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

Braneworld Black Holes and Entropy Bounds

The Bousso's D-bound entropy for the various possible black hole solutions on a 4-dimensional brane is checked. It is found that the D-bound entropy here is apparently different from that of obtained for the 4-dimensional black hole solutions. This difference is interpreted as the extra loss of information, associated to the extra dimension, when an extra-dimensional black hole is moved outward the observer's cosmological horizon. Also, it is discussed that N-bound entropy is hold for the possible solutions here. Finally, by adopting the recent Bohr-like approach to black hole quantum physics for the excited black holes, the obtained results are written also in terms of the black hole excited states.Comment: 13 pages, accepted for publication in Physics Letters

Initiating the effective unification of black hole horizon area and entropy quantization with quasi-normal modes

Black hole (BH) quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In this specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and non-strictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, this work exemplifies a series of imperative corrections that eventually permits a BH's horizon area spectrum to be generalized from strictly thermal to non-strictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the identified results are significant because quasi-normal modes (QNM) and "effective states" characterize the transitions between the established levels of the non-strictly thermal spectrum.Comment: 23 pages, review paper. Final version to appear in Advances in High Energy Physic

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

Tsallis uncertainty

It has been recently shown that the Bekenstein entropy bound is not respected by the systems satisfying modified forms of Heisenberg uncertainty principle (HUP) including the generalized and extended uncertainty principles, or even their combinations. On the other, the use of generalized entropies, which differ from Bekenstein entropy, in describing gravity and related topics signals us to different equipartition expressions compared to the usual one. In that way, The mathematical form of an equipartition theorem can be related to the algebraic expression of a particular entropy, different from the standard Bekenstein entropy, initially chosen to describe the black hole event horizon, see E. M. C. Abreu et al., MPLA 32, 2050266 (2020). Motivated by these works, we address three new uncertainty principles leading to recently introduced generalized entropies. In addition, the corresponding energy-time uncertainty relations and Unruh temperatures are also calculated. As a result, it seems that systems described by generalized entropies, such as those of Tsallis, do not necessarily meet HUP and may satisfy modified forms of HUP.Comment: Accepted version by EP