Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by Ghanam and Thompson. Here we reduce the problem of finding the general $n$-dimensional Einstein metric of SIM(n-2) holonomy, with and without a cosmological constant, to solving a set linear generalised Laplace and Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalised harmonic functions. A dimensional reduction of these multi-centre solutions gives new time-dependent Kaluza-Klein black holes and monopoles, including time-dependent black holes in a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page

Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously established result that for all extreme black holes the moduli fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio

Black-Hole-Wave Duality in String Theory

Extreme 4-dimensional dilaton black holes embedded into 10-dimensional geometry are shown to be dual to the gravitational waves in string theory. The corresponding gravitational waves are the generalization of pp-fronted waves, called supersymmetric string waves. They are given by Brinkmann metric and the two-form field, without a dilaton. The non-diagonal part of the metric of the dual partner of the wave together with the two-form field correspond to the vector field in 4-dimensional geometry of the charged extreme black holes.Comment: 12 pages, LaTeX, preprint UG-3/94, SU-ITP-94-11, QMW-PH-94-1

The Decay of Magnetic Fields in Kaluza-Klein Theory

Magnetic fields in five-dimensional Kaluza-Klein theory compactified on a circle correspond to ``twisted'' identifications of five dimensional Minkowski space. We show that a five dimensional generalisation of the Kerr solution can be analytically continued to construct an instanton that gives rise to two possible decay modes of a magnetic field. One decay mode is the generalisation of the ``bubble decay" of the Kaluza-Klein vacuum described by Witten. The other decay mode, rarer for weak fields, corresponds in four dimensions to the creation of monopole-anti-monopole pairs. An instanton for the latter process is already known and is given by the analytic continuation of the \KK\ Ernst metric, which we show is identical to the five dimensional Kerr solution. We use this fact to illuminate further properties of the decay process. It appears that fundamental fermions can eliminate the bubble decay of the magnetic field, while allowing the pair production of Kaluza-Klein monopoles.Comment: 25 pages, one figure. The discussion of fermions has been revised: We show how fundamental fermions can eliminate the bubble-type instability but still allow pair creation of monopole

Birth of Closed Strings and Death of Open Strings during Tachyon Condensation

The tremendous progress achieved through the study of black holes and branes suggests that their time dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional strings and branes. These S-brane worldvolumes are governed by S-brane actions which are on equal footing to D-brane actions, since they are derived by imposing conformality on the string worldsheet, as well as by analyzing fluctuations of time dependent tachyon configurations. As further examples we generalize previous solutions of the S-brane actions so as to describe multiple decaying and nucleating closed fundamental strings. Conceptually S-brane actions are therefore different from D-brane actions and can provide a description of time dependent strings/branes and possibly their interactions.Comment: 15 pages, 7 eps figures; invited review for Modern Physics Letters A, including new solutions for S-brane actions. v2 published version, minor typos correcte

Topology, Entropy and Witten Index of Dilaton Black Holes

We have found that for extreme dilaton black holes an inner boundary must be introduced in addition to the outer boundary to give an integer value to the Euler number. The resulting manifolds have (if one identifies imaginary time) topology $S^1 \times R \times S^2$ and Euler number $\chi = 0$ in contrast to the non-extreme case with $\chi=2$. The entropy of extreme $U(1)$ dilaton black holes is already known to be zero. We include a review of some recent ideas due to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black holes as having an inner boundary, we conclude that the entropy of {\sl all} extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the relevance of this to the vanishing of quantum corrections and the idea that the functional integral for extreme holes gives a Witten Index. We have studied also the topology of ``moduli space'' of multi black holes. The quantum mechanics on black hole moduli spaces is expected to be supersymmetric despite the fact that they are not HyperK\"ahler since the corresponding geometry has torsion unlike the BPS monopole case. Finally, we describe the possibility of extreme black hole fission for states with an energy gap. The energy released, as a proportion of the initial rest mass, during the decay of an electro-magnetic black hole is 300 times greater than that released by the fission of an ${}^{235} U$ nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New sections include discussion of the Witten index, topology of the moduli space, black hole sigma model, and black hole fission with huge energy releas

Nucleating Black Holes via Non-Orientable Instantons

We extend the analysis of black hole pair creation to include non- orientable instantons. We classify these instantons in terms of their fundamental symmetries and orientations. Many of these instantons admit the pin structure which corresponds to the fermions actually observed in nature, and so the natural objection that these manifolds do not admit spin structure may not be relevant. Furthermore, we analyse the thermodynamical properties of non-orientable black holes and find that in the non-extreme case, there are interesting modifications of the usual formulae for temperature and entropy.Comment: 27 pages LaTeX, minor typos are correcte

Particle Production and Positive Energy Theorems for Charged Black Holes in deSitter

We study quantum mechanical and classical stability properties of Reissner-Nordstrom deSitter spacetimes, which describe black holes with mass $M$ and charge $Q$ in a background with cosmological constant $\Lambda \ge 0$. There are two sources of particle production in these spacetimes; the black hole horizon and the cosmological horizon. A scattering calculation is done to compute the Hawking radiation in these spacetimes. We find that the flux from the black hole horizon equals the flux from the cosmological horizon, if and only if $|Q|=M$, indicating that this is a state of thermodynamic equilibrium. The spectrum, however, is not thermal. We also show that spacetimes containing a number of charge equal to mass black holes with $\Lambda \ge 0$, have supercovariantly constant spinors, suggesting that they may be minimum energy states in a positive energy construction. As a first step in this direction, we present a positive energy construction for asymptotically deSitter spacetimes with vanishing charge. Because the construction depends only on a spatial slice, our result also holds for spacetimes which are asymptotically Robertson-Walker.Comment: 11 pages (1 figure not included), UMHEP-39

Gyromagnetic Ratio of Charged Kerr-Anti-de Sitter Black Holes

We examine the gyromagnetic ratios of rotating and charged AdS black holes in four and higher spacetime dimensions. We compute the gyromagnetic ratio for Kerr-AdS black holes with an arbitrary electric charge in four dimensions and show that it corresponds to g=2 irrespective of the AdS nature of the spacetime. We also compute the gyromagnetic ratio for Kerr-AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe is rotating at the speed of light, it exhibits a striking feature leading to g=2 regardless of the spacetime dimension. Next, we extend our consideration to include the exact metric for five-dimensional rotating charged black holes in minimal gauged supergravity. We show that the value of the gyromagnetic ratio found in the "test-charge" approach remains unchanged for these black holes.Comment: New section added; 6 pages, RevTe

Generalized (m,k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend

We have translated fractional Brownian motion (FBM) signals into a text based on two ''letters'', as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the $\zeta '$ exponent relating the word frequency and its rank on a log-log plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of length $m<8$ made of such two letters: $\zeta '$ is varying as a power law in terms of $m$. We have also searched how the $\zeta '$ exponent of the Zipf law is influenced by a linear trend and the resulting effect of its slope. We can distinguish finite size effects, and results depending whether the starting FBM is persistent or not, i.e. depending on the FBM Hurst exponent $H$. It seems then numerically proven that the Zipf exponent of a persistent signal is more influenced by the trend than that of an antipersistent signal. It appears that the conjectured law $\zeta ' = |2H-1|$ only holds near $H=0.5$. We have also introduced considerations based on the notion of a {\it time dependent Zipf law} along the signal.Comment: 24 pages, 12 figures; to appear in Int. J. Modern Phys