The backreaction of quantum fields in their vacuum state results in equilibrium structures that surpass the Buchdahl compactness limit. Such backreaction is encapsulated in the vacuum expectation value of the renormalized stress-energy tensor (RSET). In previous works we presented analytic approximations to the RSET, obtained by dimensional reduction, available in spherical symmetry, and showed that the backreaction-generated solutions described ultracompact fluid spheres with a negative mass interior. Here, we derive a novel approximation to the RSET that does not rely on dimensional reduction, but rather on a reduction of the differential order. This approximation also leads to regular stars surpassing the Buchdahl limit. We conclude that this is a consequence of the negative energies associated with the Boulware vacuum which, for sufficiently compact fluid spheres, makes the Misner-Sharp mass negative near the center of spherical symmetry. Our analysis provides further cumulative evidence that quantum vacuum polarization is capable of producing new forms of stellar equilibrium with robust properties across different analytical approximations to the RSET.

中文翻译：

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降阶半经典重力中的超紧凑无水平物体

量子场在真空状态下的反反应会产生超过布赫达尔紧致极限的平衡结构。这种反反应被封装在重正化应力能量张量（RSET）的真空期望值中。在之前的工作中，我们提出了 RSET 的解析近似，通过降维获得，可用于球对称，并表明反反应生成的解描述了具有负质量内部的超紧凑流体球体。在这里，我们推导了一种新颖的 RSET 近似，它不依赖于降维，而是依赖于微分阶数的降低。这种近似也导致常规恒星超过布赫达尔极限。我们得出的结论是，这是与布尔韦尔真空相关的负能量的结果，对于足够致密的流体球体，使得米斯纳-夏普质量在球对称中心附近为负值。我们的分析提供了进一步的累积证据，表明量子真空极化能够产生新形式的恒星平衡，并且在 RSET 的不同解析近似中具有稳健的特性。