Greybody factor for black string in dRGT massive gravity

The greybody factor from the black string in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory is investigated in this study. The dRGT massive gravity theory is one of the modified gravity theories used in explaining the current acceleration in the expansion of the universe. By using cylindrical symmetry, black strings in dRGT massive gravity are shown to exist. When quantum effects are taken into account, black strings can emit thermal radiation called Hawking radiation. The Hawking radiation at spatial infinity differs from that at the source by the so-called greybody factor. In this paper, we examined the rigorous bounds on the greybody factors from the dRGT black strings. The results show that the greybody factor crucially depends on the shape of the potential characterized by model parameters. The results agree with ones in quantum mechanics, the higher the potential, the harder it is for the waves to penetrate and also lower the bound for the rigorous bounds.Comment: 18 pages, 12 figures; V2 accepted to EPJC, minor change, two column 11 pages, 12 figure

Quasi-normal frequencies: Key analytic results

The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for the double-delta potential in terms of the Lambert W function. V3: Minor edits for clarity. Four references added. No physics changes. Still 31 page

Solution generating theorems for perfect fluid spheres

The first static spherically symmetric perfect fluid solution with constant density was found by Schwarzschild in 1918. Generically, perfect fluid spheres are interesting because they are first approximations to any attempt at building a realistic model for a general relativistic star. Over the past 90 years a confusing tangle of specific perfect fluid spheres has been discovered, with most of these examples seemingly independent from each other. To bring some order to this collection, we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres. In addition, we develop new ``solution generating'' theorems for the TOV, whereby any given solution can be ``deformed'' to a new solution. Because these TOV-based theorems work directly in terms of the pressure profile and density profile it is relatively easy to impose regularity conditions at the centre of the fluid sphere.Comment: 8 pages, no figures, to appear in the proceedings of the NEB XII Conference (Recent Developments in Gravity), 29 June - 2 July, 2006, Napflio, Greec

Compound transfer matrices: Constructive and destructive interference

Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the compound barrier is simply given by the product of the transmission probabilities of the individual sub-barriers. In contrast if one is scattering waves (whether we are dealing with either purely classical waves or quantum Schrodinger wavefunctions) each sub-barrier contributes phase information (as well as a transmission probability), and these phases can lead to either constructive or destructive interference, with the transmission probability oscillating between nontrivial upper and lower bounds. In this article we shall study these upper and lower bounds in some detail, and also derive bounds on the closely related process of quantum excitation (particle production) via parametric resonance.Comment: V1: 28 pages. V2: 21 pages. Presentation significantly streamlined and shortened. This version accepted for publication in the Journal of Mathematical Physic

Recycled Concrete Aggregates in Roadways: A Laboratory Examination of Self-Cementing Characteristics

This paper examines the self-cementing phenomenon of the road construction material known as recycled concrete aggregate (RCA). Two RCA types were selected as study materials: (1) high-grade RCA (HRCA), a quality RCA manufactured from relatively high-strength concrete structures; and (2) road base RCA (RBRCA), a high-grade RCA blend combined with brick and general clean rubble (road base material). Laboratory tests were performed to obtain the unconfined compressive strength, indirect tension dynamic modulus, and resilient modulus of the test samples to examine their hardening characteristics when subjected to varying curing periods. These tests were performed in conjunction with microstructure analyses from X-ray diffractometry (XRD) and scanning electron microscope (SEM) techniques. The HRCA samples, which were prepared and subjected to varying curing conditions, transformed from an initially unbound material into a bound (fully stabilized) material. The results of XRD and SEM analyses clearly demonstrate that secondary hydration occurred. The RBRCA samples were able to maintain their unbound granular properties, with nonsignificant self-cementing, thus supporting the hypothesis that the mixing of nonactive materials such as bricks and clean rubble into RCA will lessen the tendency of RCA toward self-cementing

Effective refractive index tensor for weak field gravity

Gravitational lensing in a weak but otherwise arbitrary gravitational field can be described in terms of a 3 x 3 tensor, the "effective refractive index". If the sources generating the gravitational field all have small internal fluxes, stresses, and pressures, then this tensor is automatically isotropic and the "effective refractive index" is simply a scalar that can be determined in terms of a classic result involving the Newtonian gravitational potential. In contrast if anisotropic stresses are ever important then the gravitational field acts similarly to an anisotropic crystal. We derive simple formulae for the refractive index tensor, and indicate some situations in which this will be important.Comment: V1: 8 pages, no figures, uses iopart.cls. V2: 13 pages, no figures. Significant additions and clarifications. This version to appear in Classical and Quantum Gravit

Reformulating the Schrodinger equation as a Shabat-Zakharov system

We reformulate the second-order Schrodinger equation as a set of two coupled first order differential equations, a so-called "Shabat-Zakharov system", (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasise the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrodinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ODE.Comment: 18 pages, plain LaTe

Report on workshop A1: Exact solutions and their interpretation

I report on the communications and posters presented on exact solutions and their interpretation at the GRG18 Conference, Sydney.Comment: 9 pages, no figures. Many typos corrected. Report submitted to the Proceedings of GR18. To appear in CQ

Transmission probabilities and the Miller-Good transformation

Transmission through a potential barrier, and the related issue of particle production from a parametric resonance, are topics of considerable general interest in quantum physics. The authors have developed a rather general bound on quantum transmission probabilities, and recently applied it to bounding the greybody factors of a Schwarzschild black hole. In the current article we take a different tack -- we use the Miller-Good transformation (which maps an initial Schrodinger equation to a final Schrodinger equation for a different potential) to significantly generalize the previous bound.Comment: 10 pages. V2: Now 15 pages. Significantly expanded with examples and applications. Matches published versio