Black holes in higher dimensions, black strings, and the Gregory-Laflamme instability
Final Report Abstract
Black Holes are a major prediction of Einstein’s general relativity. Today there is strong observational evidence for the existence of astrophysical black holes. On the other hand string theory, a major candidate for the quantum theory of gravity and the unification of all interactions, predicts in its low energy limit additional fields and also requires higher dimensions for mathematical consistency. As a result, essential properties of black holes can change dramatically. In this project we have investigated the properties of black holes and studied how they are affected by the presence of extra dimensions. In particular, we have considered black holes, black rings and black strings, i.e., black objects with different types of horizon topologies, present in higher dimensional spacetimes, and we have also addressed braneworld models. When the higher dimensions are compact, the corresponding spacetimes are not asymptotically flat. Assuming one dimension to be compact, one finds caged black holes, i.e., black holes localized in the compact dimension. When small as compared to the compact dimension, these caged black holes differ only little from Schwarzschild black holes. For larger black holes, however, the compact dimension becomes essential, since at a critical size, the horizon will cover the compact dimension completely. The horizon topology must then change, and so-called nonuniform black strings emerge. We have studied both caged black holes and nonuniform black strings in this project. In particular, we have investigated the interior of the nonuniform black strings close to the transition point, and concluded that a naked singularity will appear. Furthermore, we have studied the influence of charge on these solutions. In five spacetime dimensions for Einstein gravity in vacuum, analytical methods are available to construct black rings or systems composed of several black components, like black Saturns or black multi-rings. In six and more dimensions as well as in the presence of higher-curvature terms already in five dimensions, no such methods are available, and one has to resort to numerical methods to construct such solutions. In Einstein gravity we have demonstrated the existence of generalized black rings and black Saturns in six and seven dimensions, which, however, do not yet represent fully balanced solutions, where the repulsive centrifugal force precisely balances the attractive gravitational force and the string tension. We have, however, obtained balanced black ring solutions in five dimensions, which carry electric charge. Here we have started to map out the phase diagramm. Likewise, we have started to map out the phase diagram for black hole solutions in five dimensions in the presence of a higher-curvature (Gauss-Bonnet) term. Another class of intriguing gravitational solutions are wormholes. Discovered at first as a feature of the Schwarzschild geometry, it was realized that wormholes could connect distant regions of the Universe, thus possibly allowing for fast interstellar travel. However, to obtain traversable wormholes, the presence of some form of exotic matter seemed to be necessary. As a spin-off of our investigations we realized that by starting from a string theory motivated theory, containing a dilaton and a higher-curvature (Gauss-Bonnet) term, traversable wormholes in four dimensions can be constructed, that do not need any form of exotic matter. Moreover, (a subset of) these wormholes are stable under small (radial) perturbations. We have studied the motion of particles and light in these wormhole spacetimes, and addressed the forces that travelers approaching the wormhole throat would feel. Additionally, we have studied boson stars, showing that like compact ordinary stars they admit two stable phases, with the denser phase approaching the black hole limit. Moreover, we have obtained new solutions in the presence of non-Abelian gauge fields, which constitute a central part of the Standard Model of particle physics. http://www.pro-physik.de/details/physikjournalIssue/1089703/Issue 02 2008.html http://www.sciencenews.org/view/generic/id/70599/title/Stellar wormholes may exist http://news.discovery.com/space/wormholes-connecting-stars-110305.html#mkcpg n=rssnws1 http://content.usatoday.com/communities/sciencefair/post/2011/08/star-trek-wormhole-stringtheory/1 http://www.nwzonline.de/campus/Artikel/131/2724647/Reise-durch-ein-Wurmloch.html
Publications
- “Interior of Nonuniform Black Strings”. Phys. Lett. B 664 (2008) 210
B. Kleihaus and J. Kunz
- “New dimensions for black holes”. Physik J. 7N2 (2008) 41
B. Kleihaus, J. Kunz and F. Navarro-Lerida
- “d ≥ 5 static black holes with S2 × Sd−4 event horizon topology”. Phys. Lett. B 678 (2009) 301
B. Kleihaus, J. Kunz and E. Radu
- “Harrison transformation and charged black objects in Kaluza-Klein theory”. JHEP 0909 (2009) 025
B. Kleihaus, J. Kunz, E. Radu and C. Stelea
- “Generalized Weyl solutions in d = 5 Einstein-Gauss-Bonnet theory: The Static black ring”. JHEP 1002 (2010) 092
B. Kleihaus, J. Kunz and E. Radu
- “Charged Balanced Black Rings in Five Dimensions”. Phys. Lett. B 699 (2011) 192
B. Kleihaus, J. Kunz and K. Schnülle
- “New generalized nonspherical black hole solutions”. JHEP 1102 (2011) 058
B. Kleihaus, J. Kunz, E. Radu and M. J. Rodriguez
- “Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory”. Phys. Rev. Lett. 106 (2011) 151104
B. Kleihaus, J. Kunz and E. Radu
- “Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory”. Phys. Rev. Lett. 106 (2011)
P. Kanti, B. Kleihaus and J. Kunz
