Non-rotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a universal finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power law relation with the quantum area spectrum found in Non-perturbative Canonical Quantum General Relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterising this power law relation, where the canonical entropy (free energy) is seen to turn complex.The microcanonical entropy (S MC ) of generic stationary non-rotating macroscopic four dimensional black holes, modelled as isolated horizons [1], has been shown to obey, for large fixed horizon areas, the Bekenstein-Hawking Area Law (BHAL) [2] together with an infinite series of corrections, each term of which is finite and calculable [3]. The leading correction is logarithmic in area (BH entropy) with a coefficient (calculated in [3]) that has been argued to be universal [4], [5]. These results are obtained within Non-perturbative Canonical Quantum General Relativity (NCQGR), and crucially depend on the discrete spectrum of geometrical observables, especially the area [6].It is well-known in elementary statistical mechanics [7] that, unlike the canonical entropy, the definition of the microcanonical entropy in fact is not unique. One can define it as the logarithm of the degeneracy of quantum microstates characterizing the system, as has been employed in the calculations cited above [2], [3]. Alternatively, one can define it as the logarithm of the density of these microstates as a function of the energy. While both these definitions yield the same area law, they donot lead to the same logarithmic corrections. The difference actually depends on the relation between the energy (mass) of the black hole and the horizon area. This difference plays an important role when the NCQGR result is used to compute the effect of thermal fluctuations on the canonical entropy of black holes [8],In [8], the precise distinction and relationship between corrections to the BHAL arising due to quantum spacetime fluctuations, and due to thermal fluctuations within a canonical framework (admittedly heuristic), has been delineated. The logarithmic corrections due to quantum spacetime fluctuations are interpreted as 'finite size effects'. 1 Thermal fluctuations then generate additional log-area corrections which are computed in [8] for generic non-rotating antide Sitter black holes. Fortunately, the thermal fluctuation contributions to the canonical entropy can be expressed entirely in terms of the microcanonical entropy which has been computed within NCQGR as already mentioned. Unfortunately, however, the extra logarithmic contribution to the canonical entropy owing to the difference in the two definitions of the microcanonical entropy has been missed out in [8...

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The effects of thermal fluctuations of the mass (horizon area) and electric charge, on the entropy of non-rotating charged macroscopic black holes, are analyzed using a grand canonical ensemble. Restricting to Gaussian fluctuations around equilibrium, and assuming a power law type of relation between the black hole mass, charge and horizon area, characterized by two real positive indices, the grand canonical entropy is shown to acquire a logarithmic correction with a positive coefficient proportional to the sum of the indices. However, the root mean squared fluctuations of mass and charge relative to the mean values of these quantities turn out to be independent of the details of the assumed mass-area relation. We also comment on possible cancellation between log (area) corrections arising due to fixed area quantum spacetime fluctuations and that due to thermal fluctuations of the area and other quantities.

We show that four-dimensional black holes become stable below certain mass when the Einstein-Hilbert action is supplemented with higher-curvature terms. We prove this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily high order in curvature. The new black holes, which are non-hairy generalizations of Schwarzschild's solution, present a universal thermodynamic behavior for general values of the higher-order couplings. In particular, small black holes have infinite lifetimes. When the evaporation process makes the semiclassical approximation break down (something that occurs after a time which is usually infinite for all practical purposes), the resulting object retains a huge entropy, in stark contrast with Schwarzschild's case.

The stability of a strong-coupling singlet optical bipolaron is studied for the first time in two- and three-dimensional parabolic quantum dots using the Landau - Pekar variational method. It is shown that the confining potential of the quantum dot reduces the stability of the bipolaron.

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