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

Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space

We study the gravitational collapse of a homogeneous scalar field, minimally coupled to gravity, in the presence of a particular type of dynamical deformation between the canonical momenta of the scale factor and of the scalar field. In the absence of such a deformation, a class of solutions can be found in the literature [R. Goswami and P. S. Joshi, arXiv:gr-qc/0410144], %\cite{JG04}, whereby a curvature singularity occurs at the collapse end state, which can be either hidden behind a horizon or be visible to external observers. However, when the phase-space is deformed, as implemented herein this paper, we find that the singularity may be either removed or instead, attained faster. More precisely, for negative values of the deformation parameter, we identify the emergence of a negative pressure term, which slows down the collapse so that the singularity is replaced with a bounce. In this respect, the formation of a dynamical horizon can be avoided depending on the suitable choice of the boundary surface of the star. Whereas for positive values, the pressure that originates from the deformation effects assists the collapse toward the singularity formation. In this case, since the collapse speed is unbounded, the condition on the horizon formation is always satisfied and furthermore the dynamical horizon develops earlier than when the phase-space deformations are absent. These results are obtained by means of a thoroughly numerical discussion.Comment: 17 pages, 17 figure

Multiple deleted regions on the long arm of chromosome 6 in astrocytic tumours

Chromosome 6 deletions are common in human neoplasms including gliomas. In order to study the frequency and identify commonly deleted regions of chromosome 6 in astrocytomas, 159 tumours (106 glioblastomas, 39 anaplastic astrocytomas and 14 astrocytomas malignancy grade II) were analysed using 31 microsatellite markers that span the chromosome. Ninety-five per cent of cases with allelic losses had losses affecting 6q. Allelic losses were infrequent in astrocytomas malignancy grade II (14%) but more usual in anaplastic astrocytomas (38%) and glioblastomas (37%). Evidence for clonal heterogeneity in the astrocytomas and anaplastic astrocytomas was frequently observed (i.e. co-existence of subpopulations with and without chromosome 6 deletions). Clonal heterogeneity was less common in glioblastomas. Five commonly deleted regions were identified on 6q. These observations suggest that a number of tumour suppressor genes are located on 6q and that these genes may be involved in the progression of astrocytic tumours. © 2000 Cancer Research Campaig