Emergent modified gravity: Covariance regained
Emergent modified gravity: Covariance regained
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DOI：
10.1103/physrevd.108.084066
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发表时间：
2023-10
影响因子：
5
通讯作者：
M. Bojowald;Erick I. Duque
中科院分区：
文献类型：
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作者：
M. Bojowald;Erick I. Duque
在其规范表述中，广义相对论服从规范变换，只有当由哈密顿约束和微分同态约束给出的规范发生器消失时，规范变换才等价于一般协方差的时空坐标变化。由于约束及其产生的规范变换和运动方程的泊松括号所采取的特定形式对于实现一般协方差是重要的，因此不能保证规范理论的修正，例如通过量子引力方法提出的修正，与协变时空线元素的存在相兼容。即使修改保留了独立规范转换的数量，并且修改的约束仍然是一流的，这个警告也适用。本文给出了协方差条件的完整推导，从正则约束中获得协方差条件，而不假设时空具有经典结构，并将其详细应用于球对称真空模型。作为一种广泛的应用，约束括号中结构函数的存在起着至关重要的作用，最近在一项独立分析中表明，约束括号可以导致由l -∞括号给出的超曲面变形中的更高代数结构。对这里提出的一个相关特征的物理分析表明，至少在球对称的背景下，不具有高曲率形式的修正引力的新理论是可能的。
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism constraints, vanish. Since the specific form taken by Poisson brackets of the constraints and of the gauge transformations and equations of motion they generate is important for general covariance to be realized, modifications of the canonical theory, suggested for instance by approaches to quantum gravity, are not guaranteed to be compatible with the existence of a covariant space-time line element. This caveat applies even if the modification preserves the number of independent gauge transformations and the modified constraints remain first class. Here, a complete derivation of covariance conditions, regained from the canonical constraints without assuming that space-time has its classical structure, is presented and applied in detail to spherically symmetric vacuum models. As a broad application, the presence of structure functions in the constraint brackets plays a crucial role, which in an independent analysis has recently been shown to lead to higher algebraic structures in hypersurface deformations given by an L-infinity bracket. The physical analysis of a related feature presented here demonstrates that, at least within the spherically symmetric setting, new theories of modified gravity are possible that are not of higher-curvature form.