The melting of glaciers coming with climate change threatens the heritage of the last glaciation of Europe likely contained in subglacial lakes in Greenland and Svalbard. This aspect urges specialists to focus their studies (theoretical, numerical and on-field) on such fascinating objects. Along this line we have built up a numerical procedure for validating the conjecture of the existence of a subglacial lake beneath the Amundsenisen Plateau at South-Spitzbergen, Svalbard. In this work we describe the algorithm and significant representative results of the related numerical test.

This paper deals with the issue of forecasting energy production of a Photo-Voltaic (PV) plant, needed by the Distribution System Operator (DSO) for grid planning. As the energy production of a PV plant is strongly dependent on the environmental conditions, the DSO has difficulties to manage an electrical system with stochastic generation. This implies the need to have a reliable forecasting of the irradiance level for the next day in order to setup the whole distribution network. To this aim, this paper proposes the use of transfer function models.

A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an associated family of observers, the kinematical properties of which in turn may be used to geometrically characterize the original slicings.

The features of equatorial motion of an extended body in Kerr spacetime are investigated in the framework of the Mathisson-Papapetrou-Dixon model. The body is assumed to stay at quasiequilibrium and respond instantly to external perturbations. Besides the mass, it is completely determined by its spin, the multipolar expansion being truncated at the quadrupole order, with a spin-induced quadrupole tensor. The study of the radial effective potential allows us to analytically determine the innermost stable circular orbit shift due to spin and the associated frequency of the last circular orbit.

We show that causality violation in a Kerr naked singularity spacetime is constrained by the existence of (radial) potential barriers. We extend to the class of vortical non-equatorial null geodesics confined to $$\theta $$? $$=$$= constant hyperboloids (boreal orbits) previous results concerning timelike ones (Calvani et al. in Gen Rel Gravit 9:155, 1978), showing that within this class of orbits, the causality principle is rigorously satisfied.

Continuing our analytic computation of the first-order self-force contribution to the "geodetic" spin precession frequency of a small spinning body orbiting a large (nonspinning) body, we provide the exact expressions of the 10 and 10.5 post-Newtonian terms. We also introduce a new approach to the analytic computation of self-force regularization parameters based on a WKB analysis of the radial and angular equations satisfied by the metric perturbations.

Continuing our analytic computation of the first-order self-force contribution to Detweiler's redshift variable we provide the exact expressions of the ninth and ninth-and-a-half post-Newtonian terms.

An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the worldline of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction.

In this paper we consider Volterra integral equations on time scales and describe our study about the long time behavior of their solutions. We provide sufficient conditions for the stability under constant perturbations by using the direct Lyapunov method and we present some examples of application.