Stability of spherically symmetric solutions in modified theories of gravity
Stability of spherically symmetric solutions in modified theories of gravity
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DOI：
10.1103/physrevd.76.064002
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发表时间：
2007-03
影响因子：
5
通讯作者：
M. Seifert
中科院分区：
文献类型：
--
作者：
M. Seifert
近年来，人们提出了许多不同的引力理论，作为某些宇宙学问题的可能解决方案，或者作为可能但迄今未观察到的效应的玩具模型。然而，这些理论对恒星等结构稳定性的影响还没有得到充分的研究。我们使用我们的“广义变分原理，”在以前的工作中描述[M。D. Seifert和R. M. Wald，Phys.Rev.D75，084029（2007）]，以分析三种这样的替代理论中的静态球对称解对球对称扰动的稳定性：卡罗尔等人，的$f（R）$引力，Jacobson和Mattingly的"爱因斯坦-另一个理论"，以及Bekenstein的TeVeS理论。我们发现，在物质的存在下，$f（R）$引力是高度不稳定的;球对称弯曲真空Einstein-\aer {}其他背景的稳定性条件与平坦时空的线性化稳定性条件相同，只有一个例外;真空TeVeS理论的"动力学项"在弯曲背景中是不确定的，导致不稳定性。
In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such theories for the stability of structures such as stars have not been fully investigated. We use our ``generalized variational principle,'' described in a previous work [M. D. Seifert and R. M. Wald, Phys. Rev. D 75, 084029 (2007)], to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.'s $f(R)$ gravity, Jacobson and Mattingly's ``Einstein-\ae{}ther theory,'' and Bekenstein's TeVeS theory. We find that in the presence of matter, $f(R)$ gravity is highly unstable; that the stability conditions for spherically symmetric curved vacuum Einstein-\ae{}ther backgrounds are the same as those for linearized stability about flat spacetime, with one exceptional case; and that the ``kinetic terms'' of vacuum TeVeS theory are indefinite in a curved background, leading to an instability.