最近得到的特殊Buchdahl启发度规[Phys. Rev. D 107, 104008 (2023)]描述了纯Ricci平方引力中的渐近平坦时空。该度规依赖于一个新的高阶导数特征参数（Buchdahl参数）$\tilde{k}$，当$\tilde{k}=0$时退化为Schwarzschild度规。对于$\tilde{k}\in(-1,0)$的情形，已有研究表明它描述了一个可穿越的Morris-Thorne-Buchdahl (MTB)虫洞[Eur. Phys. J. C 83, 626 (2023)]，其中弱能量条件被形式上违反。本文简要回顾了特殊Buchdahl启发度规，重点讨论$ζ-$Kruskal-Szekeres (KS)图的构造以及虫洞出现的条件。有趣的是，MTB虫洞结构似乎允许闭合类时曲线（CTCs）的形成。更具体地说，一条CTC横跨虫洞喉部，由位于$ζ-$KS图相反象限的两段组成。因此，闭合类时回路两次穿过虫洞喉部，导致CTC上的（类时）旅行者经历两次时间方向反转。构造CTC的关键在于将$ζ-$KS图中虫洞喉部上的任意一对对径点$(T,X)$和$(-T,-X)$识别为同一时空事件。值得注意的是，Brans-Dicke引力中的Campanelli-Lousto度规已知支持双向可穿越虫洞，本文所呈现的CTC形成机制同样适用于Campanelli-Lousto解。
英文摘要：
The recently obtained $\textit{special}$ Buchdahl-inspired metric [Phys. Rev. D 107, 104008 (2023)] describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter $\tilde{k}$ of higher-derivative characteristic, and reduces to the Schwarzschild metric, for $\tilde{k}=0$. For the case $\tilde{k}\in(-1,0)$, it was shown that it describes a traversable Morris-Thorne-Buchdahl (MTB) wormhole [Eur. Phys. J. C 83, 626 (2023)], where the weak energy condition is formally violated. In this paper, we briefly review the $\textit{special}$ Buchdahl-inspired metric, with focuses on the construction of $ζ-$Kruskal-Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the $ζ-$KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing $\textit{two}$ reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points $(T,X)$ and $(-T,-X)$ $\textit{on the wormhole throat}$ in the $ζ-$KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli-Lousto metric in Brans-Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli-Lousto solution.
The semiclassical approximation takes into account the gravitational contribution of zero-point energies. We model this contribution via the renormalized stress-energy tensor (RSET) of a massless scalar field, which we compute in a cutoff-regularized version of the Polyakov approximation. When the field is in the Boulware vacuum state (the natural vacuum for stellar geometries), the RSET works in favor of violating the Buchdahl compactness limit. We review the family of classical constant-density stellar solutions, paying particular attention to the notion of criticality -- the presence of off…
We generalise the Buchdahl-Bondi limit for the case of static, spherically symmetric, relativistic compact stars immersed in Schwarzschild vacuum in f(R)-theory of gravity, subject to very generic regularity, thermodynamic stability and matching conditions. Similar to the case of general relativity, our result is model independent and remains true for any physically realistic equation of state of standard stellar matter. We show that an extra-massive stable star can exist in these theories, with surface redshift larger than 2, which is forbidden in general relativity. This result gives a novel…
In d+1 dimensions we solve the equations of motion for the case of gravity minimally or conformally coupled to a scalar field. For the minimally coupled system the equations can either be solved directly or by transforming vacuum solutions, as shown before in 3+1 dimensions by Buchdahl. In d+1 dimensions the solutions have been previously found directly by Xanthopoulos and Zannias. Here we first rederive these earlier results, and then extend Buchdahl's method of transforming vacuum solutions to d+1 dimensions. We also review the conformal coupling case, in which d+1 dimensional solutions can …
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We explore a curious but simple variant of the Bronnikov-Ellis (BE) wormhole spacetime with a specific `red-shift function' (i.e. $g_{00}$) in the line element. The matter required to support such a geometry violates the local Null Energy Condition (NEC) only around the throat and the global Averaged Null Energy Condition (ANEC) integral along radial null geodesics may be adjusted to arbitrarily small negative values, using metric parameters. Properties of the line element manifest in the metric functions, curvature and the required matter stress energy are delineated. Further, exact null and …
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We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from curvature singularities and an $4D$ extension of the Misner space in curved spacetime with identical causality violating properties.
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We reconsider the widely held view that the Mannheim--Kazanas (MK) vacuum solution for a static, spherically-symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those observed in galaxies, without the need for dark matter. This prediction assumes that test particles have fixed rest mass and follow timelike geodesics in the MK metric in the vacuum region exterior to a spherically-symmetric representation of the galactic mass distribution. Such geodesics are not conformally invariant, however, which leads to an apparent discrepancy with the analogous calculation per…
