Motivated by quantum mechanical corrections to the Newtonian potential, which can be translated into an -correction to the g00 component of the Schwarzschild metric, we construct a quantum mechanically corrected metric assuming −g00 = g rr . We show how the Bekenstein black hole entropy S receives its logarithmic contribution provided the quantum mechanical corrections to the metric are negative. In this case the standard horizon at the Schwarzschild radius rS increases by small terms proportional to and a remnant of the order of Planck mass emerges. We contrast these results with a positive correction to the metric which, apart from a corrected Schwarzschild horizon, leads to a new purely quantum mechanical horizon. PACS numbers: Valid PACS appear here I. INTRODUCTIONThe full theory of Quantum Gravity is one of the last unsolved challenges in fundamental science and is still eluding us. Nevertheless, some effects of Quantum Theory do enter the context of the theory of Quantum Gravity and can be handled in a rigorous way without the knowledge of the full fledged theory. Such is the case of the Hawking radiation [1] and/or the Unruh effect [2]. Apart from these paradigms there are some other interesting quantum effects related to gravity like the absence of stable orbits of fermions around a black hole [3], the quantum correction to the Bekenstein entropy S of black holes and of other black objects using different approaches to Quantum Gravity [4-33] and the quantum correction to the Newtonian potential or metrics [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] (for some applications of the new corrections see [53][54][55]). Indeed, the results regarding the corrected Newtonian potential Φ spread over a period of the last forty five years starting with the early seventies whereas the corrections to S are a relative new undertaking. Whichever model one uses it turns out that S receives corrections proportional to the logarithm of the black hole area and, in some models, also proportional to the square root of this quantity. This is also the finding of our approach starting from a different context. We will make a connection between the -corrected metric and the quantum mechanical corrections to the entropy. We will construct our quantum mechanically corrected metric by demanding (i) that it reproduces the corrected Newtonian limit, (ii) that it reproduces the standard result for the entropy of black hole including, in addition, the corrections which are similar to results established elsewhere and (iii) that it passes some consistency checks regarding the geodesic motion of a test particle moving in this metric. Point (i) which has to do with weak gravity, can be easily accommodated by invoking the classical connection between the g 00 metric component and the Newtonian potential. The second point requires the determination of the horizons and probes into the strong regime of gravity. In principle, we cannot infer the strong gravity effects from results zeroing around the weak regime as...

It has been known for some time that the cosmological Friedmann equation deduced from general relativity can also be obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop quantum gravity or non-commutative geometry.

We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor R(t) which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a cosmological constant. The previous results are contrasted with the cosmology with nonzero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann-Lamaître-Robertson-Walker metric. To this end we use a version of the energy-momentum tensor from the Müller-Israel-Stewart theory which leads to causal Navier-Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.

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We consider a Fermion in the presence of a rotating black hole immersed in a universe with positive cosmological constant. After deriving new formulae for the event, Cauchy and cosmological horizons we adopt the Carter tetrad to separate the aforementioned equation into a radial and angular equation. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that can be interpreted as the square root of the squared total angular momentum operator. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.