We study the quasinormal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically anti–de Sitter (AdS) spacetime. Some of the electromagnetic modes do not oscillate; they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar and electromagnetic perturbations in AdS spacetime, but has a similar behavior to the Schwarzschild black hole in an asymptotically flat spacetime: the imaginary part of the frequency goes as ${1/r}_{+},$ where $r_{+}$ is the horizon radius. We also investigate the small black-hole limit showing that the imaginary part of the frequency goes as $r_{+}^2.$ These results are important to the AdS/CFT conjecture since, according to it, the QNM’s describe the approach to equilibrium in the conformal field theory.

We calculate the quasinormal modes and associated frequencies of the Bañados-Teitelboim-Zanelli (BTZ) nonrotating black hole. This black hole lives in 2+1 dimensions in an asymptotically anti–de Sitter spacetime. We obtain exact results for the wave function and quasinormal frequencies of scalar, electromagnetic and Weyl (neutrino) perturbations.

First, the ideas introduced in the wormhole research field since the work of Morris and Thorne are reviewed, namely, the issues of energy conditions, wormhole construction, stability, time machines and astrophysical signatures. Then, spherically symmetric and static traversable Morris-Thorne wormholes in the presence of a generic cosmological constant $\Lambda$ are analyzed. A matching of an interior solution to the unique exterior vacuum solution is done using directly the Einstein equations. The structure as well as several physical properties and characteristics of traversable wormholes due to the effects of the cosmological term are studied. Interesting equations appear in the process of matching. For instance, one finds that for asymptotically flat and anti–de Sitter spacetimes the surface tangential pressure $\mathcal{P}$ of the thin shell, at the boundary of the interior and exterior solutions, is always strictly positive, whereas for de Sitter spacetime it can take either sign as one would expect, being negative (tension) for relatively high $\Lambda$ and high wormhole radius, positive for relatively high mass and small wormhole radius, and zero in between. Finally, some specific solutions with $\Lambda ,$ based on the Morris-Thorne solutions, are provided.

A wave impinging on a Kerr black hole can be amplified as it scatters off the hole if certain conditions are satisfied, giving rise to superradiant scattering. By placing a mirror around the black hole one can make the system unstable. This is the black-hole bomb of Press and Teukolsky. We investigate in detail this process and compute the growing time scales and oscillation frequencies as a function of the mirror’s location. It is found that in order for the system black hole plus mirror to become unstable there is a minimum distance at which the mirror must be located. We also give an explicit example showing that such a bomb can be built. In addition, our arguments enable us to justify why large Kerr-AdS black holes are stable and small Kerr-AdS black holes should be unstable.

Einstein-Maxwell equations with a cosmological constant are analyzed in a four-dimensional stationary spacetime admitting in addition a two-dimensional group $G_2$ of spatial isometries. We find charged rotating black string solutions. For open black strings the mass ($M$), angular momentum ($J$), and charge ($Q$) line densities can be defined using the Hamiltonian formalism of Brown and York. It is shown through dimensional reduction that $M$, $J$, and $Q$ are, respectively, the mass, angular momentum, and charge of a related three-dimensional black hole. For closed black strings one can define the total mass, charge, and angular momentum of the solution. These closed black string solutions have a flat torus topology. The black string solutions are classified according to the mass, charge, and angular momentum parameters. The causal structure is studied and some Penrose diagrams are shown. There are similarities between the charged rotating black string and the Kerr-Newman spacetime. The solution has Cauchy and event horizons, ergosphere, timelike singularities, closed timelike curves, and extremal cases. Both the similarities and differences of these black strings and Kerr-Newman black holes are explored. We comment on the implications these solutions might have on the hoop conjecture.