Timeline for How to choose a set of non-orthonormal basis vectors for the absolute space of a stationary and axisymmetric space-time in General Relativity?
Current License: CC BY-SA 4.0
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| Jun 9, 2022 at 11:48 | comment | added | Eric Arnéo Vespira Kengne | I'm working in the double null Foliation (2+2 splitting) and most of what I know come from: Helmut Friedrich (many of his works on the characteristic IVP in GR); Klainerman and Nicolo, the Evolution Problem in GR; R. K. Sachs, On the Characteristic Initial Value Problem in Gravitational Theory. So, the basis choice is intimately linked to the problem you want to solve... | |
| Jun 9, 2022 at 11:46 | comment | added | Eric Arnéo Vespira Kengne | For me, the choice of the basis is at the core of the problem. There are numerous basis type depending on the problem you want to solve. In general, the choice of the basis is dictated by the form of the splitting. For the 3+1 splitting, I don't know much about, especially, in the Kerr setting. But, I think that B. O'Neill, The Geometry of Kerr Black Holes can help you. On the other hand, still in the 3+1 splitting, there are many work on the search for the basis by means of Hyperbolic PDE by authors as: Choquet-Bruhat, O. Reula, Sarbach, J. York... | |
| Jun 9, 2022 at 10:36 | comment | added | Richard | Actually I am from Theoretical Physics background. So could you please suggest some references where I could find how to choose basis vectors for a given metric (particularly the Kerr metric)? That will be very helpful. | |
| Jun 9, 2022 at 10:31 | comment | added | Richard | Thank you for the answer. | |
| Jun 9, 2022 at 10:08 | comment | added | Eric Arnéo Vespira Kengne | On the other hand, I think that there are good books on the subject that can help you. Perhaps you should begin by look more closely at the differential geometry level... | |
| Jun 9, 2022 at 10:03 | comment | added | Eric Arnéo Vespira Kengne | That says, it depends on the problem you are trying to solve. The problem of the perturbation and stability of the Kerr spacetime (cf the work of Klainerman, Rodnianski, Szeftel,...), and in large, the problem of the perturbation and stability of a given class of manifold, is a fascinating and challenging one, putting together several domains of Mathematic. | |
| Jun 9, 2022 at 9:53 | history | answered | Eric Arnéo Vespira Kengne | CC BY-SA 4.0 |