Related papers: The vacuum conservation theorem
The experimental data, as well as theoretical considerations allow (and, in some cases, require) the Universe at present to rest in a false vacuum, whose approximate stability imposes constraints on the model parameters. Under very general…
We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include…
In quantum theory the vacuum is defined as a state of minimum energy that is devoid of particles but still not completely empty. It is perhaps more surprising that its definition depends on the geometry of the system and on the trajectory…
The general thermodynamic analysis of the quantum vacuum, which is based on our knowledge of the vacua in condensed-matter systems, is consistent with the Einstein earlier view on the cosmological constant. In the equilibrium Universes the…
Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…
We consider phase transitions and their contributions to vacuum energy in the manifestly local theory of vacuum energy sequestering. We demonstrate that the absence of instabilities imposes constraints on the couplings of gravitating and…
In this article, we extend a construction of [6] to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form $M \# M$, where $M$ is…
The highly non-trivial structure of the $\theta$--vacuum encodes many of the fundamental properties of gauge theories. In particular, the response of the vacuum to the $\theta$--term perturbation is sensitive to the existence of…
Based on some observations, the apparent energy, associated with gravity, of vacuums is defined, with that of normal vacuums to be zero and that of the vacuums losing some energy to be negative. An important application of the energy is its…
It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the…
Increasing improvements in the independent determinations of the Hubble constant and the age of the universe now seem to indicate that we need a small non-vanishing cosmological constant to make the two independent observations consistent…
Under the hypothesis that the cosmological constant vanishes in the true ground state with lowest possible energy density, we argue that the observed small but finite vacuum-like energy density can be explained if we consider a theory with…
A direct very simple proof that there can be no closed trapped surfaces (ergo no black hole regions) in spacetimes with all curvature scalar invariants vanishing is given. Explicit examples of the recently introduced ``dynamical horizons''…
Using Heisenberg's uncertainty principle it is shown that the gravitational stability condition for a crystalline vacuum cosmic space implies to obtain an equation formally equivalent to the relation first used by Gamow to predict the…
In a previous paper [9], we proved the following singularity theorem applicable to cosmological models with a positive cosmological constant: if a four-dimensional spacetime satisfying the null energy condition contains a compact Cauchy…
We prove that compact Cauchy horizons in a smooth spacetime satisfying the null energy condition are smooth. As an application, we consider the problem of determining when a cobordism admits Lorentzian metrics with certain properties. In…
We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational…
A diverse set of observations now compellingly suggest that Universe possesses a nonzero cosmological constant. In the context of quantum-field theory a cosmological constant corresponds to the energy density of the vacuum, and the wanted…
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…
A variant of the divergence theory for vacuum-condensation developed in a previous communication is analyzed from the viewpoint of a 'time' asymmetric law in vacuum. This law is found to establish a substantial distinction between…