We examine the dual conformal field theory for extremal charged black holes in five-dimensional minimal supergravity with 2 independent angular momenta. The conformal field theory Virasoro algebra, central charge, and temperature are calculated. Additionally the conformal field theory entropy is calculated using the Cardy formula and agrees with the Bekenstein-Hawking black hole entropy. The central charges are directly proportional to the angular momentum components of the black hole. In five and higher dimensions, rotations of the spacetime correspond to rotations of the central charges leading to an apparent symmetry relating the conformal field theories dual to each black hole. A rotationally invariant central charge, which is proportional to the total angular momentum, is used to discuss the supersymmetric BMPV black hole limits.

We consider an alternative to inflation for the generation of superhorizon perturbations in the Universe in which the speed of sound is faster than the speed of light. We label such cosmologies, first proposed by Armendariz-Picon, tachyacoustic, and explicitly construct examples of noncanonical Lagrangians which have superluminal sound speed, but which are causally self-consistent. Such models possess two horizons, a Hubble horizon and an acoustic horizon, which have independent dynamics. Even in a decelerating (noninflationary) background, a nearly scale-invariant spectrum of perturbations can be generated by quantum perturbations redshifted outside of a shrinking acoustic horizon. The acoustic horizon can be large or even infinite at early times, solving the cosmological horizon problem without inflation. These models do not, however, dynamically solve the cosmological flatness problem, which must be imposed as a boundary condition. Gravitational wave modes, which are produced by quantum fluctuations exiting the Hubble horizon, are not produced.

The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstroumlm domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schroumldinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schroumldinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schroumldinger equation becomes nonlocal, but the wave function describing the system is nonsingular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.

We discover that a class of bubbles of nothing are embedded as time dependent scaling limits of previous spacelike-brane solutions. With the right initial conditions, a near bubble solution can relax its expansion and open the compact circle. Thermodynamics of the new class of solutions is discussed and the relationships between brane/flux transitions, tachyon condensation and imaginary D-branes are outlined. Finally, a related class of simultaneous connected S-branes are also examined.

In our earlier paper [JHEP 0310 (2003) 058], we considered higher dimensional cosmological models with hyperbolic spaces. In particular the eternal accelerating expansion was obtained by studying small perturbation around the critical non-accelerated solution for $D > 10$. In this addendum, we show that there is also such a solution in the critical case $D = 10$.

In our earlier paper [JHEP 0310 (2003) 058], we considered higher dimensional cosmological models with hyperbolic spaces. In particular the eternal accelerating expansion was obtained by studying small perturbation around the critical non-accelerated solution for D > 10. In this addendum, we show that there is also such a solution in the critical case D=10.

The tremendous progress achieved through the study of black holes and branes suggests that their time-dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional strings and branes. These S-brane worldvolumes are governed by S-brane actions which are on equal footing to D-brane actions, since they are derived by imposing conformality on the string worldsheet, as well as by analyzing fluctuations of time-dependent tachyon configurations. As further examples we generalize previous solutions of the S-brane actions so as to describe multiple decaying and nucleating closed fundamental strings. Conceptually S-brane actions are therefore different from D-brane actions and can provide a description of time-dependent strings/branes and possibly their interactions.

While in string theory the subject of sources in imaginary time has received some attention, we demonstrate the power of imaginary sources by proving that they constitute in several field theories a complete basis for all smooth and time dependent source free solutions. These proofs promote the study of imaginary sources to a new and crucial viewpoint for understanding time dependent backgrounds. From our field theory examples we further propose a completeness conjecture that every regular solution to a field equation of motion has a corresponding imaginary source configuration. We define charges for spacelike sources and show their compatibility with the usual charge definition for timelike sources. Many new non-singular time dependent field theory solutions are discussed, including Wick rotations of abelian instantons which demonstrate a close relationship between electric-magnetic duals and analytic continuation.

To capture important physical properties of a spacetime we construct a new diagram, the card diagram, which accurately draws generalized Weyl spacetimes in arbitrary dimensions by encoding their global spacetime structure, singularities, horizons, and some aspects of causal structure including null infinity. Card diagrams draw only nontrivial directions providing a clearer picture of the geometric features of spacetimes as compared to Penrose diagrams, and can change continuously as a function of the geometric parameters. One of our main results is to describe how Weyl rods are traversable horizons and the entirety of the spacetime can be mapped out. We review Weyl techniques and as examples we systematically discuss properties of a variety of solutions including Kerr-Newman black holes, black rings, expanding bubbles, and recent spacelike-brane solutions. Families of solutions will share qualitatively similar cards. In addition we show how card diagrams not only capture information about a geometry but also its analytic continuations by providing a geometric picture of analytic continuation. Weyl techniques are generalized to higher dimensional charged solutions and applied to generate perturbations of bubble and S-brane solutions by Israel-Khan rods.

