Spacetime Structure Explored by Elementary Particles : Microscopic Origin for the Riemann-Cartan Geometry

The central conceptual idea of the contemporary theory of general relativity--or geometrodynamics--is the identification of matter with the structure of space-time. No entities foreign to space-time, like masses, charges, or independent fields are needed, and physics thus becomes identical with the geometry of space-time. This idea implies a philosophical description of the universe that is monistic and organic, characterized by an all-encompassing interdependence of events. Moreover, it is an idea with deep roots in the history of philosophy. For these reasons, the author of this important study strives to clarify these philosophical and historical issues before proceeding to the details of the physical theory of geometrodynamics.Graves develops a general philosophical framework of realism, asserting that scientific theories have ontological import in determining the real structure of the world, and in particular that models play a central role as ontological hypotheses. He introduces two factors, the empiricist error and the logical errors that he feels have contributed to past misinterpretations of the nature of reality that were based on general relativity theory.The historic continuities that join the metaphysics of Plato and Descartes with the monistic, organic nature of geometrodynamics are contrasted with the latter's radical break with the Newtonian or atomistic worldview which is predicated on a basic separation between matter and space. The Newtonian independence and distinctness of objects is at the polar extreme from their Einsteinian interdependence and continuity.In discussing the physical principles of relativity, the author begins with a review of Einstein's original formulation (classical general relativity) and the significance of its basic assumptions and equations. He then presents the remarkable recent developments in geometrodynamics, which allow the program of identifying matter with space-time to be carried further than even Einstein suspected possible. The surprising discovery that electromagnetism can be incorporated into geometrodynamics without modifying Einstein's original equations appears to be formally correct, but reliance on multiply-connected topologies (wormholes) to represent charge raises various unresolved questions.Graves concludes that the present language of physics, like that of everyday life, is based on concepts of independence and separation, and that a wholly new language may be needed to describe the world in terms of geometrodynamics, in which space-time appears as the only substance, with curvatures as its attributes, and in which objects have no absolute individuality, distinctness, or location.

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves.

This thesis presents recent research into analytic topics in the classical theory of General Relativity. It is a thesis in two parts. The first part features investigations into the spectrum of perturbed, rotating black holes. These include the study of near horizon perturbations, leading to a new generic frequency mode for black hole ringdown; an treatment of high frequency waves using WKB methods for Kerr black holes; and the discovery of a bifurcation of the quasinormal mode spectrum of rapidly rotating black holes. These results represent new discoveries in the field of black hole perturbation theory, and rely on additional approximations to the linearized field equations around the background black hole. The second part of this thesis presents a recently developed method for the visualization of curved spacetimes, using field lines called the tendex and vortex lines of the spacetime. The works presented here both introduce these visualization techniques, and explore them in simple situations. These include the visualization of asymptotic gravitational radiation; weak gravity situations with and without radiation; stationary black hole spacetimes; and some preliminary study into numerically simulated black hole mergers. The second part of thesis culminates in the investigation of perturbed black holes using these field line methods, which have uncovered new insights into the dynamics of curved spacetime around black holes.

In general relativity, an inertial frame can only be established in a small region of spacetime, and local inertial frames are mathematically represented by a tetrad field in gravity. The tetrad field is not unique due to the freedom to perform Lorentz transformations in local inertial frames, and there exists freedom to choose the local inertial frame at each spacetime point. The local Lorentz transformations are known as non-Abelian gauge transformations for the tetrad field, and to fix the gauge freedom corresponding to the Lorentz gauge ∂μAμ=0 and the Coulomb gauge ∂iAi=0 in electrodynamics, the Lorentz gauge and Coulomb gauge for tetrad fields are proposed in the present work. Moreover, properties of the Lorentz gauge and the Coulomb gauge for tetrad fields are discussed to show their similarities to those in electromagnetic fields.

Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. The metric of the 5-dimensional affine spacetimes governed by the Bargmann groups considered in Paper I (central extensions of the Poincaré and Galilei groups) is generalized to curved spacetime by extending the usual 1 + 3 (traditionally ‘3 + 1’) formalism of general relativity on 4-dimensional spacetime to a 1 + 3 + 1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1 + 3 formalism. Spacetime tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid are presented, along with their 1 + 3 + 1 decompositions; these reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force). These spacetime laws of motion for particles and fluids also suggest that a strong-field Galilei general relativity would involve a limit in which not only c→∞ but also G→∞, such that G/c2 remains constant.

This research is motivated by developments in modern physics which show that black holes, which in classical general relativity are considered the most stable and permanent entities in the universe, actually undergo evaporation through Hawking radiation. This phenomenon has profound philosophical implications regarding the nature of physical existence, the status of information, the structure of space-time, and the direction of cosmological time. This study aims to analyze the ontological and epistemological implications of black hole evaporation in the context of micro-macro relationships, relational ontology, and the concept of time as an emergent phenomenon. This study uses a qualitative method based on literature review and conceptual analysis by integrating the perspectives of theoretical physics, philosophy of science, and modern cosmology. The results of this study show that black hole evaporation confirms that there are no physical entities that are absolute and permanent. Physical existence is more accurately understood as a relational phenomenon that depends on the interaction between space-time geometry, quantum fluctuations, and cosmic thermodynamic processes. Furthermore, the black hole information paradox can be understood as a limitation of human epistemological description, rather than an ontological loss of physical reality. This research also confirms that the direction of time is a consequence of the emergence of increased entropy in the universe. The novelty of this research lies in the integration of the phenomenon of black hole evaporation with a structural-relational ontological approach to explain physical reality as a dynamic and emergent process.

Classical spinning particles interacting with external gravitational fields

We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in mathcal{N} = 8 supergravity. We propose criteria, generalizing explicit calculations at next-to-leading order, for determining the terms in amplitudes that contribute to local observables. For general relativity, we construct the relevant classical integrand through generalized unitarity in two distinct ways, (1) in a heavy-particle effective theory and (2) in general relativity minimally-coupled to scalar fields. With a suitable prescription for the matter propagator in the former, we find agreement between the two methods, thus demonstrating the absence of interference of quantum and classically-singular contributions. The classical mathcal{N} = 8 integrand for massive scalar fields is constructed through dimensional reduction of the known five-point one-loop integrand. Our calculation exhibits novel features compared to conservative calculations and inclusive observables, such as the appearance of master integrals with intersecting matter lines and the appearance of a classical infrared divergence whose absence from classical observables requires a suitable definition of the retarded time.

The big bang and the Schwarzschild singularities are space-like. They are generally regarded as the "final frontiers" at which space-time ends and general relativity breaks down. We review the status of such space-like singularities from three increasingly more general perspectives. They are provided by (i) A reformulation of classical general relativity motivated by the Belinskii, Khalatnikov, Lifshitz conjecture on the behavior of the gravitational field near space-like singularities; (ii) The use of test quantum fields to probe the nature of these singularities; and, (iii) An analysis of the fate of these singularities in loop quantum gravity due to quantum geometry effects. At all three levels singularities turn out to be less menacing than one might a priori expect from classical general relativity. Our goal is to present an overview of the emerging conceptual picture and suggest lines for further work. In line with the \emph{Introduction to Current Research} theme, we have made an attempt to make it easily accessible to all researchers in gravitational physics.

