Kei-Ichi Maeda

We study collision of two domain walls in 5-dimensional asymptotically Anti de Sitter spacetime. This may provide the reheating mechanism of an ekpyrotic (or cyclic) brane universe, in which two BPS branes collide and evolve into a hot big bang universe. We evaluate a change of scalar field making the domain wall and can investigate the effect of a negative cosmological term in the bulk to the collision process and the evolution of our universe.

We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in $D$-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system, we explicitly give the solutions in 11-dimensional M theory for the case with M2-M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we show that these solutions include the BMPV black hole and the Brinkmann wave solution. We also find new solutions similar to the Brinkmann wave. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field F, which is a rotational part of gravity, is self-dual. We also discuss non-spherical "black" objects (e.g., a ring topology and an elliptical shape) by use of other curvilinear coordinates.

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with that in the four-dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bounded from above. We also apply a catastrophe theory to analyze the stability of black rings. It indicates a branch of black rings with higher rotational energy is unstable, which should be a different type of instability from the Gregory-Laflamme one.

Studying Yang-Mills field and gravitational field in class A Bianchi spacetimes, we find that chaotic behavior appears in the late phase (the asymptotic future). In this phase, the Yang-Mills field behaves as that in Minkowski spacetime, in which we can understand it by a potential picture, except for the types VIII and IX. At the same time, in the initial phase (near the initial singularity), we numerically find that the behavior seems to approach the Kasner solution. However, we show that the Kasner circle is unstable and the Kasner solution is not an attractor. From an analysis of stability and numerical simulation, we find a Mixmaster-like behavior in Bianchi I spacetime. Although this result may provide a counterexample to the BKL (Belinskii, Khalatnikov and Lifshitz) conjecture, we show that the BKL conjecture is still valid in Bianchi IX spacetime. We also analyze a multiplicative effect of two types of chaos, that is, chaos with the Yang-Mills field and that in vacuum Bianchi IX spacetime. Two types of chaos seem to coexist in the initial phase. However, the effect due to the Yang-Mills field is much smaller than that of the curvature term.

Studying the Yang-Mills field and the gravitational field in class A Bianchi spacetimes, we find that chaotic behavior appears in the late phase (the asymptotic future). In this phase, the Yang-Mills field behaves as that in Minkowski spacetime, in which we can understand it by a potential picture, except for types VIII and IX. At the same time, in the initial phase (near the initial singularity), we numerically find that the behavior seems to approach the Kasner solution. However, we show that the Kasner circle is unstable and the Kasner solution is not an attractor. From an analysis of stability and numerical simulation, we find a Mixmaster-like behavior in Bianchi I spacetime. Although this result may provide a counterexample to the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture, we show that the BKL conjecture is still valid in Bianchi IX spacetime. We also analyze a multiplicative effect of two types of chaos, that is, chaos with the Yang-Mills field and that in vacuum Bianchi IX spacetime. Two types of chaos seem to coexist in the initial phase. However, the effect due to the Yang-Mills field is much smaller than that of the curvature term.

We study time-dependent solutions in M and superstring theories with higher order corrections. We first present general field equations for theories of Lovelock type with stringy corrections in arbitrary dimensions. We then exhaust all exact and asymptotic solutions of exponential and power-law expansions in the theory with Gauss-Bonnet terms relevant to heterotic strings and in the theories with quartic corrections corresponding to the M-theory and type II superstrings. We discuss interesting inflationary solutions that can generate enough e-foldings in the early universe.

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with than that in four dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bounded from above. We also apply a catastrophe theory to analyze the stability of black rings. It indicates a branch of black rings with higher rotational energy is unstable, which should be a different type of instability from the Gregory-Laflamme's one.