The extended uncertainty principle inspires the R\'{e}nyi entropy

We use the extended uncertainty principle (EUP) in order to obtain the R\'{e}nyi entropy for a black hole (BH). The result implies that the non-extensivity parameter, appeared in the R\'{e}nyi entropy formalism, may be evaluated from the considerations which lead to EUP. It is also shown that, for excited BHs, the R\'{e}nyi entropy is a function of the BH principal quantum number, i.e. the BH quantum excited state. Temperature and heat capacity of the excited BHs are also investigated addressing two phases while only one of them can be stable. At this situation, whereas entropy is vanished, temperature may take a non-zero positive minimum value, depending on the value of the non-extensivity parameter. The evaporation time of excited BH has also been studied

A non-geodesic motion in the R^-1 theory of gravity tuned with observations

In the general picture of high order theories of gravity, recently, the R^-1 theory has been analyzed in two different frameworks. In this letter a third context is added, considering an explicit coupling between the R^-1 function of the Ricci scalar and the matter Lagrangian. The result is a non-geodesic motion of test particles which, in principle, could be connected with Dark Matter and Pioneer anomaly problems.Comment: Accepted for Modern Physics Letters

Einstein and Rastall Theories of Gravitation in Comparison

We profit by a recent paper of Visser claiming that Rastall gravity is equivalent to Einstein gravity to compare the two gravitational theories in a general way. Our conclusions are different from Visser's ones. We indeed argue that these two theories are not equivalent. In fact, Rastall theory of gravity is an "open" theory when compared to Einstein general theory of relativity. Thus, it is ready to accept the challenges of observational cosmology and quantum gravity.Comment: 8 pages, comment on the paper arXiv:1711.11500, "Rastall gravity is equivalent to Einstein gravity", by Matt Visser. Final version matching the paper published in the European Physical Journal

Tuning the stochastic background of gravitational waves using the WMAP data

The cosmological bound of the stochastic background of gravitational waves is analyzed with the aid of the WMAP data, differently from lots of works in literature, where the old COBE data were used. From our analysis, it will result that the WMAP bounds on the energy spectrum and on the characteristic amplitude of the stochastic background of gravitational waves are greater than the COBE ones, but they are also far below frequencies of the earth-based antennas band. At the end of this letter a lower bound for the integration time of a potential detection with advanced LIGO is released and compared with the previous one arising from the old COBE data. Even if the new lower bound is minor than the previous one, it results very long, thus for a possible detection we hope in the LISA interferometer and in a further growth in the sensitivity of advanced projects.Comment: 9 pages, 2 figures, published in Modern Physics Letters A. arXiv admin note: substantial text overlap with arXiv:0901.119