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

The cosmic no hair conjecture is tested in the spherically symmetric Einstein-Maxwell-dilaton (EMD) system with a positive cosmological constant Λ. First, we analytically show that once gravitational collapse occurs in the massless dilaton case, the system of field equations breaks down inevitably in outer communicating regions or at the boundary provided that a future null infinity I⁺ exists. Next, we find numerically the static black hole solutions in the massive dilaton case and investigate their properties for comparison with the massless case. It is shown that their Abbott-Deser (AD) mass is infinite, which implies that a spacetime with finite AD mass does not approach a black hole solution after gravitational collapse. These results suggest that I⁺ cannot appear in the EMD system once gravitational collapse occurs and hence the cosmic no hair conjecture is violated in both the massless and massive cases, in contrast with general relativity.