Gravitational instability of the inner static region of a Reissner-Nordstrom black hole

Reissner--Nordstr\"om black holes have two static regions: r > \ro and 0 < r < \ri, where \ri and \ro are the inner and outer horizon radii. The stability of the exterior static region has been established long time ago. In this work we prove that the interior static region is unstable under linear gravitational perturbations, by showing that field perturbations compactly supported within this region will generically excite a mode that grows exponentially in time. This result gives an alternative reason to mass inflation to consider the space time extension beyond the Cauchy horizon as physically irrelevant, and thus provides support to the strong cosmic censorship conjecture, which is also backed by recent evidence of a linear gravitational instability in the interior region of Kerr black holes found by the authors. The use of intertwiners to solve for the evolution of initial data plays a key role, and adapts without change to the case of super-extremal \rn black holes, allowing to complete the proof of the linear instability of this naked singularity. A particular intertwiner is found such that the intertwined Zerilli field has a geometrical meaning -it is the first order variation of a particular Riemann tensor invariant-. Using this, calculations can be carried out explicitely for every harmonic number.Comment: 24 pages, 4 figures. Changes and corrections in proof using intertwiners, also in figure

Astrophysical limits on quantum gravity motivated birefringence

We obtain observational upper bounds on a class of quantum gravity related birefringence effects, by analyzing the presence of linear polarization in the optical and ultraviolet spectrum of some distant sources. In the notation of Gambini and Pullin we find $\chi < 10^{-3}$.Comment: 4 pages, submitted to Phys. Rev. Let

The effect of radiative gravitational modes on the dynamics of a cylindrical shell of counter rotating particles

In this paper we consider some aspects of the relativistic dynamics of a cylindrical shell of counter rotating particles. In some sense these are the simplest systems with a physically acceptable matter content that display in a well defined sense an interaction with the radiative modes of the gravitational field. These systems have been analyzed previously, but in most cases resorting to approximations, or considering a particular form for the initial value data. Here we show that there exists a family of solutions where the space time inside the shell is flat and the equation of motion of the shell decouples completely from the gravitational modes. The motion of the shell is governed by an equation of the same form as that of a particle in a time independent one dimensional potential. We find that under appropriate initial conditions one can have collapsing, bounded periodic, and unbounded motions. We analyze and solve also the linearized equations that describe the dynamics of the system near a stable static solutions, keeping a regular interior. The surprising result here is that the motion of the shell is completely determined by the configuration of the radiative modes of the gravitational field. In particular, there are oscillating solutions for any chosen period, in contrast with the "approximately Newtonian plus small radiative corrections" motion expectation. We comment on the physical meaning of these results and provide some explicit examples. We also discuss the relation of our results to the initial value problem for the linearized dynamics of the shell

On the evolution of the momentarily static radiation free data in the Apostolatos - Thorne cylindrical shell model

We study the evolution of the "Momentarily Static and Radiation Free" (MSRF) initial data for the Apostolatos - Thorne cylindrical shell model. We analyze the relation between the parameters characterizing the MSRF data those for the corresponding final static configuration, and show that there is a priori no conflict for any choice of initial MSRF data, in contrast with some recent results of Nakao, Ida and Kurita. We also consider the problem in the linear approximation, and show that the evolution is stable in all cases. We find that the approach to the final state is very slow, with an inverse logarithmic dependence on time at fixed radius. To complement these results we introduce a numerical computation procedure that allows us to visualize the explicit form of the evolution of the shell and of the gravitational field up to large times. The results are in agreement with the qualitative behaviour conjectured by Apostolatos and Thorne, with an initial damped oscillatory stage, but with oscillations about a position that approaches slowly that of the static final state, as indicated by our analysis. We also include an Appendix, where we prove the existence of solutions of the cylindrical wave equation with vanishing initial value for $r > R_0$, ($R_0 > 0$ some finite constant), that approach a constant value for large times. This result is crucial for the proof of compatibility of arbitrary MSRF initial data and a final static configuration for the system.Comment: 27 pages, 12 figure