Gravitational Field Theory Research Articles

Black hole scalarization from the breakdown of scale invariance

Electro-vacuum black holes are scale-invariant; their energy-momentum tensor is traceless. Quantum corrections of various sorts, however, can often produce a trace anomaly and a breakdown of scale-invariance. The (quantum-corrected) black hole solutions of the corresponding gravitational effective field theory (EFT) have a non-vanishing Ricci scalar. Then, the presence of a scalar field with the standard non-minimal coupling $\xi \phi^2 R$ naturally triggers a spontaneous scalarisation of the corresponding black holes. This scalarisation phenomenon occurs for an (infinite) discrete set of $\xi$. We illustrate the occurrence of this phenomenon for two examples of static, spherically symmetric, asymptotically flat black hole solution of EFTs. In one example the trace anomaly comes from the matter sector -- a novel, closed form, generalisation of the Reissner-Nordstr\"om solution with an $F^4$ correction -- whereas in the other example it comes from the geometry sector -- a noncommutative geometry generalization of the Schwarzschild black hole. For comparison, we also consider the scalarisation of a black hole surrounded by (non-conformally invariant) classical matter (Einstein-Maxwell-dilaton black holes). We find that the scalarised solutions are, generically, entropically favoured.

Covariant Canonical Gauge Gravitation and Cosmology

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations necessarily embrace a quadratic Riemann term added to Einstein’s linear equation. The quadratic term endows space-time with inertia generating a dynamic response of the space-time geometry to deformations relative to (Anti) de Sitter geometry. A “deformation parameter” is identified, the inverse dimensionless coupling constant governing the relative strength of the quadratic invariant in the Hamiltonian, and directly observable via the deceleration parameter q0. The quadratic invariant makes the system inconsistent with Einstein’s constant cosmological term, Λ = const. In the Friedman model this inconsistency is resolved with the scaling ansatz of a “cosmological function”, Λ(a), where a is the scale parameter of the FLRW metric. The cosmological function can be normalized such that with the A CDM parameter set the present-day observables, the Hubble constant and the deceleration parameter, can be reproduced. With this parameter set we recover the dark energy scenario in the late epoch. The proof that inflation in the early phase is caused by the “geometrical fluid” representing the inertia of space-time is yet pending, though. Nevertheless, as according to the CCGG theory the present-day cosmological function, identified with the currently observed Λobs, is a balanced mix of two contributions. These are the (A)dS curvature plus the residual vacuum energy of space-time and matter. The curvature term is proportional to the deformation parameter given by the coupling strength of the quadratic Riemann term. This allows for a fresh look at the Cosmological Constant Problem that plagues the standard Einstein-Friedman cosmology.

Introdução à Teoria de Gauge da Gravitação

The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental interaction of gravitation is very well described by Einstein's General Relativity in a Riemannian spacetime metric, but General Relativity has been over time a gravitational field theory apart from the Standard Model. The theory of Gauge allows under symmetries of the group of Poincar\'e to impose invariances in the functional of the action of the spinor field that result in the gravitational interaction with the fermions. In this approach the gravitational field, besides being described by the equation similar to General Relativity, also brings a spin-gravitational interaction in a Riemann-Cartan spacetime.

