Existence and disappearance of conical singularities in Gleyzes-Langlois-Piazza-Vernizzi theories
Existence and disappearance of conical singularities in Gleyzes-Langlois-Piazza-Vernizzi theories
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DOI：
10.1103/physrevd.92.124060
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发表时间：
2015-08
影响因子：
5
通讯作者：
A. D. Felice;R. Kase;S. Tsujikawa
中科院分区：
文献类型：
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作者：
A. D. Felice;R. Kase;S. Tsujikawa
在一类Gleyzes-Langlois-Piazza-Vernizzi （GLPV）理论中，我们在标量场$\phi$对半径$r$的导数为零的条件下导出了真空和内部Schwarzschild解。如果表征偏离霍恩德斯基理论的参数$\alpha_{\rm H}$在球对称体的中心接近非零常数，我们发现圆锥奇点出现在$r=0$处，其里奇标量由$R=-2\alpha_{\rm H}/r^2$给出。这源于对四维曲率量几何结构的违背。对于参数$\alpha_{\rm H}$在$r \to 0$的极限内消失的模型，圆锥奇点可以消失。我们提出了没有圆锥奇点的显式模型，通过适当地设计经典拉格朗日量，使$\alpha_{\rm H}$的主要贡献来自$r=0$周围的场导数$\phi'(r)$。我们证明了具有全音耦合的协变伽利略的扩展允许在所谓的Vainshtein半径内恢复广义相对论行为。在这种情况下，第五种力的传播和对霍恩德斯基理论的偏离都被抑制在紧致体之外，因此该模型与太阳系内部的局部重力实验是相容的。
In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $\phi$ with respect to the radius $r$ vanish. If the parameter $\alpha_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2\alpha_{\rm H}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The conical singularity can disappear for the models in which the parameter $\alpha_{\rm H}$ vanishes in the limit that $r \to 0$. We propose explicit models without the conical singularity by properly designing the classical Lagrangian in such a way that the main contribution to $\alpha_{\rm H}$ comes from the field derivative $\phi'(r)$ around $r=0$. We show that the extension of covariant Galileons with a diatonic coupling allows for the recovery of general relativistic behavior inside a so-called Vainshtein radius. In this case, both the propagation of a fifth force and the deviation from Horndeski theories are suppressed outside a compact body in such a way that the model is compatible with local gravity experiments inside the solar system.