We provide an exhaustive analysis of the complete set of solutions of the equations of stellar equilibrium under semiclassical effects. As classical matter we use a perfect fluid of constant density; as the semiclassical source we use the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field in the Boulware vacuum (the only vacuum consistent with asymptotic flatness and staticity). For the RSET we use a regularized version of the Polyakov approximation. We present a complete catalogue of the semiclassical self-consistent solutions which incorporates regular as well as singular solutions, showing that the semiclassical corrections are highly relevant in scenarios of high compactness. Semiclassical corrections allow the existence of ultracompact equilibrium configurations which have bounded pressures and masses up to a central core of Planckian radius, precisely where the regularized Polyakov approximation is not accurate. Our analysis strongly suggests the absence of a Buchdahl limit in semiclasical gravity, while indicating that the regularized Polyakov approximation used here must be improved to describe equilibrium configurations of arbitrary compactness that remain regular at the center of spherical symmetry.

中文翻译：

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正则化 Polyakov 近似中的半经典常密度球体

我们对半经典效应下恒星平衡方程的完整解集进行了详尽的分析。作为经典物质，我们使用密度恒定的完美流体；作为半经典源，我们使用 Boulware 真空（唯一与渐近平坦性和静态一致的真空）中最小耦合的无质量标量场的重整化应力-能量张量 (RSET)。对于 RSET，我们使用 Polyakov 近似的正则化版本。我们提供了一个完整的半经典自洽解目录，其中包含正则解和奇异解，表明半经典修正在高度紧凑的场景中是高度相关的。半经典修正允许超紧凑平衡配置的存在，这些配置的压力和质量有界，直到普朗克半径的中心核心，而正则化的 Polyakov 近似不准确。我们的分析强烈表明半经典引力中不存在 Buchdahl 极限，同时表明必须改进此处使用的正则化 Polyakov 近似，以描述在球对称中心保持规则的任意紧凑性的平衡配置。