General Relativistic Spacetimes Research Articles

Probing the matter and dark energy sources in a viable Big Rip model of the Universe

Chevallier–Polarski–Linder (CPL) parametrization for the equation of state (EoS) of dark energy in terms of cosmic redshift or scale factor have been frequently studied in the literature. In this study, we consider cosmic time-based CPL parametrization for the EoS parameter of the effective cosmic fluid that fills the fabric of spatially flat and homogeneous Robertson–Walker (RW) spacetime in General Relativity. The model exhibits two worthy features: (i) It fits the observational data from the latest H(z) and Union 2.1 SN Ia compilations matching the success of ΛCDM model. (ii) It describes the evolution of the Universe from the matter-dominated phase to the recent accelerating phase similar to the ΛCDM model but leads to Big Rip end of the Universe contrary to the everlasting de Sitter expansion in the ΛCDM model. We investigate the matter and dark energy sources in the model, in particular, behavior of the dynamical dark energy responsible for the Big Rip end of Universe.

Quantum inequality for a scalar field with a background potential

Quantum inequalities are bounds on negative time-averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background potential (i.e., a mass that varies with spacetime position) in Minkowski space. We treat the potential as a perturbation and explicitly calculate the first-order correction to a quantum inequality with an arbitrary sampling function, using general results of Fewster and Smith. For an arbitrary potential, we give bounds on the correction in terms of the maximum values of the potential and its first three derivatives. The techniques we develop here will also be applicable to quantum inequalities in general spacetimes with small curvature, which are necessary to rule out exotic phenomena.

The Sagnac effect in conformal Weyl gravity

We investigate the Sagnac effect, representing the difference in travel time or phase shift observed for relativistic matter or light beams counter-propagating in a rotating interferometer. This is done for the Schwarzschild-like and Kerr-like vacuum solutions of conformal gravity which describe the field around a massive static and rotating object respectively, in the fourth order theory. To do this we employ the formal analogy between the Sagnac and Aharonov–Bohm effects that has been used earlier to study this effect in flat and curved spacetimes in general relativity. In particular we show that the linear term in the static metric of conformal gravity has a diminishing effect on the Sagnac time delay. Moreover using the expression for the Sagnac effect in the rotating Kerr-like spacetime, we show that the detection of the Weyl gravity contributions to the Sagnac time delay in the case of the Earth, lies beyond the capability of current experiments.

A Proposal for a Bohmian Ontology of Quantum Gravity

The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a quantum theory of space-time and therefore focus on loop quantum gravity. We conceive atoms of space, represented in terms of nodes linked by edges in a graph, as the primitive ontology of the theory and show how a non-local law in which a universal and stationary wave-function figures can provide an order of configurations of such atoms of space such that the classical space-time of general relativity is approximated. Although there is as yet no fully worked out physical theory of quantum gravity, we regard the Bohmian approach as setting up a standard that proposals for a serious ontology in this field should meet and as opening up a route for fruitful physical and mathematical investigations.

Scalar particle in general inertial and gravitational fields and conformal invariance revisited

The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen representation. Similarity of manifestations of conformal invariance for massless scalar and Dirac particles is proved. New exact Foldy-Wouthuysen Hamiltonians are derived for both massive and massless scalar particles in a general static spacetime and in a frame rotating in the Kerr field approximated by a spatially isotropic metric. The latter case covers an observer on the ground of the Earth or on a satellite and takes into account the Lense-Thirring effect. High-precision formulas are obtained for an arbitrary spacetime metric. General quantum-mechanical equations of motion are derived. Their classical limit coincides with corresponding classical equations.

Are quantization rules for horizon areas universal?

Doubts have been expressed on the universality of holographic/string-inspired quantization rules for the horizon areas of stationary black holes or the products of their radii, already in simple 4-dimensional general relativity. Realistic black holes are not stationary but time-dependent. Using two examples of 4D general-relativistic spacetimes containing dynamical black holes for at least part of the time, it is shown that the quantization rules (even counting virtual horizons) cannot hold, except possibly at isolated instants of time, and do not seem to be universal.

On the null trajectories in conformal Weyl gravity

In this work we find analytical solutions to the null geodesics around a black hole in theconformal Weyl gravity. Exact expressions for the horizons are found, and they depend onthe cosmological constant and the coupling constants of the conformal Weyl gravity. Then,we study the radial motion from the point of view of the proper and coordinate frames,and compare it with that found in spacetimes of general relativity. The angular motionis also examined qualitatively by means of an effective potential; quantitatively,the equation of motion is solved in terms of ℘-Weierstrass elliptic function.Thus, we find the deflection angle for photons without using any approximation,which is a novel result for this kind of gravity.

