Reasonable Spacetimes Research Articles

Null Fluid Collapse in Rastall Theory of Gravity

AbstractA Vaidya spacetime is considered for gravitational collapse of a type II fluid in the context of the Rastall theory of gravity. For a linear equation of state for the fluid profiles, the conditions under which the dynamical evolution of the collapse can give rise to the formation of a naked singularity are examined. It is shown that depending on the model parameters, strong curvature, naked singularities would arise as exact solutions to the Rastall's field equations. The allowed values of these parameters satisfy certain conditions on the physical reliability, nakedness, and the curvature strength of the singularity. It turns out that Rastall gravity, in comparison to general relativity, provides a wider class of physically reasonable spacetimes that admit both locally and globally naked singularities.

Globally hyperbolic spacetimes can be defined without the ‘causal’ condition

Reasonable spacetimes are non-compact and of dimension larger than two. We show that these spacetimes are globally hyperbolic if and only if the causal diamonds are compact. That is, there is no need to impose the causality condition, as it can be deduced. We also improve the definition of global hyperbolicity for the non-regular theory (non C1,1 metric) and for general cone structures by proving the following convenient characterization for upper semi-continuous cone distributions: causality and the causally convex hull of compact sets is compact. In this case the causality condition cannot be dropped, independently of the spacetime dimension. Similar results are obtained for causal simplicity.

Catalyst ignition and extinction: A microkinetics-based bifurcation study of adiabatic reactors for oxidative coupling of methane

Understanding ignition and extinction behavior is of crucial importance for oxidative coupling of methane (OCM). Therefore, for the first time the bifurcation behavior of OCM has been investigated while considering both homogeneous gas phase reactions and heterogeneous reactions using a detailed microkinetic model. Three different adiabatic reactor models are considered: a plug flow reactor (PFR), a continuously stirred tank reactor (CSTR) and a lumped thermal reactor (LTR) model. The latter represents the limiting case with zero backmixing (cf. PFR behavior) for species and perfect thermal backmixing (cf. CSTR behavior). For homogeneous processes this reactor type could for example be realized by adding a high thermal conductivity inert to the reactor tubes, for catalytic processes a high thermal conductivity catalyst could be used.The bifurcation behavior in these reactor types is compared with a focus on methane conversion, C2 yields and their dependence on operating conditions such as inlet composition, inlet temperature and space time. Steady state multiplicity is observed for adiabatic CSTR and LTR models. This multiplicity of steady states is not observed for isothermal reactor models, indicating that it is caused solely by thermal backmixing and is not related to chemical feedback features such as autocatalysis. The start-up procedures or initial conditions determine the actual steady state that is obtained. Among the three investigated reactor types, a LTR shows the highest product yields and the lowest extinction temperatures, which allows autothermal operation at a much lower inlet temperature compared to a PFR and CSTR. For OCM without catalyst, autothermal operation on the ignited branch at ambient inlet temperatures and reasonable space times is only possible by using methane-to-oxygen ratios below 3 leading to low selectivities. For catalytic OCM compared to OCM without catalyst, the range for autothermal operation is much broader and it is much easier to find feasible operating conditions allowing autothermal operation at ambient inlet temperatures.By operating a LTR on the ignited branch at ambient inlet temperature of 300 K, methane-to-oxygen ratio CH4:O2 = 6, space time V/FCH4,0 = 0.02 s, bulk density of Sn-Li/MgO = 1000 kgcat/m3 and pressure P = 1 bar, overall C2 selectivities (i.e. sum of ethane, ethylene and acetylene selectivity) of 80% can be obtained at methane conversions as high as 30%.

The attached point topology of the abstract boundary for spacetime

Singularities play an important role in general relativity and have been shown to be an inherent feature of most physically reasonable spacetimes. Despite this, there are many aspects of singularities that are not qualitatively or quantitatively understood. The abstract boundary construction of Scott and Szekeres has proven to be a flexible tool with which to study the singular points of a manifold. The abstract boundary construction provides a ‘boundary’ for any n-dimensional, paracompact, connected, Hausdorff, C∞ manifold. Singularities may then be defined as entities in this boundary—the abstract boundary. In this paper a topology is defined, for the first time, for a manifold together with its abstract boundary. This topology, referred to as the attached point topology, thereby provides us with a description of how the abstract boundary is related to the underlying manifold. A number of interesting properties of the topology are considered, and in particular, it is demonstrated that the attached point topology is Hausdorff.

