Action Principle for Isotropic General Relativity
Action Principle for Isotropic General Relativity
复制标题
各向同性广义相对论的作用原理
DOI：
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发表时间：
2018
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影响因子：
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通讯作者：
Thomas C. Bachlechner
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文献类型：
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作者：
Thomas C. Bachlechner
我们研究控制具有均匀能量密度的各向同性时空区域的一般协变理论。Gibbons，Hawking和York证明了固定诱导边界度规会产生一个适定的变分问题。然而，正如我们所证明的，固定边界度量值违反了一般协方差，并允许后孔的质量变化。这一观察结果对路径积分产生了戏剧性的影响：具有固定边界度规的时空之和就是经典不同黑洞的和。相反，我们只要求存在坐标，使得边界上的度规是具有固定质量M和两个球半径R的Schwarzschild-(A)DS度规。我们推导出了在这些物理边界条件下产生适定变分问题的作用量。对于所有静止的和各向同性的时空，这个作用力都会消失。消失作用量意味着施瓦希尔德黑洞和纯德西特空间都有一个唯一的半经典态。我们的结果为量子引力中的几个长期存在的问题，如宇宙的波函数、黑洞信息悖论、真空衰减率和永恒膨胀的测量问题，提供了一种新的和从根本上保守的方法。
We study the generally covariant theory governing an isotropic spacetime region with uniform energy density. Gibbons, Hawking and York showed that fixing the induced boundary metric yields a well-posed variational problem. However, as we demonstrate, fixing the boundary metric violates general covariance and allows the mass of a back hole to vary. This observation has dramatic consequences for path integrals: A sum over spacetimes with fixed boundary metrics is a sum over classically distinct black holes. Instead, we merely demand that coordinates exist such that the metric at the boundary is the Schwarzschild-(A)dS metric of fixed mass M and two-sphere radius R. We derive the action that yields a well-posed variational problem for these physical boundary conditions. The action vanishes for all stationary and isotropic spacetimes. A vanishing action implies that both a Schwarzschild black hole and pure de Sitter space each have one unique semiclassical state. Our results provide a novel and radically conservative approach to several long-standing issues in quantum gravity, such as the wavefunction of the universe, the black hole information paradox, vacuum decay rates and the measure problem of eternal inflation.