090510 with the resonantly excited $g_1$- and $g_2$-modes. We present, in addition, that the inferred frequencies of these two $g$-modes provide a novel avenue to estimate the spin of the NS, which can be applied to any SGRB preceded by two or more precursors. This presumably, $g$-mode-related phenomenon can also benefit in constraining the equation of state (EOS) since the EOS candidates can be grouped in terms of $g$-mode frequency.
On the other hand, $f$-mode excitation accelerates the merger course, leading to a ``tidal plunge'' phase; thereby, a phase shift is rendered in the associated gravitational waveform, which dictates the evolutionary track of the binary. Although the adiabatic tide attributes much more to the phase shift than the dynamical ones if the NS rotates slowly, the situation for fast spinning stars is different: a few hundred radiants of shift may be rendered.

The second part of this thesis is dedicated to the study of the dynamics of compact objects, viz.~NSs and black holes (BHs), in alternative gravity theories in the strong gravity regime. In particular, we consider some scalar-involved theories such as the (multi-)scalar-tensor theory and scalar-Gauss-Bonnet theory. In the theory with three scalar fields, the scalar field of static stars dies out in the power of $-2$ of distance, thus not constrained by pulsar experiments, and they are of discrete topological types, characterised by topological charge.
For the zero charge configurations, we show that up to three stable stars exist for a certain range of central energy density, and the stability is lost right at the occurrence of the most massive (either scalarized or non-scalarized) star. Accretions may therefore bring a stable scalarized NS into an unstable state, where a descalarization would be triggered, generating the gravitational phase transition (PT) that mimics well the traditional, material PT while accompanied by scalar-induced gravitational waves (SGWs). Some observational signatures -- both gravitational and electromagnetic -- are discussed.
In addition to the accreting process, we consider the spherically-symmetric core collapse for the scalar-tensor and the scalar-Gauss-Bonnet theories. Although a scalarized BH is absent in the former theory due to no-hair reason, we can construct one in the latter theory. In particular, we numerically demonstrate scalarization in a remnant BH behind stellar collapse, giving a first example on the production channel for scalarized BHs in the scalar-Guass-Bonnet theory.

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