Makoto Narita

Toward the no-scalar-hair conjecture in asymptotically de Sitter spacetime

Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan(February 7, 2008)We discuss the no-hair conjecture in the presence of a cosmological constant. For the first stepthe real scalar field is considered as the matter field and the spacetime is assumed to be staticspherically symmetric. If the scalar field is massless or has a convex potential such as a mass term,it is proved that there is no regular black hole solution. For a general positive potential, we searchfor black hole solutions which support the scalar field with a double well potential, and find themby numerical calculations. The existence of such solutions depends on the values of the vacuumexpectation value and the self-coupling constant of the scalar field. When we take the zero horizonradius limit, the solution becomes a boson star like solution which we found before. However newsolutions are found to be unstable against the linear perturbation. As a result we can conclude thatthe no-scalar hair conjecture holds in the case of scalar fields with a convex or double well potential.04.70.-s, 04.70.Bw, 04.20.Jb, 95.30.SfI. INTRODUCTION

Upper bound for entropy in asymptotically de Sitter space-time

We investigate the nature of asymptotically de Sitter space-times containing a black hole. We show that if the matter fields satisfy the dominant energy condition and cosmic censorship holds in the considered space-time, the area of the cosmological event horizon for an observer approaching a future timelike infinity does not decrease; i.e., the second law is satisfied. We also show under the same conditions that the total area of the black hole and the cosmological event horizon, a quarter of which is the total Bekenstein-Hawking entropy, is less than 12\ensuremath{\pi}/\ensuremath{\Lambda}, where \ensuremath{\Lambda} is the cosmological constant. The physical implications are also discussed.

Chronology protection and non-naked singularity

We test the chronology protection conjecture in classical general relativity by investigating finitely vicious spacetimes. First we present singularity theorems in finitely vicious spacetimes by imposing some restrictions on the chronology-violating sets. In the theorems we can refer to the location of an occurring singularity and do not assume any asymptotic conditions such as the existence of null infinities. Furthermore, introducing the concept of a non-naked singularity, we show that a restricted class of chronology violations cannot arise if all occurring singularities are non-naked singularities. Our results suggest that the causal feature of the occurring singularities is the key to prevent the appearance of causality violation.

Is the cosmic no hair conjecture true in the Einstein-Maxwell-dilaton system?

We investigate the gravitational collapsing phenomenon in the spherically symmetric Einstein–Maxwell-dilaton system with a positive cosmological constant. As a preparation, we first study some general properties of the horizons in asymptotically de Sitter space–time and prove that the area of the horizons does not decrease and has an upper bound if the matter fields satisfy the dominant energy condition. By using these results, we analytically show that once gravitational collapse occurs from any initial data on a null hypersurface, the system of field equations breaks down inevitably in the domain of outer communications or the boundary, i.e. the black hole event horizon provided that a future null infinity ℐ+ exists, or the asymptotic structure at ℐ+ is broken and the universe will recollapse. In order to clarify which history does the universe trace, we perform a numerical simulation. Then, the dilaton field diverges faster than the logarithmic function almost uniformly and the asymptotic structure would be broken. This implies that the cosmic no hair conjecture is violated in the generalized theory of gravity.

String excitation inside generic black holes

We calculate how much a first-quantized string is excited after crossing the inner horizon of charged Vaidya solutions, as a simple model of generic black holes. To quantize a string suitably, we first show that the metric is approximated by a plane-wave metric near the inner horizon when the surface gravity of the horizon

Can we construct the enhançon configuration with D2-D6 branes shell?

{\ensuremath{\kappa}}_{I}

Violation of the cosmic no hair conjecture in the Einstein-Maxwell-dilaton system

is small enough. Next, it is analytically shown that the string crossing the inner horizon is excited infinitely in an asymptotically flat spacetime, while it is finite in an asymptotically de Sitter spacetime and the string can pass across the inner horizon when

Rigid singularity theorem in globally hyperbolic spacetimes

{\ensuremath{\kappa}}_{I}l2\ensuremath{\kappa}\ensuremath{\mathrel{:=}}2\mathrm{min}{{\ensuremath{\kappa}}_{B},{\ensuremath{\kappa}}_{C}},

Scalar hair on the black hole in asymptotically anti-de Sitter spacetime

where

The stability of the shell of D6-D2 branes in a N=2 supergravity solution

{\ensuremath{\kappa}}_{B}({\ensuremath{\kappa}}_{C})