[工程科技]GoursatsProblemandtheHolographicPrinciple.pdfVIP

IFT-UAM/CSIC-04-01 hep-th/0401220 Goursat’s Problem and the Holographic Principle. ´ Enrique Alvarez, Jorge Conde and Lorenzo Hern´andez 4 0 0 2 Instituto de F´ısica Te´orica UAM/CSIC, C-XVI, and Departamento de F´ısica Te´orica, n a C-XI, J 8 Universidad Aut´onoma de Madrid E-28049-Madrid, Spain 2 1 v 0 2 Abstract 2 1 0 The whole idea of holography as put forward by Gerard ’t Hooft assumes that 4 0 / data on a boundary determine physics in the volume. This corresponds to h t- a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) p e problem in the lorentzian setting. Is this last aspect of the problem that is h : v explored here for Ricci flat spaces with vanishing cosmological constant. i X r a 1 1 Introduction Ever since its inception, the whole idea of holography (cf. [22] [21]) stand as one of the most original and mysterious suggestions ever made in fundamental physics. From a certain abstract viewpoint, it certainly includes at least two facts . The first one is that it should be possible to recover volume information on the physical fields from data given on a certain surface, namely the boundary of the volume. That is, fields in the volume do not obey an ordinary Cauchy problem (for which also derivatives of the field at the boundary would also be needed), but rather a degenerate one, in which the derivative cannot be imposed independently. This happens both for timelike and null initial surfaces.