We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields. The absence or presence of either or both of these fields could restrict the equations of state of the underlying perfect fluid sources. As the representative of each family of solutions, we consider those spaces that include the cosmological term as a dark fluid source with the equation of state $p=-ρ= constant$.
We discuss the linear gravitoelectromagnetic approach used to solve Einstein equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the Solar System, where the approximation holds true. In particular, we discuss the analogy according to which Einstein equations can be written as Maxwell-like equations and focus on the definition of the gravitoelectromagnetic fields in non stationary conditions. Furthermore, we examine to what extent, starting from a given solution of Einstein equations, …
Recent researches suggest an analogy between the theory of general relativity (GR) and fluid dynamics. As a result of this analogy, the Navier-Stokes equations and Einstein field equations are the same, and it is possible to study the properties of space-time by using fluid mechanics. In this paper, we present a new model to describe gravitational phenomena by an inviscid and compressible fluid called space-time fluid (STF). The analogy method is used to obtain the gravity field of both static and rotating masses from the flow field of STF around static and rotating point sinks. In addition, e…
An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt equation describing stable stationary states of the model. We assume that the previous sources of quantum instability that have been discussed in the literature (particle production, and tunnelling to zero size) are absent. We then show, under rather general assumptions, that a further source of quantum instability prevents the existence of stationary states with…
The classic black hole mechanics and thermodynamics are formulated for stationary black holes with event horizons. Alternative theories of gravity of interest for cosmology contain a built-in time-dependent cosmological "constant" and black holes are not stationary. Realistic black holes are anyway dynamical because they interact with astrophysical environments or, at a more fundamental level, because of backreaction by Hawking radiation. In these situations the teleological concept of event horizon fails and apparent or trapping horizons are used instead. Even as toy models, black holes embed…
It is commonly known that the steady-state model of the universe was proposed and championed in a series of influential papers around mid-twenty century by Fred Hoyle, Hermann Bondi, and Thomas Gold. In contrast it is little known that, many years before, Albert Einstein briefly explored the same idea; that is of a 'dynamic steady state' universe. In 1931 during his first visit to Caltech, Einstein tried to develop a model where the universe expanded and where matter was supposed to be continuously created. This latter process was proposed by him to keep the matter density of the universe cons…
We construct the gravitating mass of an isolated composite system on asymptotically-flat spacetimes within conventional general relativity and investigate when this quantity is well defined. For stationary spacetimes, this quantity is known to exactly equal the physical (ADM) mass. However, it remains an open question whether these two masses are equal in the absence of a timelike Killing vector. This is especially apropos since our universe has an `origin' and hence no such Killing vector. Further, if these masses failed to agree then composite systems could behave as if they had a `dark comp…
The properties of light rays around compact objects surrounded by a plasma are affected by both strong gravitational fields described by a general-relativistic spacetime and by a dispersive and refractive medium, characterized by the density distribution of the plasma. We study these effects employing the relativistic Hamiltonian formalism under the assumption of stationarity and axisymmetry. The necessary and sufficient conditions on the metric and on the plasma frequency are formulated, such that the rays can be analytically determined from a fully separated Hamilton-Jacobi equation. We demo…
In stationary spacetimes global equilibrium states can be defined, applying the maximum entropy principle, by the introduction of local thermodynamic fields determined solely by geometry. As an example, we study a class of equilibrium states for a scalar field in Einstein's static universe, characterized by inhomogeneous thermodynamic properties and nonvanishing angular momentum.
