Gravitational Field Theory Research Articles

How universe evolves with cosmological and gravitational constants

With a basic varying space–time cutoff ℓ˜, we study a regularized and quantized Einstein–Cartan gravitational field theory and its domains of ultraviolet-unstable fixed point gir≳0 and ultraviolet-stable fixed point guv≈4/3 of the gravitational gauge coupling g=(4/3)G/GNewton. Because the fundamental operators of quantum gravitational field theory are dimension-2 area operators, the cosmological constant is inversely proportional to the squared correlation length Λ∝ξ−2. The correlation length ξ characterizes an infrared size of a causally correlate patch of the universe. The cosmological constant Λ and the gravitational constant G are related by a generalized Bianchi identity. As the basic space–time cutoff ℓ˜ decreases and approaches to the Planck length ℓpl, the universe undergoes inflation in the domain of the ultraviolet-unstable fixed point gir, then evolves to the low-redshift universe in the domain of ultraviolet-stable fixed point guv. We give the quantitative description of the low-redshift universe in the scaling-invariant domain of the ultraviolet-stable fixed point guv, and its deviation from the ΛCDM can be examined by low-redshift (z≲1) cosmological observations, such as supernova Type Ia.

Holography of the BTZ black hole, inside and out

We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS$_3$. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.

How to Be Perceived as a Fair Third Party in Joint Decision Making: A Quantitative Framework Based on Gravitational Field Theory

Many purchasing decisions are made jointly with a third party (such as a salesperson) who serves as a facilitator, advisor, or arbitrator. A good example is a couple who works with a salesperson at a car dealership to find the right car. A challenge for marketers is maintaining perceptions of fairness among joint decision makers by not appearing to favor one party over another. Drawing on gravitational field theory in physical science, we develop a quantitative framework to help the third party maintain perceptions of fairness. We also describe several propositions that will be helpful for marketers in joint decision making contexts. This framework can be used for practitioners in other social contexts, such as organizational decision making and conflict resolution, among others.

Cartographic generalization of urban street networks based on gravitational field theory

The automatic generalization of urban street networks is a constant and important aspect of geographical information science. Previous studies show that the dual graph for street–street relationships more accurately reflects the overall morphological properties and importance of streets than do other methods. In this study, we construct a dual graph to represent street–street relationship and propose an approach to generalize street networks based on gravitational field theory. We retain the global structural properties and topological connectivity of an original street network and borrow from gravitational field theory to define the gravitational force between nodes. The concept of multi-order neighbors is introduced and the gravitational force is taken as the measure of the importance contribution between nodes. The importance of a node is defined as the result of the interaction between a given node and its multi-order neighbors. Degree distribution is used to evaluate the level of maintaining the global structure and topological characteristics of a street network and to illustrate the efficiency of the suggested method. Experimental results indicate that the proposed approach can be used in generalizing street networks and retaining their density characteristics, connectivity and global structure.

