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arXiv 2607.04483hep-thgr-qcquant-ph
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Rindler时空中某些空间维度的紧致化对Fulling-Rindler真空中带电标量场平方和能量-动量张量的真空期望值的拓扑效应

Topological effects in the polarization of the Fulling-Rindler vacuum

Institute of Physics, Yerevan State University（埃里温国立大学物理研究所）；Institute of Mechanics RA（亚美尼亚共和国力学研究所）

A. A. Saharian, G. V. Mirzoyan, V. S. Torosyan

备注：
23 pages, 7 fugures
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AI总结：

研究Rindler时空空间维度紧致化对Fulling-Rindler真空态下带电标量场相关真空期望值的影响，通过环面紧致化及准周期性条件，明确各分量，揭示拓扑效应及特殊情况，还应用于黑洞视界附近。

摘要：

我们研究了Rindler时空中某些空间维度的紧致化如何影响在Fulling-Rindler真空态下制备的带电标量场的场平方和能量-动量张量的真空期望值（VEVs）。考虑了环面紧致化以及场算符沿紧致维度的准周期性条件。这些条件的相位根据紧致维度所包围的磁通量来解释。对于一般数量的空间维度，明确分离了VEVs的分量，对应于Minkowski真空中的期望值。作为极限情况，在具有平凡拓扑的Rindler时空中恢复了VEVs。我们证明，对于周期性条件中的非零相位，真空能量-动量张量在紧致子空间中表现出具有非对角分量。在Rindler视界附近，场平方和能量-动量张量对角分量的渐近展开中的主导项与具有平凡拓扑的Rindler时空中的相应VEVs一致。能量-动量张量的非对角分量在Rindler视界上消失。对于小加速度，Fulling-Rindler和Minkowski真空中VEVs之间的差异呈指数级小。唯一的例外是周期性条件中相位为零的无质量场。在这种特殊情况下，差异作为加速度的函数根据幂律衰减。作为应用，我们考虑了圆柱黑洞和具有环面视界的拓扑黑洞视界附近的VEVs。

英文摘要：

We investigate how the compactification of some spatial dimensions in Rindler spacetime affects the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a charged scalar field prepared in the Fulling-Rindler vacuum state. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. For a general number of spatial dimensions, the components of the VEVs are explicitly separated, corresponding to the expectation values in the Minkowski vacuum. As a limiting case, the VEVs are retrieved in Rindler spacetime with trivial topology. We demonstrate that, for non-zero phases in the periodicity conditions, the vacuum energy-momentum tensor exhibits off-diagonal components with indices in the compact subspace. Near the Rindler horizon, the leading terms in the asymptotic expansions of the field squared and the diagonal components of the energy-momentum tensor coincide with the corresponding VEVs in Rindler spacetime with trivial topology. The off-diagonal components of the energy-momentum tensor vanish on the Rindler horizon. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. The exception to this is a massless field with zero phases in the periodicity conditions. In this special case, the difference decays according to a power law as a function of acceleration. As an application, we consider the VEVs near the horizon of cylindrical black holes and topological black holes with toroidal horizons.

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