arXiv:gr-qc/0611124v2 4 Apr 2007 The Linear Stability of Lorentzian Space-Time Asher Yahalom a,b a Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom b College of Judea and Samaria, Ariel 44284, Israel e-mail: asya@yosh.ac.il February 7, 2008 Abstract It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type η μν = diag (1, -1, -1, -1) this is usually presented as an independent axiom of the theory, which can not be deduced from other assumptions. In this work we show that the above assertion is a consequence of a standard linear stability analysis of the Einstein equations and need not be assumed. PACS: 03.30.+p, 04.20.Cv keywords: General Relativity; Stability of Solutions; 1 Introduction It is well known that our daily space-time is approximately of Lorentz (Minkowski) type that is, it possess the metric η µν = diag (1, -1, -1, -1). The above statement is taken as one of the central assumptions of the theory of special relativity and has been supported by numerous experiments. Some may be satisfied by the overwhelming evidence that space-time is Lorentzian and see no need to investigate this issue any further, others including the author of this paper see it as a profound mystery of nature and ask why should it be so? Further more it is assumed in the general theory of relativity that any space-time is locally of the type η µν = diag (1, -1, -1, -1), although it 1