In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawking's temperature and entropy for the noncommutative Schwarzschild black hole.

The Wheeler-DeWitt (WDW) equation for the Kantowski-Sachs model can also be understood as the WDW-equation corresponding to the Schwarzschild black hole due to the well known diffeomorphism between these two metrics. The WDW-equation and its solutions are "ignorant" of the coordinate patch one is using, only by imposing coordinate conditions we can differentiate between cosmological and black hole models. At that point, the foliation parameter t or r will appear in the solution of interest. In this work we supersymmetrize this WDW-equation obtaining an extra term in the potential with two posible signs. The WKB method is then applied, given rise to two classical equations. It is shown that the event horizon can never be reached because, very near to it the extra term in the potential, for each one of the equations, is more relevant than the one that corresponds to Schwarzschild. One can then study the asymptotic cases in which one of the two terms in the Hamiltonian dominates the behavior. One of them corresponds to the usual Schwarzschild black hole. We will study here the other two asymptotic regions; they provide three solutions. All of them have a singularity in r = 0 and depending on an integration constant C they can also present a singularity in r = C 2 . Neither of these solutions have a Newtonian limit. The black hole solution we study is analyzed between the singularity r = C 2 and a maximum radius r m . We find an associated mass, considering the related cosmological solution inside r = C 2 , and based on the holographic principle an entropy can be assigned to this asymptotic solution.

In this work we derive a generalized Newtonian gravitational force and show that it can account for the anomalous galactic rotation curves. We derive the entropy-area relationship applying the Feynman-Hibbs procedure to the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole. We obtain the modifications to the Newtonian gravitational force from the entropic formulation of gravity.

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In this work, we study a Friedmann–Robertson–Walker (FRW) universe derived from a modified entropy–area relationship. By applying the first law of thermodynamics to the so-called apparent horizon and a modified entropy–area relationship, we obtain a modified Friedmann equation. Solving this model for a perfect fluid with vanishing cosmological constant, we find that for early times, the scale factor is the same as that of an FRW universe. In the late-time regime, although the cosmological constant is zero, the asymptotic behavior of the scale factor is exponential, and therefore, we can identify an effective cosmological constant. The origin of the effective cosmological constant can be traced to the modifications of the entropy–area relation.