Kengo Maeda

Static spherically symmetric gravitational equilibria of the real scalar field are discussed in the presence of the cosmological constant. We find nontrivial solutions if we take the self-interaction of the field into account while there is no such equilibria in the noninteracting case. The system has critical parameters beyond which new solutions disappear. They are determined by the ratio of the cosmological horizon to the “Compton radius” of the scalar field. We also discuss the stability of the solutions by means of a linear perturbation method and find that the number of unstable modes depends on the node number of the scalar field.

We discuss the no-hair conjecture in the presence of a cosmological constant. For the first step the real scalar field is considered as the matter field and the spacetime is assumed to be static spherically 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 search for black hole solutions which support the scalar field with a double well potential, and find them by numerical calculations. The existence of such solutions depends on the values of the vacuum expectation value and the self-coupling constant of the scalar field. When we take the zero horizon radius limit, the solution becomes a boson star like solution which we found before. However new solutions are found to be unstable against the linear perturbation. As a result we can conclude that the no-scalar-hair conjecture holds in the case of scalar fields with a convex or double well potential.

A new mechanism for causing naked singularities is found in an effective superstring theory. We investigate the gravitational collapse in a spherically symmetric Einstein-Maxwell-dilaton system in the presence of a pure cosmological-constant “potential,” where the system has no static black hole solution. We show that once gravitational collapse occurs in the system, naked singularities necessarily appear in the sense that the field equations break down in the domain of outer communications. This suggests that in generalized theories of gravity, the nonminimally coupled fields generically cause naked singularities in the process of gravitational collapse if the system has no static or stationary black-hole solution.

A new mechanism for causing naked singularities is found in an effective superstring theory. We investigate the gravitational collapse in a spherically symmetric Einstein-Maxwell-dilaton system in the presence of a pure cosmological constant "potential", where the system has no static black hole solution. We show that once gravitational collapse occurs in the system, naked singularities necessarily appear in the sense that the field equations break down in the domain of outer communications. This suggests that in generalized theories of gravity, the non-minimally coupled fields generically cause naked singularities in the process of gravitational collapse if the system has no static or stationary black hole solution.

We test the chronology protection conjecture in classical general relativity by investigating finitely vicious space-times. First we present singularity theorems in finitely vicious space-times 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. Further introducing the concept of a non-naked singularity, we show that a restricted class of chronology violations cannot arise if all occurring singularities are the non-naked singularities. Our results suggest that the causal feature of the occurring singularities is the key to prevent the appearance of causality violation.

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 12π/Λ, where Λ is the cosmological constant. The physical implications are also discussed.

We test the chronology protection conjecture in classical general relativity by investigating finitely vicious space-times. First we present singularity theorems in finitely vicious space-times 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. Further introducing the concept of a non-naked singularity, we show that a restricted class of chronology violations cannot arise if all occurring singularities are the non-naked singularities. Our results suggest that the causal feature of the occurring singularities is the key to prevent the appearance of causality violation.