No abstract

In previous work [1] we proposed an improvement of the WKB-based semianalytic technique of Iyer and Will for calculation of the quasiormal modes of black holes by constructing the Padé approximants of the formal series for ω 2 . It has been demonstrated that (within the domain of applicability) the diagonal Padé transforms P 6 6 and P 6 7 are always in a very good agreement with the numerical results. In this paper we present a further extension of the method. We show that it is possible to reproduce many known numerical results with a great accuracy (or even exactly) if the Padé transforms are constructed from the perturbative series of a really high order. In our calculations the order depends on the problem but it never exceeds 700. For example, the frequencies of the gravitational mode l = 2, n = 0 calculated with the aid of the Padé approximants and within the framework of the continued fractions method agree to 24 decimal places. The use of such a large number of terms is necessary as the stabilization of the quasinormal frequencies can be slow. Our results reveal some unexpected features of the WKB-based approximations and may shed some fresh light on the problem of overtones.

Heavy metals are constantly emitted into the environment and pose a major threat to human health, particularly in urban areas. The threat is linked to the presence of Cd, Cr, Cu, Ni, Pb, and Zn in street dust, which consists of mineral and organic particles originating from the soil, industrial emitters, motor vehicles, and fuel consumption. The study objective was to determine the level of street dust contamination with trace metals in Lublin and to indicate their potential sources of origin. The analyses were carried out with an energy-dispersive X-ray fluorescence spectrometer. The sampling sites (49) were located within the city streets characterised by varying intensity of motor traffic. The following mean content values and their variation (SD) were determined:

We consider the most general higher order corrections to the pure gravity action in $D$ dimensions constructed from the basis of the curvature monomial invariants of order 4 and 6, and degree 2 and 3, respectively. Perturbatively solving the resulting sixth-order equations we analyze the influence of the corrections upon a static and spherically symmetric back hole. Treating the total mass of the system as the boundary condition we calculate location of the event horizon, modifications to its temperature and the entropy. The entropy is calculated by integrating the local geometric term constructed from the derivative of the Lagrangian with respect to the Riemann tensor over a spacelike section of the event horizon. It is demonstrated that identical result can be obtained by integration of the first law of the black hole thermodynamics with a suitable choice of the integration constant. We show that reducing coefficients to the Lovelock combination, the approximate expression describing entropy becomes exact. Finally, we briefly discuss the problem of field redefinition and analyze consequences of a different choice of the boundary conditions in which the integration constant is related to the exact location of the event horizon and thus to the horizon defined mass

No abstract