What Is a Physically Reasonable Space-Time?

Cosmologists often use certain global properties to exclude “physically unreasonable” cosmological models from serious consideration. But, on what grounds should these properties be regarded as physically unreasonable if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

On the existence of time in non-singular spacetimes

I show that a physically reasonable spacetime (i.e. a chronological spacetime in which the null convergence and the null genericity conditions hold) which is null geodesically complete admits a time function.

Is spacetime hole-free?

Here, we examine hole-freeness—a condition sometimes imposed to rule out seemingly artificial spacetimes. We show that under existing definitions (and contrary to claims made in the literature) there exist inextendible, globally hyperbolic spacetimes which fail to be hole-free. We then propose an updated formulation of the condition which enables us to show the intended result. We conclude with a few general remarks on the strength of the definition and then formulate a precise question which may be interpreted as: Are all physically reasonable spacetimes hole-free?

A 2D model of causal set quantum gravity: the emergence of the continuum

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this ‘entropy problem’ in a model of causal set quantum gravity corresponding to a discretization of 2D spacetimes. Using results from the theory of partial orders we show that, in the large volume or continuum limit, its partition function is dominated by causal sets which approximate to a region of 2D Minkowski space. This model of causal set quantum gravity thus overcomes the entropy problem and predicts the emergence of a physically reasonable geometry.

Eternal inflation and the initial singularity.

It is shown that a physically reasonable spacetime that is eternally inflating to the future must possess an initial singularity.

Observer fields in Weylian spacetime models

Resting upon the Ehlers-Pirani-Schild axiomatic approach to spacetime theory, the author considers Weyl manifolds as reasonable spacetime models. He defines and discuss several concepts associated with a timelike vector field (=observer field=reference frame) on such a spacetime model. In particular, he derives propagation equations for rotation, expansion and shear of V, prove some kinematical vorticity theorems and present a new method how to measure length curvature operationally. As important mathematical tools, he uses the orthogonal decomposition of the Lie derivative and of the covariant derivative; the latter is the Weylian generalization of the Fermi-Walker derivative.

The existence of singularities in general relativity despite isolated failures of geodesic focusing

A key ingredient of the singularity theorems of general relativity is that geodesics will focus under certain conditions. While the conditions that are generally imposed are fairly weak and can be expected to hold for most geodesics in any reasonable space-time, the question arises of what the consequences might be if these conditions happen to fail to hold for isolated geodesics. The standard singularity theorems in the literature do not cover such cases. A result is presented here that demonstrates that a singularity will exist even in cases where geodesic focusing does not occur for some geodesics.

The Goldstone Theorem in a Curved Spacetime

The Goldstone theorem for a quantum field theory in Minkowski space is well known.ll· 2' But what happens, if we depart from flat spacetime and describe quantum field theories in a curved space? It has been conjectured8' that for the de Sitter space with symmetry group S0(2.3) the Goldstone theorem holds just as in Minkowski space, only that the Goldstone particle acquires a small mass. However, this model, with closed timelike geodesics, and hence the impossibility of time-ordering/' cannot serve as a physically reasonable spacetime. On the other hand, the (1+4) de Sitter space4> with symmetry group S0(1.4) could well be viewed as revealing something of the global structure of the world, which locally (in the limit of vanishing curvature) gives back the flat Minkowski spacetime. The significance of both models lies in the fact that S0(2.3) and S0(1.4) are the only groups which can be contracted into the connected component of the Poincare group S0(1.3)Q9T4• Thus we want to investigate in the following the nature of the Goldstone theorem in (1+4) de Sitter space. Scalar fields r/J in de Sitter space are characterized by the eigenvalue equation of the Casimir operator 11 of SO(l.4) ,4>