We study the evolution of massless scalar waves propagating on spherically symmetric spacetimes with a nonzero cosmological constant. Considering test fields on both Schwarzschild-de Sitter and Reissner-Nordström-de Sitter backgrounds, we demonstrate the existence of exponentially decaying tails at late times. Interestingly the ℓ = 0 mode asymptotes to a non-zero value, contrasting the asymptotically flat situation. We also compare these results, for ℓ = 0, with a numerical integration of the Einstein-scalar field equations, finding good agreement between the two. Finally, the significance of these results to the study of the Cauchy horizon stability in black hole-de Sitter spacetimes is discussed.

We consider the evolution of a scalar field propagating in Schwarzschild-de Sitter spacetime. The field is non-minimally coupled to curvature through a coupling constant ξ. The spacetime has two distinct time scales, te = re/c and tc = rc/c, where re is the radius of the black-hole horizon, rc the radius of the cosmological horizon, and c the speed of light. When rc ≫ re, the field's time evolution can be separated into three epochs. At times t ≪ tc, the field behaves as if it were in pure Schwarzschild spacetime; the structure of spacetime far from the black hole has no influence on the evolution. In this early epoch, the field's initial outburst is followed by quasi-normal oscillations, and then by an inverse power-law decay. At times t < ∼ tc, the power-law behavior gives way to a faster, exponential decay. In this intermediate epoch, the conditions at radii r > ∼ re and r < ∼ rc both play an important role. Finally, at times t ≫ tc, the field behaves as if it were in pure de Sitter spacetime; the structure of spacetime near the black hole no longer influences the evolution in a significant way. In this late epoch, the field's behavior depends on the value of the curvaturecoupling constant ξ. If ξ is less than a critical value ξc = 3/16, the field decays exponentially, with a decay constant that increases with increasing ξ. If ξ > ξc, the field oscillates with a frequency that increases with increasing ξ; the amplitude of the field still decays exponentially, but the decay constant is independent of ξ. We establish these properties using a combination of numerical and analytical methods.

We study critical behavior in the collapse of massive spherically symmetric scalar fields. We observe two distinct types of phase transition at the threshold of black hole formation. Type II phase transitions occur when the radial extent $(\lambda)$ of the initial pulse is less than the Compton wavelength ($\mu^{-1}$) of the scalar field. The critical solution is that found by Choptuik in the collapse of massless scalar fields. Type I phase transitions, where the black hole formation turns on at finite mass, occur when $\lambda \mu \gg 1$. The critical solutions are unstable soliton stars with masses $\alt 0.6 \mu^{-1}$. Our results in combination with those obtained for the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to the Einstein-matter equations may be relevant to the critical point of other matter models.Comment: 5 pages, RevTex, 4 postscript figures included using psfi

We begin a program of work aimed at examining the interior of a rotating black hole with a non{zero cosmological constant. The generalisation of Teukolsky's equation for the radial mode functions is presented. It is shown that the energy uxes of scalar, electromagnetic and gravity w a v es are regular at the Cauchy horizon whenever the surface gravity there is less than the surface gravity at the cosmological horizon. This condition is narrowly allowed, even when the cosmological constant i s v ery small, thus permitting an observer to pass through the hole, viewing the naked singularity along the way.1

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the nonlinear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the free gravitational data allows us to solve the field equations along a null surface crossing the Cauchy Horizon. As in the spherical case, the results indicate that a diverging influx of gravitational energy, in concert with an outflux across the CH, is responsible for the singularity. The spacetime is asymptotically Petrov type N, the same algebraic type as a gravitational shock wave. Implications for the continuation of spacetime through the singularity are briefly discussed.