论文标题
在通用的四阶重力理论中，在空间紧凑的固定源外的重力场
The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity
论文作者
论文摘要
By applying the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, the metric for the external gravitational field of a spatially compact stationary source is provided in $F(X,Y,Z)$ gravity, a generic fourth-order theory of gravity, where $X:=R$ is Ricci scalar, $Y:=R_{μν}R^{μν}$ is ricci Square和$ z：= r_ {μνρσ} r^{μνρσ} $是riemann Square。提出了一种新型的规格条件，以便大大简化了$ f（x，y，z）$重力的线性化重力场方程，然后得出了源外部区域的固定度量。在应用结果的过程中，仅在源占据的域上进行集成。还提供了$ f（x，y，z）$重力在空间紧凑的固定源中的多极扩展。在扩展中，$ f（x，y，z）$重力的校正是类似于Yukawa的，取决于两个特征长度。校正中出现了另外两组质量源多极矩，而表征它们的显着特征是表达式中的集成总是由与源分布相关的常见径向因子调节。
By applying the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, the metric for the external gravitational field of a spatially compact stationary source is provided in $F(X,Y,Z)$ gravity, a generic fourth-order theory of gravity, where $X:=R$ is Ricci scalar, $Y:=R_{μν}R^{μν}$ is Ricci square, and $Z:=R_{μνρσ}R^{μνρσ}$ is Riemann square. A new type of gauge condition is proposed so that the linearized gravitational field equations of $F(X,Y,Z)$ gravity are greatly simplified, and then, the stationary metric in the region exterior to the source is derived. In the process of applying the result, integrations are performed only over the domain occupied by the source. The multipole expansion of the metric potential in $F(X,Y,Z)$ gravity for a spatially compact stationary source is also presented. In the expansion, the corrections of $F(X,Y,Z)$ gravity to General Relativity are Yukawa-like ones, dependent on two characteristic lengths. Two additional sets of mass-type source multipole moments appear in the corrections and the salient feature characterizing them is that the integrations in their expressions are always modulated by a common radial factor related to the source distribution.