量子真空能及其对引力规范理论的启示

电磁规范理论及其推广(Yang-Mills理论)在量子场论和粒子物理领域取得了成功要求引力理论也应当是某种局域规范对称下的规范场论；对于量子真空能巨大引力效应与宇宙学观察事实之间的矛盾等问题的探究表明传统引力理论可能是一个低能唯象理论，可能还存在新的高能引力相互作用基本理论。本文介绍了一个新的自旋联络引力规范理论，它以局域Lorentz群为规范对称群、以自旋仿射联络作为非Abel规范场。在低能条件下，我们可以获得一个度规的三阶微分方程作为引力场方程，而爱因斯坦引力场方程作为其一个首次积分解呈现。在该理论中，量子真空能巨大引力效应不再存在，并产生了一个等效宇宙学常数(作为首次积分解的积分常数)，这可能为解决宇宙学常数之谜提供了一条思路。对引力规范理论本身及其在宇宙学中的运用作了一些讨论, 如该引力规范理论会呈现一种准流体(它在四维宇宙中类似暗辐射；在五维宇宙中，则呈现更为丰富的物态)，因此基于该引力规范理论的五维宇宙学在不需要引入真实暗物质和暗能量的条件下也能产生等效的暗物质和暗能量效应。Since electromagnetic gauge theory and its generalization (Yang-Mills gauge field theory) have succeeded in quantum field theory and particle physics, it requires that the theory of gravitation also be a gauge field theory under certain local gauge symmetries, e.g., local Lorentz or Poincare invariance. The discrepancy between unusually large quantum vacuum energy density and ob-servational cosmology may indicate that the generic gravity theory of Einstein is a low-energy phenomenological theory, and a more fundamental theory of gravity might be hidden behind it. A new spin-connection gauge theory for gravitational interaction at high energies (close to the Planck energy scale) is introduced. In such a gravitational gauge field theory, the local Lorentz group is the gauge symmetry group, and the spin-affine connection serves as a non-Abel gauge field (fundamental dynamical variable). A third-order differential equation of metric can be obtained as the gravitational gauge field equation, where the Einstein field equation of gravitation is a first-integral solution. As the vacuum energy density is a constant, the covariant derivative of its energy-momentum tensor unavoidably vanishes. Therefore, the quantum vacuum energy term disappears in the gravitational gauge field equation, and the anomalously large vacuum energy density does not make a practical contribution to gravity. This would enable us to seek for a new route to the longstanding vacuum-energy cosmological constant problem. Some topics relevant to gravitational gauge theory and its applications in cosmology are also addressed. For example, the five-dimensional cosmology within the framework of the present gravitational gauge theory, in which a quasi fluid is emergent, can exhibit the effects of equivalent dark matter and dark energy.

Gravitational field routing strategy considering the distribution of traffic flow

Traffic flow transmission is a constantly important aspect of complex networks, geographical information science, and other science and engineering fields. Previous studies have shown that vehicle flow is more strongly correlated with morphological properties of streets than those of axial lines. In addition, street-based topological representations are more suitable for vehicle flow prediction, as well as more memory-oriented and global in nature. In this study, we construct a dual graph to represent the street–street relationship and propose a routing strategy for networks on the basis of gravitational field theory. We aim to diminish traffic congestion and enhance the transmission performance of networks. We borrow from gravitational field theory in establishing a gravitational field stimulated by a node in packet transmission and in defining the corresponding gravitational field equation. On the basis of this study, we present a mathematical model and a routing strategy. Experimental results indicate that compared with the shortest path routing strategy, the proposed method considerably enhances network capacity and effectively balances network traffic flow, especially for congested networks. We achieve critical gravitation that can always maximize network capacity, regardless of the values of other parameters.

Gravitational Field Equations and Theory of Dark Matter and Dark Energy

The main objective of this article is to derive new gravitational field equations and to establish a unified theory for dark energy and dark matter. The gravitational field equations with a scalar potential $\varphi$ function are derived using the Einstein-Hilbert functional, and the scalar potential $\varphi$ is a natural outcome of the divergence-free constraint of the variational elements.Gravitation is now described by the Riemannian metric$g_{\mu\nu}$, the scalar potential $\varphi$ and their interactions, unified by the new field equations.From quantum field theoretic point of view, the vector field $\Phi_\mu=D_\mu \varphi$, the gradient of the scalar function $\varphi$, is a spin-1 massless bosonic particle field. The field equations induce a natural duality between the graviton (spin-2 massless bosonic particle) and this spin-1 massless bosonic particle. Both particles can be considered as gravitational force carriers, and as they are massless, the induced forces are long-range forces. The (nonlinear) interaction between these bosonic particle fields leads to a unified theory for dark energy and dark matter. Also, associated with the scalar potential $\varphi$ is the scalar potential energy density $\frac{c^4}{8\pi G} \Phi=\frac{c^4}{8\pi G} g^{\mu\nu}D_\mu D_\nu \varphi$, which represents a new type of energy caused by the non-uniform distribution of matter in the universe.The negative part of this potential energy density produces attraction, and the positive part produces repelling force. This potential energy density is conserved with mean zero: $\int_M \Phi dM=0$.The sum of this potential energy density$\frac{c^4}{8\pi G} \Phi$ and the coupling energy between the energy-momentum tensor $T_{\mu\nu}$ and the scalar potential field $\varphi$ gives rise to a unified theory for dark matter and dark energy:The negative part ofthis sum represents the dark matter, which produces attraction,and the positive part represents the dark energy, which drives the acceleration of expanding galaxies.In addition, the scalar curvature of space-time obeys $R=\frac{8\pi G}{c^4} T + \Phi$.Furthermore, the proposed field equations resolve a few difficulties encountered by the classical Einstein field equations.

