AI 中文总结
研究四维非投影霍拉瓦引力中静态恒星精确解，考虑z = 3霍拉瓦引力中黑洞解为恒星外部时空，得到不可压缩恒星精确解及相关结果，发现UCOs和负质量恒星，还证明了布赫达尔定理。
AI 中文摘要
本文研究了四维非投影霍拉瓦引力中静态恒星的一个特定精确解。通过z>1的各向异性缩放摒弃爱因斯坦时空平等对待，该模型被提出作为无鬼问题的可重整化引力模型。考虑z = 3霍拉瓦引力中球对称静态黑洞解作为恒星外部时空，得到了具有任意宇宙学常数和各向同性压力且λ = 1时不可压缩（均匀密度）静态恒星的精确解，其中伯克霍夫定理成立。对于宇宙学常数为零的情况，得到了均匀密度恒星最大紧致性的修正布赫达尔界，范围从4/9到1。还发现紧致性C>1的超紧致物体（UCOs）在存在负压时也存在，且令人惊讶地满足所有四个标准能量条件，包括质量高于极端黑洞质量的正则（非奇异）黑洞解。此外，还发现了违反所有标准能量条件的正压负质量恒星。最后，证明了非投影霍拉瓦引力中的布赫达尔定理，证明使用了平均密度的权重单调性条件、伯克霍夫定理以及平均密度非增的通常假设。
英文摘要
I study a particular exact solution for static stars in four-dimensional non-projectable Horava gravity, which has been proposed as a renormalizable gravity model without the ghost problem by abandoning Einstein's equal-footing treatment of space and time through anisotropic scaling with z > 1. Considering the spherically symmetric static black-hole solutions in z = 3 Horava gravity as the exterior spacetimes of stars, I obtain an exact solution for incompressible (i.e., uniform-density) static stars with an arbitrary cosmological constant and isotropic pressure, and lambda=1, in which Birkhoff's theorem holds. For a vanishing cosmological constant, I obtain a modified Buchdahl bound on the maximum compactness for uniform-density stars, which ranges from 4/9 to 1. By contrast, I find that Ultra-Compact Objects (UCOs) with compactness C > 1 also exist with negative pressure while, surprisingly, satisfying all four standard energy conditions. UCOs include the regular (non-singular) black-hole solutions with masses above the extremal black-hole mass. In these solutions, the matter is localized at the timelike core region bounded by the inner horizon, while their exterior metrics are unaffected by the core matter and identical to the corresponding vacuum Horava black-hole solutions. These long-sought regular black-hole solutions are essential manifestations of Birkhoff's theorem in Horava gravity. I also find negative-mass stars with positive pressure that violate all standard energy conditions. Finally, I prove Buchdahl's theorem in non-projectable Horava gravity. The proof uses a weight-monotonicity condition on the average density and Birkhoff's theorem, together with the usual assumption that average density is non-increasing.
Comments21 pages, 5 figures, 1 table
