TeVeS gets caught on caustics
TeVeS gets caught on caustics
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DOI：
10.1103/physrevd.78.044034
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发表时间：
2008-08-01
影响因子：
5
通讯作者：
Withers, Benjamin
中科院分区：
文献类型：
--
作者：
Contaldi, Carlo R.;Wiseman, Toby;Withers, Benjamin
TeVeS使用具有类时单位范数约束的动态向量场来指定优选的局部框架。当物质在这个框架中缓慢运动时，即所谓的准静态状态，就会产生修正的牛顿动力学。具有这种矢量的理论（如爱因斯坦-以太）倾向于矢量动力学形成奇点，使它们的经典演化成为问题。在这里，我们分析了TeVeS中的向量在各种情况下的动态。我们开始分析表明，真空解决方案TeVeS形式下的一大类物理合理的初始扰动焦散奇点。这表明TeVeS的经典演化在没有物质的情况下似乎是有问题的。然后，我们通过研究黑洞的解决方案来考虑问题。我们发现大类新的黑洞解决方案与静态几何形状，其中由矢量场产生的曲线被吸引到黑洞，并可能形成焦散。我们继续考虑充分的动力学与物质的数值模拟，假设球对称，标量的引力坍缩，和一个最初几乎静态的玻色子星星的演变。我们发现，在这两种情况下，我们的初始数据的演变，使矢量场发展焦散奇点的时间尺度上的顺序的重力下降时间。在表明奇点的形成是通用的，无论有没有物质，贝肯斯坦的TeVeS的原始配方出现动态问题。我们认为，通过修改矢量场动力学项更一般的形式所使用的爱因斯坦-乙醚，这个问题可能会被避免。
TeVeS uses a dynamical vector field with timelike unit-norm constraint to specify a preferred local frame. When matter moves slowly in this frame-the so-called quasistatic regime-modified Newtonian dynamics results. Theories with such vectors (Such as Einstein-Aether) are prone to the vector dynamics forming singularities that render their classical evolution problematic. Here, we analyze the dynamics of the vector in TeVeS in various situations. We begin by analytically showing that the vacuum solution of TeVeS forms caustic singularities under a large class of physically reasonably initial perturbations. This shows the classical evolution of TeVeS appears problematic in the absence of matter. We then consider matter by investigating black hole solutions. We find large classes of new black hole solutions with static geometries, where the curves generated by the vector field are attracted to the black hole and may form caustics. We go on to consider the full dynamics with matter by numerically simulating, assuming spherical symmetry, the gravitational collapse of a scalar, and the evolution of an initially nearly static boson star. We find that in both cases our initial data evolves so that the vector field develops caustic singularities on a time scale of order the gravitational in-fall time. Having shown singularity formation is generic with or without matter, Bekenstein's original formulation of TeVeS appears dynamically problematic. We argue that by modifying the vector field kinetic terms to the more general form used by Einstein-Aether, this problem may be avoided.