We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix A(u) is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer "power-law type"), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile A(u) ∼ u −2 , the scale invariance of the latter reflecting the power-law behaviour of the singularities. 1
We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution of the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.
We study string-gas cosmology in dilaton gravity, inspired by the fact that it naturally arises in a string theory context. Our main interest is the thermodynamical treatment of the stringgas and the resulting implications for the cosmology. Within an adiabatic approximation, thermodynamical equilibrium and a small, toroidal universe as initial conditions, we numerically solve the corresponding equations of motions in two different regimes describing the string-gas thermodynamics: (i) the Hagedorn regime, with a single scale factor, and (ii) an almost-radiation dominated regime, which includes the leading corrections due to the lightest Kaluza Klein and winding modes, with two scale factors. The scale factor in the Hagedorn regime exhibits very slow time evolution with nearly constant energy and negligible pressure. By contrast, in case (ii) we find interesting cosmological solutions where the large dimensions continue to expand and the small ones are kept undetectably small.
We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u −2 -behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic power-law singularities of this type the oscillator frequencies of the resulting homogeneous singular plane wave turn out to lie in a range which is known to allow for an analytic extension of string modes through the singularity. The discussion is phrased in terms of the recently obtained covariant characterisation of the Penrose limit; the relation with null geodesic deviation is explained in detail. 1
We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is brokenà la Scherk-Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density ρ(R), or cosmological constant. For SS twists different from Z 2 we always find, for both orbifolds and orientifolds, a monotonic ρ(R) < 0, eventually driving the system to a tachyonic instability. For Z 2 twists, orientifold models can have a different behavior, leading either to a runaway decompactification limit or to a negative minimum at a finite value R 0 . The last possibility is obtained for a 4D chiral orientifold model where a more accurate but yet preliminary analysis seems to indicate that R 0 → ∞ or towards the tachyonic instability, as the dependence on the other geometric moduli is included.
a b s t r a c tOver the last 25 years solar power plants based on parabolic trough concentrators have been developed for the commercial power industry. On the other hand, in recent years, a way to harness the solar energy is to cogenerate through Concentrated Solar Power (CSP) technology coupled to an Organic Rankine Cycle (ORC) with potential applications to industrial processes. In this work we present a study of a small CSP plant coupled to an ORC with a novel configuration since useful energy is directly used to feed the power block and to charge the thermal storage. In order to analyze this novel configuration we consider a case study with cogeneration applied to textile industrial process at medium temperature. It turns out that this configuration reduces the size of the thermal storage disposal. The performance of the solar power plant was simulated with TRNSYS to emulate real operating conditions. We show the design, study and simulation results, including the production and efficiency curves for our load profile. Our results show that our system is a promising option for applications to medium temperature processes where electrical and heat generation is required.
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