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Register a new userOn the first $G_1$ stiff fluid spike solution in General Relativity
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Using the Geroch transformation we obtain the first example of an exact stiff fluid spike solution to the Einstein field equations in a closed form exhibiting a spacelike $G_1$ group of symmetries (i.e., with a single isometry). This new solution is of Petrov type I and exhibits a spike crossing which persists to the past, which allows us to better understand spike crossings in the context of structure formation.
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In this paper we expand upon our previous work [1] by using the entire family of Bianchi type V stiff fluid solutions as seed solutions of the Stephani transformation. Among the new exact solutions generated, we observe a number of important physical phenomena. The most interesting phenomenon is exact solutions with intersecting spikes. Other interesting phenomena are solutions with saddle states and a close-to-FL epoch.
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers I and II and focuses on the fluid flow and the associated 1+3 threading congruence, used jointly with the 3+1 foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.
We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding Tolman-Oppenheimer-Volkoff (TOV) equations in covariant form in the isotropic, non-interacting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
We present results about the effect of the use of a stiffer equation of state, namely the ideal-fluid $Gamma=2.75$ ones, on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change on the critical value of the instability parameter $beta$ for the emergence of the instability when the adiabatic index $Gamma$ is changed from 2 to 2.75 in order to mimic the behavior of a realistic equation of state. In particular, we show that the threshold for the onset of the bar-mode instability is reduced by this change in the stiffness and give a precise quantification of the change in value of the critical parameter $beta_c$. We also extend the analysis to lower values of $beta$ and show that low-beta shear instabilities are present also in the case of matter described by a simple polytropic equation of state.
This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of General Relativity will be described. Then, the present situation will be reviewed presenting a number of examples. The opportunities given by astrophysical and astrometric observations will be shortly discussed. Coming to terrestrial experiments the attention will be specially focused on ringlasers and a dedicated experiment for the Gran Sasso Laboratories, named by the acronym GINGER, will be presented. Mention will also be made of alternatives to the use of light, such as particle beams and superfluid rings.
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