Evaluating solutions on an elliptic problem in a gravitational gauge field theory

An elliptic equation arising from the study of static solutions with prescribed zeros and poles of the Einstein equations coupled with the classical sigma model and an Abelian gauge field, is considered. We classify the solutions and establish the uniqueness of radially symmetric solutions. We also complete a classification of symmetric solutions of an elliptic equation on the sphere.

Analysis of network traffic flow dynamics based on gravitational field theory

For further research on the gravity mechanism of the routing protocol in complex networks, we introduce the concept of routing awareness depth, which is represented by ρ. On this basis, we define the calculation formula of the gravity of the transmission route for the packet, and propose a routing strategy based on the gravitational field of the node and the routing awareness depth. In order to characterize the efficiency of the method, we introduce an order parameter, ζ, to measure the throughput of the network by the critical value of phase transition from free flow to congestion, and use the node betweenness centrality, B, to test the transmission efficiency of the network and congestion distribution. We simulate the network transmission performance under different values of the routing awareness depth, ρ. Simulation results show that if the value of the routing awareness depth ρ is too small, then the gravity of the route is composed of the attraction of very few nodes on the route, which cannot improve the capacity of the network effectively. If the value of the routing awareness depth ρ is greater than the network's average distance 〈l〉, then the capacity of the network may be improved greatly and no longer change with the sustainable increment of routing awareness depth ρ, and the routing strategy performance enters into a constant state. Moreover, whatever the value of the routing awareness depth ρ, our algorithm always effectively balances the distribution of the betweenness centrality and realizes equal distribution of the network load.

The Theory of Static Gravitational Field

The paper discusses in detail assumptions needed for the derivation of metric for the non-rotating centrally gravitating body, which is not based on Einstein field equations. The metric derivation is then generalized to any static mass configuration. It is shown that the Schwarzschild metric, which is the famous solution of Einstein field equations for the centrally gravitating body, is only a first order approximation of the correct metric and that the Einstein field equation concept is a wrong concept for finding any metric. Several examples of observations in support of the developed theory, which are not as easily explained in the main stream literature, are also presented in this paper.

Routing strategy for complex networks based on gravitation field theory

Using the theory of gravitational field, we study the gravitational field induced by the node in the process of the network transmission, establish the gravitational filed equation, and define two parameters α and γ for adjusting the dependencs of transmission data on the unblocked degree of node, the transmission capacity of node and the path length. Based on the gravitational field of node, an efficient routing strategy is proposed, and the package will be transferred along the route with maximum gravitation. In order to characterize the efficiency of the method, we introduce an order parameter η to measure the throughput of the network by the critical value of phase transition from free state to jammed state, and use the node betweenness centrality B to test the transmission efficiency of network and the congestion distribution. We simulate the network transmission efficiencies under different values of α and γ. Simulation results show that compared with the traditional shortest routing strategy, our routing strategy improves the network capacity several times, and effectively balances the distribution of the betweenness centrality of nodes, and the average path length Lavg> shows a trend from ascent to descent with the increase of load amount R, and the change of the parameters α and γ nearly have no effect on the network transmission capacity, which suggests the efficiency of our routing strategy is independent of α and γ, the network capacities are approximately equal for any values of α and γ in the feasible region.

1912: A turning point on Einstein's way to general relativity

AbstractOn his way to general relativity, Einstein used the equivalence principle to formulate a theory of the static gravitational field. In this context he introduced an approximate coordinate transformation to an accelerated frame which turns out to be closely related to Rindler coordinates, widely used in modern general relativity. This work, published in the Annalen, led him directly to interpret gravitation in terms of spacetime curvature.

Republication of: Quantum theory of weak gravitational fields

This is an English translation of a paper by Matvei Bronstein, first published in German in 1936 in a long-extinct Soviet journal, in which he presented the first attempt at quantizing a weak (linearized) gravitational field, rather modern in its approach. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Stanley Deser and Alexei Starobinsky, and Bronstein’s brief biography written by Stanley Deser.