Making space for fundamentals

Frank Arntzenius says this book is not primarily concerned with overarching themes and that his main goal is to examine some loosely related topics. These all have to do with what theories of modern physics imply (or at least suggest) about the structure and contents of space and time. Each of the eight chapters focuses on a different potential implication and may be read independently. But the author does acknowledge that two overarching themes emerge. The first theme is that much of modern physics is best understood as positing novel spaces—physical objects distinct from ordinary 3-dimensional space (or the 4-dimensional space–time of relativity) while sharing some elements of geometric structure. The second is that ‘‘our knowledge of the structure of the world derives from one basic idea: the idea that the laws of the world are simple in terms of the fundamental objects and predicates’’. I will return to these themes after discussing the contents of each chapter. After a gentle introduction to the structure postulated for time by Newtonian and then relativistic physics, Arntzenius devotes the rest of Chapter 1 to explaining and then assessing the prospects of the view that time has no structure. Basically Julian Barbour’s view, the idea is that its metric, topological and order structure are not fundamental features of time, but rather derive from non-temporal relations among what happens at each moment. Using minimal mathematics, Arntzenius explains how to formulate Barbourian versions of Newtonian, special relativistic and general relativistic space–time theories. After showing why none of these is clearly empirically inferior to a standard version formulated within a relatively rich temporal structure, he presents and assesses objections to each. Barbourian general relativity faces the strongest such objections. Barbour himself expresses confidence that further development of his programme to encompass a combination of general relativity with quantum theory will overcome them. But Arntzenius declines to pursue his

Emergent spacetime according to effective field theory: From top-down and bottom-up

The framework of effective field theory (EFT) is a natural one in which to understand the claim that the spacetime of general relativity (GR) is an emergent low-energy phenomenon. I argue for a pragmatic understanding of EFT, given that the appropriate conception of emergence it suggests is necessarily epistemological in a sense. Analogue models of spacetime are examples of the top-down approach to EFT. They offer concrete illustrations of spacetime emergent within an EFT, and lure us toward a strong analogy between condensed matter physics and GR. I argue that we should be wary of this strong analogy, not least because the pragmatic view of EFT places limits on how much we can legitimately draw from it. On the other hand, programs that treat GR as an EFT and calculate quantum corrections are an example of the bottom-up approach and are explicitly pragmatic in character. I explore what we may learn about the nature of emergent spacetime by comparing these two approaches.

ENERGY–MOMENTUM DISTRIBUTIONS OF FIVE-DIMENSIONAL HOMOGENEOUS-ANISOTROPIC UNIVERSES

In this study, it has been investigated whether the energy and momentum can be localizable for five-dimensional homogeneous and anisotropic universes. In this connection, energy and momentum of five-dimensional Bianchi type-I, type-III and type-V spacetimes have been calculated in the framework of general relativity (GR) and teleparallel gravity (TG). Einstein, Bergmann–Thomson, Landau–Lifshitz, Papapetrou, Tolman and Møller energy–momentum complexes have been used to obtain these related quantities of given the spacetimes in GR, while Einstein, Bergmann–Thomson, Landau–Lifshitz and Møller prescriptions have been used to obtain these related quantities of the spacetimes in TG. It has been found that all of the energy and momentum distributions of five-dimensional Bianchi type-I spacetime are equal to zero in GR and TG. For five-dimensional Bianchi type-III and type-V spacetimes, Bergmann–Thomson, Einstein and Tolman energy and momentum components give the same results, however Møller, Landau–Lifshitz and Papapetrou energy–momentum distributions give different results in general relativity. Also, in TG, Bergmann–Thomson and Einstein energy and momentum components give the same results for the Bianchi type-III and type-V spacetimes, too. In this sense, it is seen that Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum descriptions of these spacetimes have been given same results in both theories, GR and TG.

Regular spherical dust spacetimes

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lemaître-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.

