Pair of accelerated black holes in a de Sitter background: the dS C-metric

Following the work of Kinnersley and Walker for flat spacetimes, we have analyzed the anti-de Sitter C-metric in a previous paper. In the de Sitter case, Podolsky and Griffiths have established that the de Sitter C-metric (dS C-metric) found by Plebanski and Demianski describes a pair of accelerated black holes in the dS background with the acceleration being provided (in addition to the cosmological constant) by a strut that pushes away the two black holes or, alternatively, by a string that pulls them. We extend their analysis mainly in four directions. First, we draw the Carter-Penrose diagrams of the massless uncharged dS C-metric, of the massive uncharged dS C-metric and of the massive charged dS C-metric. These diagrams allow us to clearly identify the presence of two dS black holes and to conclude that they cannot interact gravitationally. Second, we revisit the embedding of the dS C-metric in the 5D Minkowski spacetime and we represent the motion of the dS C-metric origin in the dS 4-hyperboloid as well as the localization of the strut. Third, we comment on the physical properties of the strut that connects the two black holes. Finally, we find the range of parameters that correspond to non-extreme black holes, extreme black holes, and naked particles.Comment: 11 pages, 11 figures (RevTeX4). Published version: references adde

Duality between Electric and Magnetic Black Holes

A number of attempts have recently been made to extend the conjectured $S$ duality of Yang Mills theory to gravity. Central to these speculations has been the belief that electrically and magnetically charged black holes, the solitons of quantum gravity, have identical quantum properties. This is not obvious, because although duality is a symmetry of the classical equations of motion, it changes the sign of the Maxwell action. Nevertheless, we show that the chemical potential and charge projection that one has to introduce for electric but not magnetic black holes exactly compensate for the difference in action in the semi-classical approximation. In particular, we show that the pair production of electric black holes is not a runaway process, as one might think if one just went by the action of the relevant instanton. We also comment on the definition of the entropy in cosmological situations, and show that we need to be more careful when defining the entropy than we are in an asymptotically-flat case.Comment: 23 pages, revtex, no figures. Major revision: two sections on the electric Ernst solution adde

Two-phonon scattering of magnetorotons in fractional quantum Hall liquids

We study the phonon-assisted process of dissociation of a magnetoroton, in a fractional quantum Hall liquid, into an unbound pair of quasiparticles. Whilst the dissociation is forbidden to first order in the electron-phonon interaction, it can occur as a two-phonon process. Depending on the value of final separation between the quasiparticles, the dissociation is either a single event involving absorption of one phonon and emission of another phonon of similar energy, or a two-phonon diffusion of a quasiexciton in momentum space. The dependence of the magnetoroton dissociation time on the filling factor of the incompressible liquid is found.Comment: 4 pages, no figure

The extremal limits of the C-metric: Nariai, Bertotti-Robinson and anti-Nariai C-metrics

In two previous papers we have analyzed the C-metric in a background with a cosmological constant, namely the de Sitter (dS) C-metric, and the anti-de Sitter (AdS) C-metric, following the work of Kinnersley and Walker for the flat C-metric. These exact solutions describe a pair of accelerated black holes in the flat or cosmological constant background, with the acceleration A being provided by a strut in-between that pushes away the two black holes. In this paper we analyze the extremal limits of the C-metric in a background with generic cosmological constant. We follow a procedure first introduced by Ginsparg and Perry in which the Nariai solution, a spacetime which is the direct topological product of the 2-dimensional dS and a 2-sphere, is generated from the four-dimensional dS-Schwarzschild solution by taking an appropriate limit, where the black hole event horizon approaches the cosmological horizon. Similarly, one can generate the Bertotti-Robinson metric from the Reissner-Nordstrom metric by taking the limit of the Cauchy horizon going into the event horizon of the black hole, as well as the anti-Nariai by taking an appropriate solution and limit. Using these methods we generate the C-metric counterparts of the Nariai, Bertotti-Robinson and anti-Nariai solutions, among others. One expects that the solutions found in this paper are unstable and decay into a slightly non-extreme black hole pair accelerated by a strut or by strings. Moreover, the Euclidean version of these solutions mediate the quantum process of black hole pair creation, that accompanies the decay of the dS and AdS spaces

Physics in the Real Universe: Time and Spacetime

The Block Universe idea, representing spacetime as a fixed whole, suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This view is however based on time-reversible microphysical laws and does not represent macro-physical behaviour and the development of emergent complex systems, including life, which do indeed exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world linesComment: 28 pages, including 9 Figures. Major revision in response to referee comment

Pair creation of anti-de Sitter black holes on a cosmic string background

We analyze the quantum process in which a cosmic string breaks in an anti-de Sitter (AdS) background, and a pair of charged or neutral black holes is produced at the ends of the strings. The energy to materialize and accelerate the pair comes from the strings tension. In an AdS background this is the only study done in the process of production of a pair of correlated black holes with spherical topology. The acceleration $A$ of the produced black holes is necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant. Only in this case the virtual pair of black holes can overcome the attractive background AdS potential well and become real. The instantons that describe this process are constructed through the analytical continuation of the AdS C-metric. Then, we explicitly compute the pair creation rate of the process, and we verify that (as occurs with pair creation in other backgrounds) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of exp(Area/4), where Area is the black hole horizon area. We also conclude that the general behavior of the pair creation rate with the mass and acceleration of the black holes is similar in the AdS, flat and de Sitter cases, and our AdS results reduce to the ones of the flat case when L=0.Comment: 13 pages, 3 figures, ReVTeX