Kei Ichi Maeda

Dilaton gravity on the brane

We derive the four-dimensional field equations for the induced metric and scalar field on the world-volume of a 3-brane in a five-dimensional bulk with Einstein gravity plus a self-interacting scalar field. We calculate the effective four-dimensional gravitational constant and cosmological constant for arbitrary forms of the brane tension and self-interaction potential for the scalar field in the bulk. In addition to the canonical energy-momentum tensor for the scalar field and ordinary matter on the brane, the effective four-dimensional Einstein equations include terms due to the scalar field and gravitational waves in the bulk. We present solutions corresponding to static Minkowski brane worlds and also dynamical Friedmann-Robertson-Walker brane world cosmologies. We discuss the induced coupling of the scalar field to ordinary matter on the brane.

Extended inflationary universes

We investigate the behavior of isotropic models in the general scalar-tensor theory of gravitation. We derive the criterion for inflation to occur in a range of such theories, including that of Brans and Dicke. The solutions used to model “extended” inflation in earlier investigations are shown to be special cases which do not follow the behaviour of the general Brans-Dicke model at early times. The conformal relationship between scalar-tensor theories and general relativity with a self-interacting scalar field is explored and used to find members of a new class of inflationary universes. These “intermediate” inflationary universes have expansion scale factors which increase as exp(tp), 0 < p < 1. The possibility of successfully of realizing the ◀old” inflationary universe scenario in these models, with the present time variation of the gravitation “constant” being acceptably small, is illustrated with a specific example.

On the dynamics of the power law inflation due to an exponential potential

Abstract The power law inflationary universe model induced by a scalar field with an exponential potential is studied. A dissipation term due to particle creation is introduced in the inflations classical equation of motion. It is shown that the power index of the inflation increases prominently with an adequate viscosity. Consequently, even in theories with a rather steep exponential such as some supergravity or superstring models, it turns out that a “realistic” power law inflation (with a power index p⪆10) is possible.

Dilatonic black holes with Gauss-Bonnet term

We discuss black holes in an effective theory derived from a superstring model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term. Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of spherically symmetric solutions, i.e., a neutral, an electrically charged, a magnetically charged and a “colored” black hole, and discuss their thermodynamical properties and fate via the Hawking evaporation process. For neutral and electrically charged black holes, we find critical point and a singular end point. Below the mass corresponding to the critical point, no solution exists, while the curvature on the horizon diverges and a naked singularity appears at the singular point. A cusp structure in the mass-entropy diagram is found at the critical point and black holes on the branch between the critical and singular points become unstable. For magnetically charged and “colored” black holes, the solution becomes singular just at the end point with a finite mass. Because the black hole temperature is always finite even at the critical point or the singular point, we may conclude that the evaporation process will not be stopped even at the critical point or the singular point, and the black hole will move to a dynamical evaporation phase or a naked singularity will appear.

Tree level string cosmology

In this paper we examine the classical evolution of a cosmological model derived from the low-energy tree-level limit of a generic string theory. The action contains the metric, dilaton, central charge and an antisymmetric tensor field. We show that with a homogeneous and isotropic metric, allowing spatial curvature, there is a formal equivalence between this system and a scalar field minimally coupled to Einstein gravity in a spatially flat metric. We refer to this system as the shifted frame and using it we describe the full range of cosmological evolution that this model can exhibit. We show that generic solutions begin (or end) with a singularity. As the system approaches a singularity the dilaton becomes large and loop corrections will become important. {copyright} {ital 1996 The American Physical Society.}

Finite-width corrections to the Nambu action for the Nielsen-Olesen string

Abstract The finite-width correction terms to the Nambu action for Nielsen-Olesen strings are calculated. They consist of an extrinsic curvature squared or rigidity term and a new “twist” term. The extrinsic curvature term prevents cusps forming, rounding them off with a curvature radius of the order of the string width.

Stability of Non-Abelian Black Holes and Catastrophe Theory

Two types of self-gravitating particle solutions found in several theories with non-Abelian fields are smoothly connected by a family of non-trivial black holes. There exists a maximum point of the black hole entropy, where the stability of solutions changes. This criterion is universal, and the changes in stability follow from a catastrophe-theoretic analysis of the potential function defined by black hole entropy.

Wormholes with scalar fields

Wormholes solutions are discussed in a theory with antisymmetric 3-rank tensor field Hmu nu rho (axion) coupled to scalar fields. The authors also consider a generalised gravity theory, which action is given by S= integral d4x square root -g(F( phi ,R)-1/2h( phi )( Del phi )2-g2 Hmu nu rho 2), with F( phi ,R) and h( phi ) being arbitrary functions of a scalar phi and a scalar curvature R. Since it is conformally equivalent to the Einstein-Hilbert system with Hmu nu rho coupled to a scalar field, the authors can apply the above discussion to such a theory. Most models (R2 model, Jordan-Brans-Dicke theory, Zees induced gravity model and the Einstein theory with non-minimal coupling) contain wormhole solutions. Although a wormhole solution cannot occur in the four-dimensional effective theory from a superstring model (Giddings and Strominger (1988)), if the effective theory has a scalar field (not dilaton) coupled non-minimally, a wormhole solution becomes possible.

Chaos in static axisymmetric spacetimes: I. Vacuum case

We study the motion of a test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (i) a local instability measured by the Weyl curvature, and (ii) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyse several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behaviour in some spacetimes, these can be accounted for by the second criterion.We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.

Cosmic colored black holes

We present spherically symmetric static solutions (a particlelike solution and a black-hole solution) of the Einstein-Yang-Mills system with a cosmological constant. Although their gravitational structures are locally similar to those of the Bartnik-McKinnon particles or the colored black holes, the asymptotic behavior becomes quite different because of the existence of a cosmological horizon. We also discuss their stability by means of a catastrophe theory as well as a linear perturbation analysis and find the number of unstable modes.