Related papers: Geodesically complete cyclic cosmologies and entro…
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…
We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI$_{h}$ models that admit an isotropic…
We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two different definitions…
Let $S_{g,n}$ be a surface of genus $g $ with $n$ marked points. Let $X$ be a complete hyperbolic metric on $S_{g,n}$ with $n$ cusps. Every isotopy class $[\gamma]$ of a closed curve $\gamma \in \pi_{1}(S_{g,n})$ contains a unique closed…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
Fluid cosmologies are consistent with the generally accepted observational evidence during intermediate and late times, and they need not have singular behavior in primordial times. A general form for fluid cosmology consistent with…
We analyze the validity of the generalized covariant entropy bound near the apparent horizon of isotropic expanding cosmological models. We encounter violations of the bound for cosmic times smaller than a threshold. By introducing an…
The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational…
We show that, in the presence of a string gas, simple higher-derivative modifications to the effective action for gravity can lead to bouncing and cyclic cosmological models. The modifications bound the expansion rate and avoid…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Matter agglomeration mesoscopic phenomena of irreversible type are well described by nonequilibrium thermodynamics formalism. The description assumes that the thermodynamic (internal) state variables are in local equilibrium, and uses the…
We develop a geometric framework for irreversible transport phenomena in which macroscopic evolution equations arise from the combined structure of a thermodynamic state metric and an Onsager-based dissipation metric. The construction…
We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…
In this paper we discuss models satisfying the limiting curvature condition. For this purpose we modify the Einstein-Hilbert action by adding a term which restricts the growth of curvature. We analyze cosmological solutions in such models.…
A perfect fluid, spatially flat cosmology in a $f(T)$ model, derived from a recently proposed general Born-Infeld type theory of gravity is studied. Four dimensional cosmological solutions are obtained assuming the equation of state…
We study Born-Infeld gravity coupled to a static, nonrotating electric field in $2+1$ dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another…
We show that an analytical continuation of the Vuorio solution to three-dimensional topologically massive gravity leads to a two-parameter family of black hole solutions, which are geodesically complete and causally regular within a certain…
The Cyclic Model is a radical, new cosmological scenario which proposes that the Universe undergoes an endless sequence of epochs which begin with a `big bang' and end in a `big crunch.' When the Universe bounces from contraction to…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…
The problem of reproducing dark energy effects is reviewed here with particular interest devoted to cosmography. We summarize some of the most relevant cosmological models, based on the assumption that the corresponding barotropic equations…