标题： 相对论和牛顿核壳模型：解析和数值结果 显示英文标题

标题： Relativistic and Newtonian core-shell models: analytical and numerical results

摘要： 我们对最近提出的描述被物质壳层包围的黑洞或中子星的牛顿和相对论核心-壳模型进行了详细分析，并在开创性意义上也涉及了星系、超新星和恒星残骸，因为许多这样的天体周围存在大质量的类似壳层结构，而且也有证据表明许多星系核隐藏着黑洞。 我们讨论了这些模型在黑洞视界处的解析性以及完全消除圆锥奇点的唯一性。 其次，我们研究了赤道平面对称性是否存在对轨道混沌行为所起的作用，这与在星系建模中普遍接受对称性作为默认假设的情况形成对比。 我们还比较了如果将真正的中心黑洞替换为牛顿中心质量时的相关效应。 数值结果是：1- 在牛顿和相对论核心-壳模型中，赤道平面反射对称性的破坏会i) 显著增强反射对称扁球壳模型中轨道的混沌性，ii) 同时显著抑制反射对称长球壳模型中混沌的发生。 特别是，在长球情况下，缺乏反射对称性为相空间提供了一个稳健的规则轨道家族，而在更高能量下通常找不到这种轨道。 2- 相对论情况下的混沌区域相对范围（即具有真正中心黑洞的情况）明显大于相应的牛顿情况（仅具有$-1/r$中心势）。 显示英文摘要

摘要： We make a detailed analysis of Newtonian as well as relativistic core-shell models recently proposed to describe a black hole or neutron star surrounded by shells of matter, and in a seminal sense also galaxies, supernovae and star remnants since there are massive shell-like structures surrounding many of them and also evidences for many galactic nuclei hiding black holes. We discuss the unicity of the models in relation to their analyticity at the black hole horizon and also to the full elimination of conical singularities. Secondly, we study the role played by the presence/lack of discrete reflection symmetries about equatorial planes in the chaotic behavior of the orbits, which is to be contrasted with the almost universal acceptance of reflection symmetries as default assumptions in galactic modeling. We also compare the related effects if we change a true central black hole by a Newtonian central mass. The numerical findings are: 1- The breakdown of the reflection symmetry about the equatorial plane in both Newtonian and relativistic core-shell models does i) enhance in a significant way the chaoticity of orbits in reflection symmetric oblate shell models and ii) inhibit significantly also the occurrence of chaos in reflection symmetric prolate shell models. In particular, in the prolate case the lack of the reflection symmetry provides the phase space with a robust family of regular orbits that is otherwise not found at higher energies. 2- The relative extents of the chaotic regions in the relativistic cases (i. e. with a true central black hole) are significantly larger than in the corresponding Newtonian ones (which have just a $-1/r$ central potential).