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We apply the thermodynamical model of the cosmological event horizon of the spatially flat FLRW metrics to the study of the recent accelerated expansion phase and to the coincidence problem. This model, called "ehT model" hereafter, led to a dark energy (DE) density Λ varying as r −2 , where r is the proper radius of the event horizon. Recently, another model motivated by the holographic principle gave an independent justification of the same relation between Λ and r. We probe the theoretical results of the ehT model with respect to the SnIa observations and we compare it to the model deduced from the holographic principle, which we call "LHG model" in the following.Our results are in excellent agreement with the observations for H0 = 64kms −1 M pc −1 , and Ω 0 Λ = 0.63 +0.1 −0.01 , which leads to q0 = −0.445 and zT ≃ 0.965.

We numerically integrate the semiclassical equations of motion for spherically symmetric Einstein-Maxwell theory with a dilaton coupled scalar field and look for zero temperature configurations. The solution we find is studied in detail close to the horizon and comparison is made with the corresponding one in the minimally coupled case.

We derive the Teixeira, Wolk and Som method [1], for obtaining electrostatic solutions from given vacuum solutions, in its inverse form. Then we use it to obtain the geometrical mass M S in the Schwarzschild spacetime, and we find M 2 S = M 2 − Q 2 , where M and Q are, respectively, the mass and charge parameters of the Reissner-Nordström spacetime. We compare M S to the corresponding active gravitational mass and mass function. *