Synchronization of Complex Network Based on the Theory of Gravitational Field

Synchronization of Complex Network Based on the Theory of Gravitational Field

Hyperunified field theory and Taiji program in space for GWD

In this paper, I present the recently established hyperunified field theory (HUFT)[Formula: see text] for all basic forces and elementary particles within the framework of gravitational quantum field theory (GQFT)[Formula: see text] in hyper-space–time. GQFT treats gravity as a gauge theory in the framework of quantum field theory to avoid the long term obstacle between general relativity and quantum mechanics. HUFT is built based on the guiding principle: the dimension of hyper-space–time correlates to intrinsic quantum numbers of basic building blocks of nature, and the action describing the laws of nature obeys the gauge invariance and coordinate independence, which is more fundamental than that proposed by Einstein for general relativity. The basic gravitational field is defined in biframe hyper-space–time as a bicovariant vector field, it is a gauge-type hyper-gravifield rather than a metric field. HUFT is characterized by a bimaximal Poincaré and hyper-spin gauge symmetry [Formula: see text] with a global and local conformal scaling invariance in biframe hyper-space–time. The gravitational origin of gauge symmetry is revealed through the hyper-gravifield that plays an essential role as a Goldstone-like field, which enables us to demonstrate the gauge-gravity and gravity-geometry correspondences and to corroborate the gravitational gauge-geometry duality with an emergent hidden general linear group symmetry [Formula: see text]. The Taiji Program in Space for the gravitational wave detection in China[Formula: see text] is briefly outlined.

Mixed global anomalies and boundary conformal field theories

We consider the relation between mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed anomalies prevent gauging them i.e, taking the orbifold by the center. The absence of anomalies impose conditions on the levels of WZW models. Next, we study the conformal boundary conditions for the original theories. We consider the existence of a conformal boundary state invariant under the action of the center. This also gives conditions on the levels of WZW models. By considering the combined action of the center and charge conjugation on boundary states, we reproduce the condition obtained in the orbifold analysis.

Gravity and Spin Forces in Gravitational Quantum Field Theory**Supported in part by the National Science Foundation of China (NSFC) under Grant Nos. 11690022 and 11475237, Strategic Priority Research Program of the Chinese Academy of Sciences (CAS), under Grant No. XDB23030100, Key Research Program QYZDYSSW-SYS007, and the CAS Center for Excellence in Particle Physics (CCEPP)

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newtonʼs gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.

Stratified scalar field theories of gravitation with self-energy term and effective particle Lagrangian

We construct a general stratified scalar theory of gravitation from a field equation that accounts for the self-interaction of the field and a particle Lagrangian, and calculate its post-Newtonian parameters. Using this general framework, we analyze several specific scalar theories of gravitation and check their predictions for the solar system post-Newtonian effects.

Point-particle explanations: the case of gravitational waves

This paper explores the role of physically impossible idealizations in model-based explanation. We do this by examining the explanation of gravitational waves from distant stellar objects using models that contain point-particle idealizations. Like infinite idealizations in thermodynamics, biology and economics, the point-particle idealization in general relativity is physically impossible. What makes this case interesting is that there are two very different kinds of models used for predicting the same gravitational wave phenomena, post-Newtonian models and effective field theory models. The paper contends that post-Newtonian models are explanatory while effective field theory models are not, because only in the former can we eliminate the physically impossible point-particle idealization. This suggests that, in some areas of science at least, models invoking ineliminable infinite idealizations cannot have explanatory power.

Gravity Theories with Background Fields and Spacetime Symmetry Breaking

An overview is given of effective gravitational field theories with fixed background fields that break spacetime symmetry. The behavior of the background fields and the types of excitations that can occur depend on whether the symmetry breaking is explicit or spontaneous. For example, when the breaking is spontaneous, the background field is dynamical and massless Nambu–Goldstone and massive Higgs excitations can appear. However, if the breaking is explicit, the background is nondynamical, and in this case additional metric or vierbein excitations occur due to the loss of local symmetry, or these excitations can be replaced by dynamical scalar fields using a Stückelberg approach. The interpretation of Noether identities that must hold in each case differs, depending on the type of symmetry breaking, and this affects the nature of the consistency conditions that must hold. The Noether identities also shed light on why the Stückelberg approach works, and how it is able to restore the broken spacetime symmetry in a theory with explicit breaking.

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime**Supported by National Science Foundation of China (NSFC) (11690022, 11475237, 11121064) and Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100) as well as the CAS Center for Excellence in Particle Physics (CCEPP)

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincaré symmetry P(1,5)=SO(1,5)⋉P1,5 as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.

