Brane-Localized Gravity by Philip D. Mannheim

By Philip D. Mannheim

This well timed and worthwhile publication presents an in depth pedagogical creation and remedy of the brane-localized gravity application of Randall and Sundrum, within which gravitational indications may be able to localize round our 4-dimensional global within the occasion that it's a brane embedded in an infinitely-sized, greater dimensional anti-de Sitter bulk house. a very self-contained improvement of the fabric wanted for brane-world reports is equipped for either scholars and employees within the box, with an important quantity of the cloth being formerly unpublished. specific awareness is given to matters now not regularly handled within the brane-world literature, equivalent to the completeness of tensor gravitational fluctuation modes, the causality of brane-world propagators, and the prestige of the massless graviton fluctuation mode in brane worlds within which it's not normalizable.

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However, ~ of more interest to the brane world is that in certain circumstances it is also possible for the brane geometry to readjust into some new static solution, with this being found to be the case for both de Sitter (dS4) and anti-de Sitter (AdS4) branes, cases we will analyze in detail below in Chapter 8. 2 The embedded sheet Riemann tensor and its weak gravity limit Even though the static 2-brane model discussed above is one in which the bulk is devoid of matter fields, it does not follow that in it the bulk is flat.

2plz1/8 cyz where cy is arbitrary. 2That this model possessed no static solution in the particular case of p = - p was shown in [Vilenkin (1981)]. 12) we see that the junction conditions also require p = -p/4. As such, our analysis shows that it is only possible to obtain a static solution to this model if p = - p / 4 , to thus require a quite unusual form of matter on the brane, viz. matter with negative pressure, with such matter (more generally with equation of state p = wp where w is some negative constant) being thought to potentially be of relevance to cosmology [Caldwell, Dave and Steinhardt (1998)] where it then goes under the generic name of quintessence.

For instance, for the typical case of an initial region with compact support at w = 0, any new information originating from the boundary a t w = -cc would reach the forward lightcone of the initial region at a time t = 1/2b (see Fig. 1)). And even in cases where no such new information does in fact come in, in determining the late time response at w = 0 to an initial disturbance at w = 0, one still has to allow for the fact that the null signal which originates from w = 0 at t = 0 and which arrives at w = -cc at a time t = l / b can then reflect back off the boundary and return t o w = 0 at a time t = 2 / b .

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