Smooth time dependent supergravity solutions corresponding to analytic continuations of Kerr black holes are constructed and limits with a local de Sitter phase are found. These solutions are non-singular due to a helical twist in space and a fine tuning of the energy flow in the spacetime. For the extremal limit in which the mass and twist parameters are equal the S-brane undergoes de Sitter expansion. Subextremal limits show the formation and decay of a twisted circle and closed string tachyon condensation backreaction effects can be followed. For small values of the twist deformation, a short lived ergosphere envelopes the S-brane and leads to the production of closed timelike curves.

The time dependent formation of an electric flux tube (fundamental string) is reviewed. The main tool used for analysis is the Spacelike brane, which is a kink in time of the rolling tachyon. Both the S-brane and rolling tachyon are attempts to extend the D-brane concept to time dependent backgrounds. While S-branes are similar to Euclidean counterparts of the more familiar timelike D-branes, S-branes can smoothly change their worldvolume signature from spacelike to timelike which we interpret as the formation of a topological defect.

By analytically continuing recently-found instantons, we construct time-dependent solutions of Einstein-Maxwell de Sitter gravity which smoothly bounce between two de Sitter phases. These deformations of de Sitter space undergo several stages in their time evolution. Four and five-dimensional de Sitter bounces can be lifted to non-singular time-dependent solutions of M-theory.

We derive effective actions for "spacelike branes" (S-branes) and find a solution describing the formation of fundamental strings in the rolling tachyon background. The S-brane action is a Dirac-Born-Infeld action for Euclidean world volumes defined in the context of time-dependent tachyon condensation of non-BPS (Bogomol'nyi-Prasad-Sommerfield) branes. It includes gauge fields and, in particular, a scalar field associated with translation along the time direction. We show that the BIon spike solutions constructed in this system correspond to the production of a confined electric flux tube (a fundamental string) at late time of the rolling tachyon.

We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility that our universe is a hyperbolic space and provide exact Milne type solutions, as well as intersecting S-brave solutions. When both the usual 4D spacetime and the m-dimensional internal space are hyperbolic, we find eternally accelerating cosmologies for mgreater than or equal to7, with and without form field backgrounds. In particular, the effective potential for a magnetic field background in the large 3 dimensions is positive definite with a local minimum and thus enhances the eternally accelerating expansion.

We study compactifications of Einstein gravity on product spaces in vacuum and their acceleration phases. Scalar potentials for the dimensionally reduced effective theory are found to be of exponential form and exact solutions are obtained for a class of product spaces. The inflation in our solutions is not sufficient for the early universe. We comment on the possibility of obtaining sufficient inflation by compactification in general.

Using S(pacelike)-branes defined through rolling tachyon solutions, we show how the dynamical formation of D(irichlet)-branes and strings in tachyon condensation can be understood. Specifically we present solutions of S-brane actions illustrating the classical confinement of electric and magnetic flux into fundamental strings and D-branes. The role of S-branes in string theory is further clarified and their RR charges are discussed. In addition, by examining ``boosted'' S-branes, we find what appears to be a surprising dual S-brane description of strings and D-branes, which also indicates that the critical electric field can be considered as a self-dual point in string theory. We also introduce new tachyonic S-branes as Euclidean counterparts to non-BPS branes.

Spacelike branes are new time-dependent systems to explore and it has been observed that related supergravity solutions can be obtained by analytically continuing known D-brane solutions. Here we show that analytic continuation of known solutions of the Dirac-Born-Infeld equations also lead to interesting analogs of time dependent gravity solutions. Properties of these new solutions, which are similar to the Witten bubble of nothing and S-branes, are discussed. We comment on how these new bubble solutions seem relevant to the tachyon condensation process of non-BPS branes, and remark on their application to cosmological scenarios. Unstable brane configurations which resemble S-brane type solutions are also discussed.

Spacelike branes are new time-dependent systems to explore and it has been observed that related supergravity solutions can be obtained by analytically continuing known D-brane solutions. Here we show that analytic continuation of known solutions of the Dirac-Born-Infeld equations also lead to interesting analogs of time dependent gravity solutions. Properties of these new solutions, which are similar to the Witten bubble of nothing and S-branes, are discussed. We comment on how these new bubble solutions seem relevant to the tachyon condensation process of non-BPS branes, and remark on their application to cosmological scenarios. Unstable brane configurations which resemble S-brane type solutions are also discussed. ∗hllywd2@phys.ntu.edu.tw