Signature Change on the Brane

Abstract

We explore the possibility of having a good description of classical signature change in the brane scenario.PACS Numbers: 04.50.+h, 98.80.Cq, 11.10.Kk, 04.20.Gz.The aim of this letter is to show, in simple terms, that a natural scenario for the change of signature in the physical spacetime is provided by the brane-world models [1][2][3] (see also [4][5][6] for an exhaustive list of references) or, in general, by every higher-dimensional theory [7] which may contain domain walls and/or branes.The main idea behind our proposal is that d-branes are nothing but timelike (d + 1)-surfaces in a higherdimensional spacetime (the bulk) [8]. However, nothing prevents the possibility of having perfectly regular branes which change its character from (say) spacelike to timelike, or which are partly null, or even more complicated possibilities. The first case corresponds to a signaturechanging brane. The interesting property is that both the bulk and the brane can be regular everywhere even though the change of signature may appear as a dramatical event when seen from within the brane. Notice that the signature in the bulk is left unchanged, so that our work differs significantly from other recent studies [9]. In our proposal, the study of the change of signature becomes the simple geometrical analysis of imbedded submanifolds in the bulk: a well-posed mathematical problem without pathologies. It is remarkable that many of the traditional ad hoc assumptions concerning signature change [10] are shown to become pure necessary conditions in the brane case, which indirectly proves the plausibility of our idea and makes it worth exploring it, possibly sheding some light into the "signature-change controversy" [10].Whether a signature change occurred in our effective spacetime is debatable, and several independent works have considered this possibility [12,11]. From a classical viewpoint, a signature change may serve to avoid the singularities of general relativity [13], such as the big-bang, which might be replaced by a Euclidean region prior to the birth of time. Signature change has also been vindicated as an effective classical description of both the no-boundary proposal [14] and the quantum tunneling [15] approach for the prescription of the Universe's wave function in quantum cosmology. In general, every process which can be studied by resorting to the "imaginary time", e.g. [14], can be also analyzed by means of change of the signature. All these possibilities could be naturally considered in our proposal.As a matter of concreteness we will focus on the recent models based on a single 3-brane embedded into a five-dimensional Lorentzian manifold with a noncompact fifth dimension [3] (a more geometrically focused review of this model can be found in [5]) and [16,17]. We can think of such a brane model as consisting of two Lorenztian regions joined together across corresponding smooth timelike boundaries. The matching between the two manifolds can be performed as long as the induced metrics on the two boundaries are isometric....

Axially symmetric equilibrium regions of Friedmann–Lemaître–Robertson–Walker universes

“…The existence of these so-called rigging vector fields is not ensured when the boundaries have null points in some situations [16]. Now, the Riemann tensor in (V, g) can be defined in a distributional form [14].…”

Quintessence and effective RN de Sitter brane geometries

“…Since closed strings are tangential to a D p -brane, Einstein a e-mail: kppandey@physics.du.ac.in b e-mail: abhishek151983@gmail.com c e-mail: sunita@physics.du.ac.in d e-mail: richa.phy@du.ac.in e e-mail: skkar@physics.du.ac.in gravity is believed to decouple from a D p -brane world volume [2]. Nevertheless a non-linear U (1) gauge field is well known to describe an effective open string metric on a D pbrane and leads to a number of near horizon geometries [3][4][5][6][7][8][9][10][11][12][13][14][15]. In fact a constant Neveu-Schwarz (NS) two form background in an open string theory, in combination with an electromagnetic field, forms a gauge invariant field strength which governs the non-linear U (1) charge on a D p -brane.…”

“…For instance, we consider a dynamical two form in a U (1) gauge theory on a D 4 -brane in the presence of a nontrivial background metric sourced by the global modes of NS two form in the open string bulk. The background metric for a D 4 -brane gauge dynamics presumably describes a hiddenD 4 -brane in the formalism. A priori, the D 4 -brane vacuum may be seen to be governed by an effective black hole essentially sourced by the global modes of a NS two form [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Multi-dimensional classical and quantum cosmology: exact solutions, signature transition and stabilization

“…Also, in studying the quantum cosmology of such models the question arises as to should one consider the bulk first and the creation of the brane later or should they both come into being at the same time. For a more detailed discussion of the above issues, the reader is referred to [5].…”