Editorial note to: Matvei P. Bronstein, Quantum theory of weak gravitational fields

A scientific introduction and short biography to accompany the translation of Matvei P. Bronstein, "Quantum theory of weak gravitational fields", Phys. Zeitschr. der Sowjetunion 9, 140 157 (1936), to appear as a "Golden Oldie" in JGRG.

Scale-invariant alternatives to general relativity

We study the general class of gravitational field theories constructed on the basis of scale invariance (and therefore absence of any mass parameters) and invariance under transverse diffeomorphisms (TDiff), which are the 4-volume conserving coordinate transformations. We show that these theories are equivalent to a specific type of scalar-tensor theories of gravity (invariant under all diffeomorphisms) with a number of properties, making them phenomenologically interesting. They contain, in addition to the dimensionless coupling constants of the original theory, an arbitrary dimensionful parameter $\Lambda_0$. This parameter is associated with an integration constant of the equations of motion, similar to the arbitrary cosmological constant appearing in unimodular gravity. We focus on the theories where Newton's constant and the electroweak scale emerge from the spontaneous breaking of scale invariance and are unrelated to $\Lambda_0$. The massless particle spectrum of these theories contains the graviton and a new particle -- dilaton. For $\Lambda_0=0$, the massless dilaton has only derivative couplings to matter fields and the bounds on the existence of a 5th force are easily satisfied. As for the matter fields, we determine the conditions leading to a renormalizable low-energy theory. If $\Lambda_0\neq 0$, scale invariance is broken. The arbitrary constant $\Lambda_0$ produces a "run-away" potential for the dilaton. As a consequence, the dilaton can act as a dynamical dark energy component. We elucidate the origin of the cosmological constant in the class of theories under consideration and formulate the condition leading to its absence. If this condition is satisfied, dark energy is purely dynamical and associated to the dilaton.

Topological field theory and thermal responses of interacting topological superconductors

We investigate the three-dimensional, time-reversal invariant topological superconductors with generic interaction by their response to external fields. The first description is a gravitational topological field theory, which gives a ${Z}_{2}$ classification of topological superconductors, and predicts a half quantized thermal Hall effect on the surface. The second description introduces an $s$-wave proximity pairing field on the surface, and the associated topological defects give an integer $Z$ classification of the topological superconductors.

Concordances among electromagnetic, fluid dynamical, and gravitational field theories

We demonstrate mathematical concordances among the theories of electrodynamics, fluid dynamics, and gravitation when the latter two are extended by including a differential geometric structure that we call a vortex field. Experimental data and theoretical arguments for considering such vortex fields in these theories are discussed.

Gravitational waves and cosmological back reaction

Cosmological back reaction of gravitational waves and matter density fluctuations is revisited through a new general mean field theory of relativistic gravitation. Computations are done for all wave-lengths and Isaacson's results are confirmed for high-frequency waves. It is found that back reaction is typically much stronger for gravitational waves than for matter density fluctuations. In particular, a bath of gravitational waves of relative amplitude 10−5 and frequency 10−12 Hz (compatible with today's constraints) would generate an effective large-scale radiation of amplitude comparable to the unperturbed matter density of the universe.

GALILEAN COVARIANCE AND THE GRAVITATIONAL FIELD

This paper is concerned with the development of a gravitational field theory having locally a covariant version of the Galilei group. We show that this Galilean gravity can be used to study the advance of perihelion of a planet, following in parallel with the result of the (relativistic) theory of general relativity in the post-Newtonian approximation.

Multiscale cosmological dynamics

The recently developed mean field theory of relativistic gravitation predicts the emergence of an “apparent matter” field at large scales describing the net effect of small-scale fluctuations on the large-scale dynamics of the universe. It is found that this so-called back reaction effect is much stronger for gravitational waves than for matter density fluctuations. At large scales, gravitational waves behave like radiation and, for them, the perturbative effect scales as the squared relative amplitude times squared frequency. In particular, a bath of gravitational waves of relative amplitude 1 0 − 5 and frequency 1 0 − 12 Hz would not be directly detectable by today’s technology but would generate an effective large-scale radiation of amplitude comparable to the unperturbed matter density of the universe.