Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved by the vanishing of commutative torsion.Finally, the noncommutative corrections to the action are computed up to second order. * Electronic address: compean@fis.cinvestav.mx † Electronic address: octavio@ifug3.ugto.mx ‡ Permanent address:

By implementing a genetic algorithm we search for stable vacua in Type IIB nongeometric flux compactification on an isotropic torus with orientifold 3-planes. We find that the number of stable dS and AdS vacua are of the same order. Moreover we find that in all dS vacua the multi-field slow-roll inflationary conditions are fulfilled. Specifically we observe that inflation is driven by the axio-dilaton and the Kähler moduli. We also comment on the existence of one stable dS vacuum in the presence of exotic orientifolds. 1 cesaredas@fisica.ugto.mx 2 luisreydb@fisica.ugto.mx 3 oloaiza@fisica.ugto.mx 4 msabido@fisica.ugto.mx 1 arXiv:1302.0529v3 [hep-th] 10 Nov 2013Recently, there has been a huge interest in the search for classical de Sitter (dS) vacua within the context of superstring compactification. In the last few years, some constraints have been imposed by estimating the contributions to the effective scalar potential from each of the components that play a role in the compactification process. For instance, there is a no-go theorem, indicating that the existence of dS vacua in compactifications threaded with standard NS-NS and R-R fluxes is incompatible with inflation[1]. Recently, in the context of these standar type IIB compactifications, it has been shown the existence of classical dS vacua in specific and suitable D-brane configurations with orientifold planes [2][3][4]. On the other hand, further studies show that by considering a bigger set of allowed fluxes and more general structures for the internal geometry, it is possible to find some stable dS vacua [5][6][7][8][9][10][11][12][13][14][15][16][17][18] although their compatibility with inflation has not been studied in detail. In this work we present some stable dS vacua consistent with inflation.There are some essential ingredients string compactifications should contain to enhance the chances of finding stable dS vacua: a negative curved internal manifold and a small number of moduli fields [19][20][21].Here, we take the approach consisting in computing the scalar potential from a superpotential with all the above features. Specifically, a compactification on a negatively curved manifold with a superpotential W that depends at tree level on a small set of moduli is achieved by considering a type II string compactification on a six-dimensional isotropic torus in the presence of non-geometric fluxes [22][23][24][25]. (2.12) where J = (j±, k) and M = (m±). The Bianchi identity Q · H 3 = 0 decomposes as A M J · A M J = (A M J ) δ (A M J ) λ η δλ = 0, (2.13) for j = j , diag(η) = {−1, 1, 1, 1} and for the combinations M = (0+), J = {(2, 0+), (1, 3−)} and M = (3−), J = {(1, 2−), (2, 1+)}, while Q · Q = 0 decomposes as,

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 possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. This gives us a way towards the description of noncommutative gravitational instantons as well as noncommutative local gravitational anomalies. * Electronic address: compean@fis.cinvestav.mx † Electronic address: octavio@ifug3.ugto.mx; Permanent adress:

Several eigenvalue equations that could describe quantum black holes have been proposed in the canonical quantum gravity approach. In this paper, we choose one of the simplest of these quantum equations to show how the usual Feynman's path integral method can be applied to obtain the corresponding statistical properties. We get a logarithmic correction to the Bekenstein-Hawking entropy as already obtained by other authors by other means.