Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior
Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior
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恒星塌陷的规范不变和坐标无关的扰动 I：内部
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发表时间：
1999
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影响因子：
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通讯作者：
Carsten Gundlach
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文献类型：
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作者：
Carsten Gundlach
在天体物理学感兴趣的许多情况下，球对称是广义相对论中模拟星星的一个很好的近似。超越这种近似的一个可能的方向是允许任意的线性扰动，以便在图像中加入引力辐射。这引入了新的物理学，因为星星现在可以通过引力辐射失去能量，以及一个新的观察窗口，因为这种引力辐射可以被检测到。引力波探测器预计将在几年内首次以必要的灵敏度运行，目前正在进行大量工作，以模拟可能的引力辐射源。如果我们允许球形背景解依赖于时间，就像我们在这里所做的那样，我们可以模拟例如（稍微非球形的）超新星爆炸中发出的引力辐射。这里我们假设物质是一种理想流体，由状态方程p = p（ρ，s）描述，其中p是压强，ρ是总能量密度，s是每个粒子的熵。作为理想流体近似的结果，s被假定为沿沿着粒子轨迹的常数，也就是说，我们忽略了熵产生的可能来源：热通量、粘性和化学反应。我们还假设只有一种流体存在。对于超新星来说，近似球对称和理想流体物质的假设都可能是不现实的。有些超新星现在被证实是相当非球形的，中微子输运被认为起着重要的作用。在这里，我们专注于给一个干净的数学描述的一个几乎球形的完美流体，相信这种近似将是有用的，在某些应用中。关于静态球形星星的线性扰动有很多论文，特别是Thorne及其同事的一系列论文[1-6]，Cunningham、Price和Moncrief的另一系列论文[7]，以及Ipser和Price的一篇论文[8]。球对称性允许人们将扰动解耦为球谐函数。由于背景的时间无关性，可以考虑形式为exp（iωt）f（r）的扰动模式并求解常微分方程
In many situations of astrophysical interest, spherical symmetry is a good approximation for modeling a star in general relativity. One possible direction in which to go beyond that approximation is to allow for arbitrary linear perturbations, in order to add gravitational radiation to the picture. This introduces new physics, as the star can now lose energy through gravitational radiation, and a new window of observation, as this gravitational radiation can be detected. Gravitational wave detectors are expected to operate at the necessary sensitivity for the first time within a few years, and a large effort is under way to model possible sources of gravitational radiation. If one allows the spherical background solution to be time-dependent, as we shall do here, one can model for example the gravitational radiation emitted in a (slightly nonspherical) supernova explosion. We assume here that the matter content is a perfect fluid described by an equation of state p = p(ρ, s) where p is the pressure, ρ the total energy density, and s the entropy per particle. As a consequence of the perfect fluid approximation, s is assumed to be constant along particle trajectories, that is, we neglect the possible sources of entropy generation: heat fluxes, viscosity and chemical reactions. We also assume that there is only a single fluid present. Both the assumptions of approximate spherical symmetry and perfect fluid matter may be unrealistic for supernovae. Some supernovae are now conjectured to be quite nonspherical, and neutrino transport is believed to play an important role. Here we concentrate on giving a clean mathematical description of an almost spherical perfect fluid, in the belief that this approximation will be useful in some applications. There are many papers on the linear perturbations of a static spherical star, notably a series of papers by Thorne and coworkers [1–6], another series by Cunningham, Price and Moncrief [7], and a paper by Ipser and Price [8]. The spherical symmetry allows one to decouple the perturbations into spherical harmonics. Because of the timeindependence of the background, one can consider perturbation modes of the form exp(iωt)f(r) and solve an ODE