Abstract. The topological derivative gives the sensitivity of a cost function when the domain under consideration is perturbed by the introduction of a hole. In particular, the topological derivative was already applied for solving topology design of several engineering problems. Alternatively, this same idea can also be used to calculate the sensitivity of the problem when, instead of a hole, ...

Using the inverse scattering method we construct an exact stationary asymptotically flat 4+1-dimensional vacuum solution describing “black saturn”: a spherical black hole surrounded by a black ring. Angular momentum keeps the configuration in equilibrium. Black saturn reveals a number of interesting gravitational phenomena: (1) The balanced solution exhibits 2-fold continuous non-uniqueness for...

Using the inverse scattering method we construct an exact stationary asymptotically flat 4+1-dimensional vacuum solution describing “black saturn”: a spherical black hole surrounded by a black ring. Angular momentum keeps the configuration in equilibrium. Black saturn reveals a number of interesting gravitational phenomena: (1) The balanced solution exhibits 2-fold continuous non-uniqueness for...

We investigate the effect of inverse-Compton scattering of flares of soft radiation in different geometries of a hot, Comptonizing region and a colder accretion disk around a solar-mass black hole. The photon-energy dependent light curves, their Fourier transforms, power spectra and Fourier-period dependent time lags of hard photons with respect to softer photons are discussed. On the basis of ...

The Fundamental Plane for black hole activity constitutes a tight correlation between jet power, X-ray luminosity, and black hole mass. Under the assumption that a Blandford–Znajek-type mechanism, which relies on black hole spin, contributes non-negligibly to jet production, the sufficiently small scatter in the Fundamental Plane shows that black hole spin differences of | a| ∼ 1 are not typica...

The Fundamental Plane for black hole activity constitutes a tight correlation between jet power, X-ray luminosity, and black hole mass. Under the assumption that a Blandford–Znajek-type mechanism, which relies on black hole spin, contributes non-negligibly to jet production, the sufficiently small scatter in the Fundamental Plane shows that black hole spin differences of | a| ∼ 1 are not typica...

In an insightful approach, Robinson and Wilczek proposed that Hawking radiation can be obtained as the compensation of a breakdown of general covariance and gauge invariance and the radiation is a black body radiation at Hawking temperature. We apply this method to two types of black holes in three dimensional spacetime, which share the general form of the metric in that the tt component of the...

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Vira...

Bridges are one the most important and useful river structure and as a key of Communication ways are very significant. Local Scouring is one the most reason of Instability of bridges and finally its failure annually immense human and financial cost to the government imposes. So far, several studies on ways to control and reduce scouring around piers of the bridges has been done among them, the ...