The Divergent Energy-Momentum Flux in Nonlocal Gravity

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題名:	The Divergent Energy-Momentum Flux in Nonlocal Gravity
作者:	Zuroida, Afidah;Zuroida, Afidah
貢獻者:	物理學系
關鍵詞:	energy-momentum flux;nonlocal;divergent;energy-momentum flux;nonlocal;divergent
日期:	2021-01-18
上傳時間:	2021-03-18 17:05:58 (UTC+8)
出版者:	國立中央大學
摘要:	這項研究是[arXiv：1811.04647]的延續，他們計算了非局部重力模型中的能量動量通量f[R/□]，其中R是Ricci純量，□ 是d′ Alembertian運算符。在（3 + 1）D Minkowski時空中，當r →∞，重力能量動量通量會趨近正比於1/r^2，其中r 是觀察者到場源的距離。為了檢查能量通量符合此條件，我們需要對非局部模型的運動方程式度規進行微擾，到二階微擾。在這項工作中，我們研究了一些非局部重力模型，例如Deser-Woodard的第二個模型、VAAS模型和ABN模型。我們發現，在Minkowski條件下，VAAS和ABN模型沒有解析解。因此，在以平坦時空加上微小修正項形成的Fermi-Normal Coordinate（FNC）宇宙學背景下，我們套入這兩個模型，其中的修正項以自由落體觀測者到場源的距離來表示。我們獲得對應於f[Y]的Deser-Woodard II模型，其中Y由R/□組成，可以透過設 f^′ [0]=0來避免通量發散，這類似於Deser-Woodard的第一個模型的案例。但是，非局部重力m^2 (R/□)(稱為VAAS) 和M^4 (R/□^2)(稱為ABN)會出現能量通量發散的情況，因為其能量動量通量分別趨近正比於r^0和r^2。根據到目前為止的研究結果，我們需要更深入地理解非局部引力，以構建一個可產生與愛因斯坦廣義相對論相容的重力輻射通量的模型。;This work is a continuation of [arXiv:1811.04647], which computed the energy-momentum flux in $f[R/\Box]$ nonlocal gravity model, where $R$ is the Ricci Scalar and $\Box$ is the d′Alembertian operator. In (3+1)D Minkowski spacetime, the gravitational energy-momentum flux is supposed to scale at most $1/r^{2}$ as $r \rightarrow \infty$, where $r$ is the distance from the observer to the source. To examine the energy flux, we need to perturb the equation of motions from the nonlocal models up to quadratic order in metric perturbation. In this work, we investigate some nonlocal gravity models likewise the second model of the Deser-Woodard, VAAS model, and ABN model. We find that the VAAS and ABN models do not have an exact solution in Minkowski background. So, we work both models in Fermi-Normal-Coordinates (FNC) cosmological background that consist of flat spacetime and corrections in terms of the distance from the free-falling observer to the source. We obtain the Deser-Woodard II model that corresponds to $f[Y]$, where $Y$ consists of $R/\Box$, can avoid the divergent flux by setting $f′[0]=0$, similar in the case from the first model of Deser-Woodard. However, the nonlocal gravity $m^{2}(R/\Box)$, called VAAS and $M^{4}(R/\Box^{2})$, called ABN suffers from the divergent flux because the energy-momentum flux scale as $r^{0}$ and $r^{2}$ respectively. From our works so far, the nonlocal gravity needs deeper understanding to construct the model that yields a sensible gravitational radiation flux comparable to that of Einstein′s General Relativity.
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