We investigate the effects to all orders in the Planck length from a generalized uncertainty principle (GUP) on black holes thermodynamics. We calculate the corrected Hawking temperature, entropy, and examine in details the Hawking evaporation process. As a result, the evaporation process is accelerated and the evaporation end-point is a zero entropy, zero heat capacity and finite non zero temperature black hole remnant (BHR). In particular we obtain a drastic reduction of the decay time, in comparison with the result obtained in the Hawking semi classical picture and with the GUP to leading order in the Planck length.PACS: 04.60.-m, 05.70.-a

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We investigate the effects to all orders in the Planck length, from a generalized uncertainty principle (GUP), on the thermodynamic parameters of radiating Schwarzschild black holes in a scenario with large extra dimensions. We show that black holes in this framework are hotter, have less degrees of freedom and decay faster compared to black holes in the Hawking picture and in the framework with GUP to leading order in the Planck length. Particularly, we show that the final stage of the evaporation process is a black hole remnant with zero entropy, zero heat capacity and non zero finite temperature. We finally compare our results with the ones obtained in the standard Hawking picture and with the generalized uncertainty principle to leading order in the Planck length.

It is expected that the implementation of minimal length in quantum models leads to a consequent lowering of Planck's scale. In this paper, using the quantum model with minimal length of Kempf et al [3], we examine the effect of the minimal lenght on the Casimir force between parallel plates.

We investigate the impact of the generalized uncertainty principle to all orders in the Planck length on thermodynamics parameters and on the stability of the Schwarzschild black hole within isothermal cavities. Using the Euclidean action formalism, the thermodynamics properties of the black hole are derived with important corrections compared to the standard case. In particular, we find that the black hole remnant is unstable and may decay to a stable large black hole via a phase transition of first order.

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In this paper we have studied the problem of scalar particles pair creation by an electric field in the presence of a minimal length. Two sets of exact solutions for the Klein Gordon equation are given in momentum space. Then the canonical method based on Bogoliubov transformation connecting the "in" with the "out" states is applied to calculate the probability to create a pair of particles and the mean number of created particles. The number of created particles per unit of time per unit of length, which is related directly to the experimental measurements, is calculated. It is shown that, with an electric field less than the critical value, the minimal length minimizes the particle creation. It is shown, also, that the limit of zero minimal length reproduces the known results corresponding to the ordinary quantum fields.

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