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The Lagrangian derivation of the Equations of Motion for topological static spherically symmetric metrics in $$\mathcal{F }(R,G)$$-modified gravity is presented and the related solutions are discussed. In particular, a new topological solution for the model $$\mathcal{F }(R,G)=R+\sqrt{G}$$ is found. The black hole solutions and the First Law of thermodynamic are analyzed. Furthermore, the coupling with electromagnetic field is also considered and a Maxwell solution is derived. [ABSTRACT FROM AUTHOR]

In the present paper, Unruh-DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh-DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein-de Sitter universe (that is a more realistic situation in the frame of ΛCDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation. [ABSTRACT FROM AUTHOR]

A Lagrangian derivation of the Equations of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits one to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in F(R)-gravity. All known exact solutions are recovered. We also exhibit a new non-trivial solution with non-constant Ricci scalar. [ABSTRACT FROM AUTHOR]

Abstract: This work describes a study of GPS heights, gravity and hydrological time series collected by stations located in northeastern Italy. During the last 12 years, changes in the long-term behaviors of the GPS heights and gravity time series are observed. In particular, starting in 2004–2005, a height increase is observed over the whole area. The temporal and spatial variability of these parameters has been studied as well as those of key hydrological variables, namely precipitation, hydrological balance and water table by using the Empirical Orthogonal Functions (EOF) analysis. The coupled variability between the GPS heights and the hydrological balance and precipitation data has been investigated by means of the Singular Value Decomposition (SVD) approach. Significant common patterns in the spatial and temporal variability of these parameters have been recognized. In particular, hydrology-induced variations are clearly observable starting in 2002–2003 in the southern part of the Po Plain for the longest time series, and from 2004–2005 over the whole area. These findings, obtained by means of purely mathematical approaches, are supported by sound physical interpretation suggesting that the climate-related fluctuations in the regional/local hydrological regime are one of the main contributors to the observed variations. A regional scale signal has been identified in the GPS station heights; it is characterized by the opposite behavior of the southern and northern stations in response to the hydrological forcing. At Medicina, in the southern Po Plain, the EOF analysis has shown a marked common signal between the GPS heights and the Superconducting Gravimeter (SG) data both over the long and the short period. [Copyright &y& Elsevier]

We use relative zeta functions technique of W. Müller to investigate the regularized partition function of a finite temperature quantum field theory on an ultrastatic space-time with noncompact spatial section. As an application, we study the case of massless scalar field with singular delta-like potential, as described in [1]. [Copyright &y& Elsevier]

Abstract: Series of gravity recordings at the stations Medicina (Italy) and Wettzell (Germany) are investigated to separate seasonal gravity variations from long-term trends in gravity. The findings are compared to height variations monitored by continuous GPS observations. To study the origin of these variations in height and gravity the environmental parameters at the stations are included in the fact finding. In Medicina, a clear seasonal signal is visible in the gravity and height data series, caused by seasonal fluctuations in the atmosphere including mass redistribution, the ocean, groundwater but also by geo-mechanical effects such as soil consolidation and thermal expansion of the structure supporting the GPS antenna. In Wettzell, no seasonal effect could be clearly identified, and the long-term trend in gravity is mainly caused by ground water variations. The successful combination of height and gravity series with the derived ratio of gravity to height changes indicates that the long-term trends in height and gravity are most likely due to mass changes rather than to tectonic movements. [Copyright &y& Elsevier]

The calculation of the static potential (Casimir energy) for p-brane compactified on Kaluza-Klein space-times of the form T × П $$S^{N_\alpha} $$ × П ( H / Γ )× R , T= S , $$S^{N_\alpha} $$ is a N -dimensional sphere, H / Γ is a compact Riemannian surface of genus g >1, is presented. The analysis is given in the framework of one-loop effective potential approximation. It is shown that quantum behaviour of the potential and its extrema depend on the choice of twist. [ABSTRACT FROM AUTHOR]

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