Explicit solution of Sylvester and Lyapunov equations

Rotella, R.; Borne, Pierre

doi:10.1016/0378-4754(89)90163-8

Cited by 8 publications

(2 citation statements)

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“…5 The Sylvester equation (B. 19) has a unique solution for every C, if and only if A and ´B have no common eigenvalues [55]. In our case…”

Section: B3 the Dynamics Of The Bimetric Lorentz Framementioning

confidence: 78%

The mean gauges in bimetric relativity

Torsello

2019

Class. Quantum Grav.

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The choice of gauge in numerical relativity is crucial in avoiding coordinate and curvature singularities. In addition, the gauge can affect the well-posedness of the system. In this work, we consider the mean gauges, established with respect to the geometric mean metric h :" g`g´1f˘1 {2 in bimetric relativity. We consider three gauge conditions widely used in numerical relativity, and compute them with respect to the geometric mean: The 1+log gauge condition and the maximal slicing for the lapse function of h, and the Γdriver gauge condition for the shift vector of h. In addition, in the bimetric covariant BSSN formalism, there are other arbitrary choices to be made before evolving the system. We show that it is possible to make them by using the geometric mean metric, which is determined dynamically by the system, rather than using an arbitrary external metric, as in general relativity. These choices represent opportunities to recast the system in a well-posed form.

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