2000 膜世界的黑洞-精品文档资料整理.pdf
《2000 膜世界的黑洞-精品文档资料整理.pdf》由会员分享,可在线阅读,更多相关《2000 膜世界的黑洞-精品文档资料整理.pdf(10页珍藏版)》请在淘文阁 - 分享文档赚钱的网站上搜索。
1、arXiv:hep-th/9909205v2 21 Oct 1999Brane-World Black HolesA. Chamblin, S.W. Hawkingand H.S. ReallDAMTPUniversity of CambridgeSilver Street, Cambridge CB3 9EW, United Kingdom.Preprint DAMTP-1999-13329 September 1999AbstractGravitational collapse of matter trapped on a brane will produce a black hole o
2、n the brane. Wediscuss such black holes in the models of Randall and Sundrum where our universe is viewed asa domain wall in five dimensional anti-de Sitter space. We present evidence that a non-rotatinguncharged black hole on the domain wall is described by a “black cigar” solution in five dimensio
3、ns.1IntroductionThere has been much recent interest in the idea that our universe may be a brane embedded in somehigher dimensional space. It has been shown that the hierarchy problem can be solved if the higherdimensional Planck scale is low and the extra dimensions large 1, 2. An alternative solut
4、ion, proposedby Randall and Sundrum (RS), assumes that our universe is a negative tension domain wall separatedfrom a positive tension wall by a slab of anti-de Sitter (AdS) space 3. This does not require a largeextra dimension: the hierarchy problem is solved by the special properties of AdS. The d
5、rawback withthis model is the necessity of a negative tension object.In further work 4, RS suggested that it is possible to have an infinite extra dimension. In thismodel, we live on a positive tension domain wall inside anti-de Sitter space. There is a bound stateof the graviton confined to the wal
6、l as well as a continuum of Kaluza-Klein (KK) states. For non-relativistic processes on the wall, the bound state dominates over the KK states to give an inversesquare law if the AdS radius is sufficiently small. It appears therefore that four dimensional gravityis recovered on the domain wall.This
7、conclusion was based on perturbative calculations for zerothickness walls. Supergravity domain walls of finite thickness have recently been considered 5, 6, 7and a non-perturbative proof that the bound state exists for such walls was given in 8. It is importantto examine other non-perturbative gravi
8、tational effects in this scenario to see whether the predictionsof four dimensional general relativity are recovered on the domain wall.If matter trapped on a brane undergoes gravitational collapse then a black hole will form. Sucha black hole will have a horizon that extends into the dimensions tra
9、nsverse to the brane: it will bea higher dimensional object. Phenomenological properties of such black holes have been discussed inemail: H.A. Chamblindamtp.cam.ac.ukemail: S.W.Hawkingdamtp.cam.ac.ukemail: H.S.Realldamtp.cam.ac.uk19 for models with large extra dimensions. In this paper we discuss bl
10、ack holes in the RS models. Anatural candidate for such a hole is the Schwarzschild-AdS solution, describing a black hole localizedin the fifth dimension. We show in the Appendix that it is not possible to intersect such a hole witha vacuum domain wall so it is unlikely that it could be the final st
11、ate of gravitational collapse on thebrane. A second possibility is that what looks like a black hole on the brane is actually a black stringin the higher dimensional space. We give a simple solution describing such a string. The inducedmetric on the domain wall is simply Schwarzschild, as it has to
12、be if four dimensional general relativity(and therefore Birkhoffs theorem) are recovered on the wall. This means that the usual astrophysicalproperties of black holes (e.g. perihelion precession, light bending etc.) are recovered in this scenario.We find that the AdS horizon is singular for this bla
13、ck string solution. This is signalled by scalarcurvature invariants diverging if one approaches the horizon along the axis of the string. If one ap-proaches the horizon in a different direction then no scalar curvature invariant diverges. However, in aframe parallelly propagated along a timelike geo
14、desic, some curvature components do diverge. Further-more, the black string is unstable near the AdS horizon - this is the Gregory-Laflamme instability 10.However, the solution is stable far from the AdS horizon. We will argue that our solution evolves to a“black cigar” solution describing an object
15、 that looks like the black string far from the AdS horizon(so the metric on the domain wall is Schwarzschild) but has a horizon that closes offbefore reachingthe AdS horizon. In fact, we conjecture that this black cigar solution is the unique stable vacuumsolution in five dimensions which describes
16、the endpoint of gravitational collapse on the brane. Wesuspect that the AdS horizon will be non-singular for the cigar solution.2The Randall-Sundrum modelsBoth models considered by RS use five dimensional AdS. In horospherical coordinates the metric isds2= e2y/lijdxidxj+ dy2(2.1)where is the four di
17、mensional Minkowski metric and l the AdS radius. The global structure ofAdS is shown in figure 1. Horospherical coordinates break down at the horizon y = .In their first model 3, RS slice AdS along the horospheres at y = 0 and y = yc 0, retain theportion 0 y ycand assume Z2reflection symmetry at eac
18、h boundary plane. This gives a jump inextrinsic curvature at these planes, yielding two domain walls of equal and opposite tension = 62l(2.2)where 2= 8G and G is the five dimensional Newton constant. The wall at y = 0 has positive tensionand the wall at y = ychas negative tension. Mass scales on the
19、 negative tension wall are exponentiallysuppressed relative to those on the positive tension one. This provides a solution of the hierarchyproblem provided we live on the negative tension wall. The global structure is shown in figure 1.The second RS model 4 is obtained from the first by taking yc .
20、This makes the negativetension wall approach the AdS horizon, which includes a point at infinity. RS say that their modelcontains only one wall so presumably the idea is that the negative tension brane is viewed as an auxiliarydevice to set up boundary conditions. However, if the geometry makes sens
21、e then it should be possibleto discuss it without reference to this limiting procedure involving negative tension objects. If onesimply slices AdS along a positive tension wall at y = 0 and assumes reflection symmetry then thereare several ways to analytically continue the solution across the horizo
22、n. These have been discussedin 11, 12, 13, 14. There are two obvious choices of continuation. The first is simply to assume thatbeyond the horizon, the solution is pure AdS with no domain walls present. This is shown in figure2Figure 1: 1. Anti-de Sitter space. Two horospheres and a horizon are show
23、n. The vertical lines rep-resent timelike infinity. 2. Causal structure of Randall-Sundrum model with compact fifth dimension.The arrows denote identifications.Figure 2: Possible causal structures for Randall-Sundrum model with non-compact fifth dimension.The dots denote points at infinity.2. An alt
24、ernative, which seems closer in spirit to the geometry envisaged by RS, is to include furtherdomain walls beyond the horizon, as shown in figure 2. In this case, there are infinitely many domainwalls present.3Black string in AdSLet us first rewrite the AdS metric 2.1 by introducing the coordinate z
25、= ley/l. The metric is thenmanifestly conformally flat:ds2=l2z2(dz2+ ijdxidxj).(3.1)In these coordinates, the horizon lies at z = while the timelike infinity of AdS is at z = 0. Wenow note that if the Minkowski metric within the brackets is replaced by any Ricci flat metric thenthe Einstein equation
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 2000 膜世界的黑洞-精品文档资料整理 世界 黑洞 精品 文档 资料 整理
限制150内