This presentation gives an overview of the Dynamic Theory which offers classical thermodynamics as a new basis for the various physical theories. This leads to a five dimensional description of nature where the five dimensions are space, time, and mass. Just as in thermodynamics where an integrating factor, the temperature, ties the energy, heat, to the entropy, the Dynamic Theory produces two metrics tied by a geometrical integrating factor. One metric is integrable and, necessarily Riemannian, while the other is a non-integrable Weyl space. In the geometrical picture entropy is the arc length of the Riemannian space. The gauge function which appears in the Weyl space leads to a tencomponent gauge field tensor in which the gravitational vector field and the gravitational potential represent four components with the electric and magnetic vector fields representing the remaining six components. Isentropic states lead to a null trajectory in the entropy space, which is Einstein’ s trajectory of light, but lead to an infinite number of null trajectories in the Weyl space which are given by a generalization of quantum mechanics. The null trajectories in the Weyl space, which are quantum states, give rise to quantization of the gauge field in terms of integer units of charge and lead to a nonsingular gauge potential of the form (1/r)exp[-(lambda/r)]. The fact that the gravitational field appears as a gauge field in the five-dimensional field tensor, which comes from the gauge function, means that the gravitational field influences the quantum measurement (i.e., the least unit of action) and this shows up in the prediction of the red shifts from stellar objects. Since the gravitational potential is a non-singular form the predicted advance of the perihelion of binary stars is half that of Einstein’s General Relativity which makes a better agreement with experiment, yet yields that same prediction as General Relativity when one body is very massive compared to the other.

In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are devoted to the problem of introducing fractional derivatives or fractional integrals into the classical General Relativity (GR). There are several observational and theoretical motivations to investigate the modified or alternative theories of GR. Among other things, we cover General Relativity modified by a phenomenological approach dealing with fractional calculus. At the same time, a sufficiently large number of exact solutions of the cosmological equations modified by this approach were obtained. Some of these models may be especially relevant in the light of solving the problem of late accelerated expansion of the Universe. These studies are largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

The physical meaning of the Planck length (ell _{P}) is investigated in the framework of the unconstrained synchronous variational formulation of classical general relativity (GR). This theoretical setting permits the establishment of manifestly-covariant Lagrangian and Hamiltonian theories for the Einstein field equations of the continuum gravitational field. It is shown that such a formulation is distinguished by the existence of a novel variational contribution expressed by an infinite series summation of suitable 4-scalar terms in which the coupling coefficients are even powers of the Planck length. However, the requirement of realization of a classical GR Hamiltonian theory places stringent constraints on the admissible Planck-length power terms to be retained. In fact, excluding the trivial gauge constant, it is proved that only the Oleft( ell _{P}^{0}right) contribution of the series is ultimately permitted, namely the unique one which is independent of ell _{P}. Therefore, the Planck length is effectively not allowed to appear at the classical level for consistency with the Hamiltonian principle. This places important consequences on the mathematical establishment of the corresponding canonical quantum gravity theory, which is then found to be correct through Oleft( ell _{P}^{2}right) . Additional implications concern the physical significance of related quantum momenta and their meaning in the semi-classical limit, as well as the role of the Planck length in the same quantum-gravity realm.

This lecture is a brief introduction General Relativity. We begin with an outline of general coordinate covariance, tensor analysis, and Riemannian geometry. The Bianchi identities are derived and we include some comments on torsion, since torsion may arise when spinor fields are present. Classical General Relativity is then reviewed and the field equations are found from the Einstein-Hilbert action. The Palatini formalism is also discussed.

We investigate the Church–Kalmar–Kreisel–Turing theses theoretical concerning (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turing-type theses (not only one) and (ii) validity of some of these theses depend on the background physical theory we choose to use. In particular, if we choose classical general relativity theory as our background theory, then the above-mentioned limitations (predicted by these theses) become no more necessary, hence certain forms of the Church–Turing thesis cease to be valid (in general relativity). (For other choices of the background theory the answer might be different.) We also look at various “obstacles” to computing a nonrecursive function (by relying on relativistic phenomena) published in the literature and show that they can be avoided (by improving the “design” of our future computer). We also ask ourselves, how all this reflects on the arithmetical hierarchy and the analytical hierarchy of uncomputable functions.

A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the ‘Vierbein’ assuring local gauge invariance enters not as an independent dynamical field, but emerges as a functional of the Lorentz gauge field. The underlying geometry of the theory turns out to be a SO(1,3) Banach bundle. The most general action which is renormalizable by power-counting is constructed in terms of the gauge field and its first derivatives. It contains no higher derivative terms in the gauge field which destroy unitarity in the usual renormalizable R2-theories of gravitation. Finally equivalence of the Lorentz gauge field theory coupled to spin zero matter with general relativity is established.