Tidal deformation of a slowly rotating material body: External metric
Tidal deformation of a slowly rotating material body: External metric
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DOI：
10.1103/physrevd.91.104018
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发表时间：
2015-03
影响因子：
5
通讯作者：
P. Landry;E. Poisson
中科院分区：
文献类型：
--
作者：
P. Landry;E. Poisson
在广义相对论中，我们构造了一个缓慢旋转、潮汐变形的物质体的外度规。作用在身体上的潮汐力被假定为弱的，并随时间缓慢变化，和度量获得作为一个扰动的背景度量，描述了一个孤立的，缓慢旋转的身体的外部几何形状。潮汐环境是一般的，其特征在于两个无迹潮汐矩E_{ab}和B_{ab}，并且该物体的特征在于其质量M、半径R和无量纲角动量矢量\chi^a << 1。摄动解释了\chi^a和潮汐矩之间的所有耦合。天体对潮汐场的引力响应部分由我们熟悉的引力勒夫数K^{el}_2和K^{mag}_2来度量，但我们发现天体自转与潮汐环境之间的耦合需要引入四个新的量，我们将其命名为自转-潮汐勒夫数。所有这些勒夫数在通常意义上的微扰论中都是规范不变的，当物体是黑洞时，它们都消失了。
We construct the external metric of a slowly rotating, tidally deformed material body in general relativity. The tidal forces acting on the body are assumed to be weak and to vary slowly with time, and the metric is obtained as a perturbation of a background metric that describes the external geometry of an isolated, slowly rotating body. The tidal environment is generic and characterized by two symmetric-tracefree tidal moments E_{ab} and B_{ab}, and the body is characterized by its mass M, its radius R, and a dimensionless angular-momentum vector \chi^a << 1. The perturbation accounts for all couplings between \chi^a and the tidal moments. The body's gravitational response to the applied tidal field is measured in part by the familiar gravitational Love numbers K^{el}_2 and K^{mag}_2, but we find that the coupling between the body's rotation and the tidal environment requires the introduction of four new quantities, which we designate as rotational-tidal Love numbers. All these Love numbers are gauge invariant in the usual sense of perturbation theory, and all vanish when the body is a black hole.