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By mapping the nonadditive entropy composition law of the Bekenstein-Hawking formula to an additive one via the so-called "formal logarithm" operation, a new approach to the black hole entropy problem is considered. The new temperature function satisfies the zeroth law of thermodynamics, and turns out to be independent of the mass-energy parameter of the black hole in the case of the Schwarzschild solution. It is shown that pure isolated black holes are thermodynamically stable against spherically symmetric perturbations within this approach. [ABSTRACT FROM AUTHOR]

We consider general-relativistic rotational perturbations in homogeneous and isotropic Friedmann–Robertson–Walker (FRW) cosmologies. Taking linear perturbations of FRW models, the general solution to the field equations contains tensorial, vectorial and scalar functions. The vectorial terms are in connection with rotations in the given model and due to the Sachs–Wolfe effect they produce contributions to the temperature fluctuations of the cosmic microwave background radiation (CMBR). In this paper we obtain the analytic time dependence of these contributions in a spatially flat FRW model with pressureless ideal fluid, in the presence and the absence of a cosmological constant Λ. We find that the solution can be separated into an integrable and a nonintegrable part, as in the case of scalar perturbations. Analyzing the solutions and using the results of recent observations, we estimate the order of magnitude of the angular velocity corresponding to the rotation tensor at the time of decoupling and today. [ABSTRACT FROM AUTHOR]