Quasinormal Modes Beyond Kerr

The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are slightly deformed from Kerr. We mention two example applications: the parametric, turbulent instability of scalar fields on a background which includes a gravitational QNM, and the shifts to the QNM frequencies of Kerr when the black hole is weakly charged. This method may be of use in studies of black holes which are deformed by external fields or are solutions to alternative theories of gravity.Comment: Proceedings of the Sant Cugat Forum on Astrophysics (2014). Session on 'Gravitational Wave Astrophysics.' 7 page

Low energy expansion of the four-particle genus-one amplitude in type II superstring theory

A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed. This is applied to determine coefficients up to order s^6R^4 (where s is a Mandelstam invariant and R^4 the linearized super-curvature), and partial results are obtained beyond that order. This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus. At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler--Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values. We are careful to disentangle the analytic pieces from logarithmic threshold terms, which involves a discussion of the conditions imposed by unitarity. We further consider the compactification of the amplitude on a circle of radius r, which results in a plethora of terms that are power-behaved in r. These coefficients provide boundary `data' that must be matched by any non-perturbative expression for the low-energy expansion of the four-graviton amplitude. The paper includes an appendix by Don Zagier.Comment: JHEP style. 6 eps figures. 50 page

Diffusion-limited reactions and mortal random walkers in confined geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.Comment: 18 pages, 16 figure

Bianchi type I space and the stability of inflationary Friedmann-Robertson-Walker space

Stability analysis of the Bianchi type I universe in pure gravity theory is studied in details. We first derive the non-redundant field equation of the system by introducing the generalized Bianchi type I metric. This non-redundant equation reduces to the Friedmann equation in the isotropic limit. It is shown further that any unstable mode of the isotropic perturbation with respect to a de Sitter background is also unstable with respect to anisotropic perturbations. Implications to the choice of physical theories are discussed in details in this paper.Comment: 5 pages, some comment adde

Friedmann Equation and Stability of Inflationary Higher Derivative Gravity

Stability analysis on the De Sitter universe in pure gravity theory is known to be useful in many aspects. We first show how to complete the proof of an earlier argument based on a redundant field equation. It is shown further that the stability condition applies to $k \ne 0$ Friedmann-Robertson-Walker spaces based on the non-redundant Friedmann equation derived from a simple effective Lagrangian. We show how to derive this expression for the Friedmann equation of pure gravity theory. This expression is also generalized to include scalar field interactions.Comment: Revtex, 6 pages, Add two more references, some typos correcte

Potential-density pairs for axisymmetric galaxies: the influence of scalar fields

We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential-density pairs of galactic disks for an exponential profile and their rotation curves.Comment: 8 pages, no figures, corrected version to the one that will appear in Gen. Relativ. Gravit., where a small typo in eq. (13) is presen

Conditions for Successful Extended Inflation

We investigate, in a model-independent way, the conditions required to obtain a satisfactory model of extended inflation in which inflation is brought to an end by a first-order phase transition. The constraints are that the correct present strength of the gravitational coupling is obtained, that the present theory of gravity is satisfactorily close to general relativity, that the perturbation spectra from inflation are compatible with large scale structure observations and that the bubble spectrum produced at the phase transition doesn't conflict with the observed level of microwave background anisotropies. We demonstrate that these constraints can be summarized in terms of the behaviour in the conformally related Einstein frame, and can be compactly illustrated graphically. We confirm the failure of existing models including the original extended inflation model, and construct models, albeit rather contrived ones, which satisfy all existing constraints.Comment: 8 pages RevTeX file with one figure incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html; Revised to include extra references, results unchanged, to appear Phys Rev

The torsion cosmology in Kaluza-Klein theory

We have studied the torsion cosmology model in Kaluza-Klein theory. We considered two simple models in which the torsion vectors are $A_{\mu}=(\alpha,0,0,0)$ and $A_{\mu}=a(t)^2(0,\beta,\beta,\beta)$, respectively. For the first model, the accelerating expansion of the Universe can be not explained without dark energy which is similar to that in the standard cosmology. But for the second model, we find that without dark energy the effect of torsion can give rise to the accelerating expansion of the universe and the alleviation of the well-known age problem of the three old objects for appropriated value of the model parameter $\beta$. These outstanding features of the second torsion cosmology model have been supported by the Type Ia supernovae (SNIa) data.Comment: 12 pages, 2 figures. Accepted for publication in JCA

Charge conservation and time-varying speed of light

It has been recently claimed that cosmologies with time dependent speed of light might solve some of the problems of the standard cosmological scenario, as well as inflationary scenarios. In this letter we show that most of these models, when analyzed in a consistent way, lead to large violations of charge conservation. Thus, they are severly constrained by experiment, including those where $c$ is a power of the scale factor and those whose source term is the trace of the energy-momentum tensor. In addition, early Universe scenarios with a sudden change of $c$ related to baryogenesis are discarded.Comment: 4 page

Illusions of general relativity in Brans-Dicke gravity

Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity when omega tends to infinity is false if the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach using conformal transformations. The otherwise unaccountable limiting behavior of Brans-Dicke gravity is easily understood in terms of the conformal invariance of the theory when the sources of gravity have radiation-like properties. The rigorous computation of the asymptotic behavior of the Brans-Dicke scalar field is straightforward in this new approach.Comment: 16 pages, LaTeX, to appear in Physical Review