Geometrical origin of the cosmological constant

We show that the description of the space-time of general relativity as a diagonal four dimensional submanifold immersed in an eight dimensional hypercomplex manifold, in torsionless case, leads to a geometrical origin of the cosmological constant. The cosmological constant appears naturally in the new field equations and its expression is given as the norm of a four-vector $U$, i.e., ${\Lambda}=6g_{{\mu}{\nu}}U^{{\mu}}U^{{\nu}}$ and where U can be determined from the Bianchi identities. Consequently, the cosmological constant is space-time dependent, a Lorentz invariant scalar, and may be positive, negative or null. The resulting energy momentum tensor of the dark energy depends on the cosmological constant and its first derivative with respect to the metric. As an application, we obtain the spherical solution for the field equations. In cosmology, the modified Friedmann equations are proposed and a condition on ${\Lambda}$ for an accelerating universe is deduced. For a particular case of the vector $U$, we find a decaying cosmological constant ${\Lambda}\propto a(t)^{-6{\alpha}}$.

Charging axisymmetric space-times with cosmological constant

Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.

On Conformally Flat Almost Pseudo-Ricci Symmetric Spacetimes

We consider a conformally flat almost pseudo-Ricci symmetric spacetime. At first we show that a conformally flat almost pseudo-Ricci symmetric spacetime can be taken as a model of the perfect fluid spacetime in general relativity and cosmology. Next we show that if in a conformally flat almost pseudo-Ricci symmetric spacetime the matter distribution is perfect fluid whose velocity vector is the vector field corresponding to 1-form B of the spacetime, the energy density and the isotropic pressure are not constants. We also show that a conformally flat almost pseudo-Ricci symmetric spacetime is the Robertson-Walker spacetime. Finally we give an example of a conformally flat almost pseudo-Ricci symmetric spacetime with non-zero non-constant scalar curvature admitting a concircular vector field.

Negative Refraction of Far-Infrared Radiation in Quartz

A new design concept for optical devices comes from the mathematical view of space-time in general relativity. The desired optical path is determined by coordinate transformations.

On the Description of Motion of a Quantum Particle in the Classical Gauge Field in the Language of Stochastic Mechanics

An equation of Newton–Nelson type on the vector bundle over space-time of General Relativity is introduced and investigated. The equation is interpreted as the one describing the motion of a quantum particle in the classical gauge field in the language of stochastic mechanics.

Epistemic Primacy vs. Ontological Elusiveness of Spatial Extension: Is There an Evolutionary Role for the Quantum?

A critical re-examination of the history of the concepts of space (includ- ing spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlight- ing the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein "giving up the extensional continuum ... is like to breathe in airless space"). On the other hand, Planck's discovery of the atomization of action leads to the fundamental recognition of an ontology of non-spatial, abstract enti- ties (Quine) for the quantum level of reality (QT), as distinguished from the nec- essarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck's constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: "Wahrend also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, fur dessen Existenz seine Beobachtung vollig irrelevant war, behandelt die Quantentheorie Vorgange, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phanomene auf- leuchten, und uber die in der zwischenzeit anschaulische physikalische Aussagen sin- loss sind". An admittedly speculative, hazardous conjecture is then advanced con- cerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly,

Aharonov–Bohm effect in a draining bathtub vortex

We study planar waves in a circulating, draining fluid flow, which: (i) exhibit an analogue of the Aharonov–Bohm (AB) effect in Quantum Mechanics; (ii) obey a Klein–Gordon equation on an ‘effective spacetime’ which resembles the Kerr spacetime of General Relativity; and (iii) may be observed in the laboratory using gravity waves in a shallow basin. We describe a modified AB effect which depends on two dimensionless parameters, associated with the circulation α and draining β rates; we call this the ‘αβ effect’. We show that the αβ effect is inherently asymmetric even in the low-frequency limit, and that it leads to novel interference patterns which carry the signature of both rotation and absorption.

The deformable universe

The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.

Minimal conditions for the existence of a Hawking-like flux

We investigate the minimal conditions that an asymptotically flat general relativistic spacetime must satisfy in order for a Hawking-like Planckian flux of particles to arrive at future null infinity. We demonstrate that there is no requirement that any sort of horizon form anywhere in the spacetime. We find that the irreducible core requirement is encoded in an approximately exponential "peeling" relationship between affine coordinates on past and future null infinity. As long as a suitable adiabaticity condition holds, then a Planck-distributed Hawking-like flux will arrive at future null infinity with temperature determined by the e-folding properties of the outgoing null geodesics. The temperature of the Hawking-like flux can slowly evolve as a function of time. We also show that the notion of "peeling" of null geodesics is distinct, and in general different, from the usual notion of "inaffinity" used in Hawking's definition of surface gravity.