Cosmological energy in a thermo-horizon and the first law

We consider a cosmological horizon, named thermo-horizon, to which are associated a temperature and an entropy of Bekenstein-Hawking and which obeys the first law for an energy flow calculated through the corresponding limit surface. We point out a contradiction between the first law and the definition of the total energy contained inside the horizon. This contradiction is removed when the first law is replaced by a Gibbs' equation for a vacuum-like component associated to the event horizon

Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime

We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.Comment: 6 pages Latex, to appear in General Relativity and Gravitatio

Entropy-Corrected Holographic Dark Energy

The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called ``entropy-corrected holographic dark energy'' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called ``entropy-corrected agegraphic dark energy'' (ECADE).Comment: 11 pages, 2 tables, revtex4; v2: references adde

Covariant Kolmogorov equation and entropy current for the relativistic Ornstein-Uhlenbeck process

The relativistic Ornstein-Uhlenbeck Process (ROUP), which is a toy-model of relativistic irreversible phenomena, is studied statistically in an explicitly covariant manner. An 8-dimensional phase space is introduced (four dimensions for space-time coordinates, and four dimensions for the 4-momentum coordinates), on which `extended' probability distributions are defined (the usual probability distribution is recovered as their restriction to the mass shell). An explicitly covariant Kolmogorov equation is derived for these `extended' probability distributions. The whole formalism is used to introduce a 4-current of conditional entropy and prove that the 4-divergence of this 4-current is always positive. This constitutes an H-theorem for the ROUP

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar