The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background
The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background
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闵可夫斯基背景下线性化引力约束的代数双曲线方法
DOI：
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发表时间：
2017
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通讯作者：
J. Winicour
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文献类型：
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作者：
J. Winicour
一个代数双曲方法求解哈密顿量和动量约束最近已被证明是适定的一般非线性扰动的初始数据的Schwarzschild黑洞。这是一种新的方法来解决爱因斯坦方程的约束，不涉及椭圆方程，并有潜在的重要性，为建设的双黑洞数据。为了阐明这种方法的基础，我们考虑其应用，以获得线性化的扰动Minkowski空间的约束的解决方案。在这种情况下，我们发现令人惊讶的结果，有没有合适的柯西超曲面在闵可夫斯基空间中的线性代数双曲约束问题是适定的。
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.