The connection between black hole thermodynamics and chemistry is extended to the lowerdimensional regime by considering the rotating and charged BTZ metric in the (2 + 1)-D and a (1 + 1)-D limits of Einstein gravity. The Smarr relation is naturally upheld in both BTZ cases, where those with Q = 0 violate the Reverse Isoperimetric Inequality and are thus superentropic. The inequality can be maintained, however, with the addition of a new thermodynamic work term associated with the mass renormalization scale. The D → 0 limit of a generic D + 2-dimensional Einstein gravity theory is also considered to derive the Smarr and Komar relations, although the opposite sign definitions of the cosmological constant and thermodynamic pressure from the D > 2 cases must be adopted in order to satisfy the relation. The requirement of positive entropy implies an upper bound on the mass of a (1 + 1)-D black hole. Promoting an associated constant of integration to a thermodynamic variable allows one to define a "rotation" in one spatial dimension. Neither the D = 3 nor the D → 2 black holes exhibit any interesting phase behaviour.

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under M ↔ M −1 naturally implies a Generalized Uncertainty Principle with the linear form ∆x ∼ 1 ∆p + ∆p. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of (1 + 1)-D gravity. The temperature of sub-Planckian black holes scales as M rather than M −1 but the evaporation of those smaller than 10 −36 g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.

The generalized uncertainty principle discloses a self-complete characteristic of gravity, namely the possibility of masking any curvature singularity behind an event horizon as a result of matter compression at the Planck scale. In this paper we extend the above reasoning in order to overcome some current limitations to the framework, including the absence of a consistent metric describing such Planck-scale black holes. We implement a minimum-size black hole in terms of the extremal configuration of a neutral non-rotating metric, which we derived by mimicking the effects of the generalized uncertainty principle via a short scale modified version of Einstein gravity. In such a way, we find a self-consistent scenario that reconciles the self-complete character of gravity and the generalized uncertainty principle. *

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We analyze the thermodynamical properties of black holes in a modified theory of gravity, which was initially proposed to obtain correct dynamics of galaxies and galaxy clusters without dark matter. The thermodynamics of non-rotating and rotating black hole solutions resembles similar solutions in Einstein-Maxwell theory with the electric charge being replaced by a new mass dependent gravitational charge Q = √ αGN M . This new mass dependent charge modifies the effective Newtonian constant from GN to G = GN (1 + α), and this in turn critically affects the thermodynamics of the black holes. We also investigate the thermodynamics of regular solutions, and explore the limiting case when no horizons forms. So, it is possible that the modified gravity can lead to the absence of black hole horizons in our universe. Finally, we analyze corrections to the thermodynamics of a non-rotating black hole and obtain the usual logarithmic correction term.