arXiv 2005.141142020-05gr-qcastro-ph.HE

通过非线性扰动的涌现引力

Emergent gravity through non-linear perturbation

Karan Fernandes, Susovan Maity, Tapas K. Das

备注：: The analysis concerned the specific case of Bondi flows, but holds in a more general setting. The revised general analysis including the high and low frequency perturbation results lie beyond the scope of a replacement

摘要：

到目前为止，文献中所有可用的模拟重力模型都只处理通过跨音速流体的线性扰动出现的声学几何。它从来没有被调查是否模拟重力现象是唯一的线性扰动的结果，或者更确切地说，一个非均匀的，无粘的和无旋流体的任意扰动的一般属性。在目前的工作中，在文献中的第一次，我们证明，声学时空可能是通过高阶非线性扰动形成的，从而建立模拟重力现象比以前认为的更普遍。我们认为球形吸积天体物理系统作为一个自然的经典模拟重力模型，并发展了一种形式主义，以调查非线性扰动的吸积流到任意顺序。我们的迭代方法涉及一组耦合方程的质量吸积率和密度的流体。特别是，我们证明了波动方程的质量吸积率涉及一个声学度规，可以微扰构造的所有订单。数值求解了跨音速Bondi流动的耦合方程组。这种分析使用的边界条件设置为原来的未扰动值，与时间依赖的质量吸积率扰动采取指数阻尼。扰动的解决方案表明，二阶和更高的扰动度规一般导致原来的声学地平线振荡和改变的大小。我们详细解释了这种现象及其对吸积流的非线性扰动的影响。

英文摘要：

As of now, all analogue gravity models available in the literature deal with the emergence of an acoustic geometry through linear perturbations of transonic fluids only. It has never been investigated whether the analogue gravity phenomena is solely a consequence of linear perturbations, or rather a generic property of arbitrary perturbations of inhomogeneous, inviscid and irrotational fluids. In the present work, for the first time in the literature, we demonstrate that acoustic spacetimes may be formed through higher order non-linear perturbations, and thus establish that analogue gravity phenomena is rather more general than what was thought before. We consider spherically accreting astrophysical systems as a natural classical analogue gravity model, and develop a formalism to investigate non-linear perturbations of such accretion flows to arbitrary order. Our iterative approach involves a coupled set of equations for the mass accretion rate and the density of the fluid. In particular, we demonstrate that the wave equation for the mass accretion rate involves an acoustic metric which can be perturbatively constructed to all orders. We numerically solve the coupled equations about the leading transonic Bondi flow solution. This analysis uses boundary conditions set to the original unperturbed values, with the time dependence of the mass accretion rate perturbation taken to be exponentially damped. The perturbed solutions indicate that second order and higher perturbations of the metric generically cause the original acoustic horizon to oscillate and change in size. We explain this phenomenon in detail and its implications on non-linear perturbations of accretion flows in general.

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摘要：

英文摘要：

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