Recently, the Heisenberg's uncertainty principle has been extended to incorporate the existence of a large (cut-off) length scale in de Sitter or anti-de Sitter space, and the Hawking temperatures of the Schwarzshild-(anti) de Sitter black holes have been reproduced by using the extended uncertainty principle. I generalize the extended uncertainty to the case with an absolute minimum length and compute its modification to the Hawking temperature. I obtain a general trend that the generalized uncertainty principle due to the absolute minimum length "always" increases the Hawking temperature, implying "faster" decay, which is in conformity with the result in the asymptotically flat space. I also revisit the black hole-string phase transition, in the context of the generalized uncertainty principle.

Recently Hořava proposed a renormalizable gravity theory in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I study an IR modification which breaks "softly" the detailed balance condition in Hořava model and allows the asymptotically flat limit as well. I obtain the black hole and cosmological solutions for "arbitrary" cosmological constant that represent the analogs of the standard Schwarzschild-(A)dS solutions which can be asymptotically (A)dS as well as flat and I discuss their thermodynamical properties. I also obtain solutions for FRW metric with an arbitrary cosmological constant. I study its implication to the dark energy and find that it seems to be consistent with current observational data.

The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From counting the number of first and second class constraints, the number of dynamical degrees of freedom, which equals to the number of propagating graviton modes, is found to be 1, regardless of the value of cosmological constant. I note also that the usual equivalence with Chern-Simons gauge theory does not work for general circumstances.

We study a novel phenomena of smearing of black hole horizons from the effect of space noncommutativity. We present an explicit example in AdS 3 space, using the Chern-Simons formulation of gravity. This produces a smeared BTZ black hole which goes beyond the classical spacetime unexpectedly and there is no reality problem in our approach with the gauge group U (1, 1) × U (1, 1). The horizons are smeared, due to a splitting of the Killing horizon and the apparent horizon, and there is a metric signature change to Euclidean in the smeared region. The inner boundary of the smeared region acts as a trapped surface for timelike particles but the outer as a classical barrier for ingoing particles. The lightlike signals can escape from or reach the smeared region in a finite time, which indicates that the black hole is not so dark, even classically. In addition, it is remarked that the Hawking temperature can not be defined by the regularity in the Euclidean geometry except in the non-rotating case, and the origin can be smeared by a new (apparent) horizon. 9 This can be also observed in (22) and (25). 10 This seems to reflect the quantum gravity nature of the noncommutative geometry, as is in the beginning of the Universe [17]. 11 Particles may tunnel quantum mechanically, by their wave nature also.

Recently Hořava proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I consider a non-trivial test of the new gravity theory in FRW universe by considering an IR modification which breaks "softly" the detailed balance condition in the original Hořava model. I separate the dark energy parts from the usual Einstein gravity parts in the Friedman equations and obtain the formula of the equations of state parameter. The IR modified Hořava gravity seems to be consistent with the current observational data but we need some more refined data sets to see whether the theory is really consistent with our universe. From the consistency of our theory, I obtain some constraints on the allowed values of w 0 and w a in the Chevallier, Polarski, and Linder's parametrization and this may be tested in the near future, by sharpening the data sets.