The X-ray data obtained with XMM-Newton is used to investigate the complex structure of the gas in the atmosphere of the Virgo cluster around M87. We construct a simple model for the temperature and density distribution. This model implies that the cumulative mass of the cluster gas is a power-law of its entropy index, kT n−2/3, similar to the Hydra cluster. This supports the idea that such pow...

Starting from metric of general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermo-dynamical entropies are studied. First, by means of the " brick wall " model in which the Dirichlet condition is replaced by a scattering ansatz for the field functions at the horizon and with the Pauli-Villars regularization scheme, an expression f...

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