Equilibrium configurations in the dynamics of irrotational dust matter

Abstract

Irrotational dust solutions of Einstein's equations are suitable models to describe the general-relativistic aspects of the gravitational instability mechanism for the formation of cosmic structures. In this paper we study their state space by considering the local initial-value problem formulated in the covariant fluid approach. We consider a wide range of models, from homogeneous and isotropic to highly inhomogeneous irrotational dust models, showing how they constitute equilibrium configurations (invariant sets) of the dynamics. Moreover, we give the characterization of such configurations, which provides an initial-data characterization of the models under consideration.

Spin‐Spacetime Censorship

“…Other helpful choices of tensor S 𝜇𝜈 , some of which contain a natural spherical symmetry, can be proposed based on different stress-energy tensors (see, e.g., the survey in ref. [50]), and further generalizations, for instance to the Kaluza-Klein theory. [51,52] Replacing the stress-energy tensor T 𝜇𝜈 in EMFE with some hypothetical spherically symmetric tensor S 𝜇𝜈 carries significant consequences for classical physics; interestingly, it might soon be refuted in experiments: recent breakthroughs in measuring gravitational waves might bring soon the first observation of gravity waves induced by the electromagnetic stress-energy tensor (e.g., from newly born magnetars with extremely strong magnetic [53][54][55][56][57] ).…”

“…Other helpful choices of tensor S  , some of which contain a natural spherical symmetry, can be proposed based on different stress-energy tensors (see e.g. the survey in 41 ), and further generalizations, for instance to the Kaluza-Klein theory 42,43 .…”

Covariant fluid dynamics: a long wavelength approximation

“…As we said before, equation (19) tells us that E αβ is diagonal since σ αβ is diagonal. Then, we only need to compute the quantities E + and E − defined as in (21). The result is…”

“…The explicit form of these equations has been given in many places (see, e.g., [12][13][14]). In the case of IDMs they can be found in [21,22]. In order to set up a suitable framework for the application of the LWAS, here we will look at these equations from a different point of view than the usual one.…”