We have confidence to lead gravitational-wave science: an interview with Yueliang Wu

Abstract Yueliang Wu, chief scientist of Taiji Program, is a well-known theoretical physicist and the Vice-President of the University of Chinese Academy of Sciences (UCAS). Taiji Program, initially proposed in 2008, is one of China's ambitious plans to observe gravitational waves. Obtaining his Ph.D. at the Institute of Theoretical Physics (ITP) under the Chinese Academy of Sciences (CAS) in 1987, Wu had been working at Dortmund University and Mainz University in Germany and Carnegie-Mellon University and the Ohio-State University in the USA. In 1996, he joined the ITP and became its director in 2007. He has also served as the Director of the Kavli Institute for Theoretical Physics China at the CAS since 2006. In 2007, he was elected as a CAS member. Wu's research is focused on elementary particle physics, quantum field theory, symmetry principle and cosmophysics. In recent years, he has been proposing a gravitational quantum field theory as a new approach to reconciling the general theory of relativity and quantum mechanics. The most fundamental unanswered question of the general theory of relativity is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. To extend the general relativity to realize the reconciliation, Wu suggested a basic gravitational field be needed in the future model. Since 2012, he, together with Wenrui Hu, has been working as Taiji Program's chief scientist and promoting nationwide gravitational-wave research. National Science Review (NSR) spoke with Wu about the future of gravitational-wave research, the development of China's nationwide gravitational-wave studies and particularly the progress of Taiji Program.

Why the Road to Unification Likely Goes through Krogdahl’s Relativity

Deriving an acceptable quantum field theory of gravitation from general relativity has eluded some of the best scientific thinkers. It is gradually becoming more apparent that general relativity’s classical assumptions are simply incompatible with quantum mechanics. For instance, simultaneous certainty of the location and momentum of any moving body, regardless of size, is a fundamental feature of general relativity. And yet, special relativity and quantum mechanics (thru Heisenberg’s uncertainty) reject the very notion of simultaneity. Since special relativity is already fully integrated into quantum field theory concerning the other forces of nature, were it possible to remove the confounding smoothly curved space-time fabric of general relativity and replace it in the form of a new and improved Lorentz-invariant (flat space-time) gravitational theory, final unification might well be achievable. This brief review paper further informs the reader as to why Krogdahl’s recent Lorentz-invariant relativity model of gravitation improves on general relativity, thus providing a deeper understanding of black holes, the cosmological flatness problem and dark energy. Most importantly, since the smoothly curved space-time of general relativity may well have been the road block to unification, Krogdahl’s flat space-time model is predicted to lead to an acceptable quantum theory of gravitation (i.e., “quantum gravity”) and unification (i.e., a so-called “theory of everything”).

Noether identities in gravity theories with nondynamical backgrounds and explicit spacetime symmetry breaking

Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be mathematically invariant under general coordinate transformations and changes of local Lorentz bases. These opposing effects of having broken spacetime symmetries but invariance under mathematical observer transformations can result in theoretical inconsistency unless certain conditions hold. The consistency constraints that must hold originate from Noether identities associated with the mathematical observer invariances in the action. These identities are examined in detail and are used to investigate gravity theories with nondynamical backgrounds, including when a St\"uckelberg approach is used. Specific examples include gravity theories with fixed scalar or tensor backgrounds, Einstein-Maxwell theory with a fixed external current, and massive gravity.

A gravitational gauge field theory based on Stephenson–Kilmister–Yang gravitation with scalar and spinor fields as gravitating matter sources

A gravitational gauge theory with a spin–affine connection (Lorentz connection) as a rotational gauge potential (fundamental dynamical variable) is suggested for reformulating the theory of Stephenson–Kilmister–Yang gravity, in which the Einstein field equation of gravity is a first-integral solution of a spin-connection gravitational gauge field equation. A heavy intermediate field $$\phi $$ that accompanies a matter field $$\varphi $$ is introduced in order to remove the conventional dimensionful gravitational coupling. Such a $$\varphi $$ – $$\phi $$ coupling can lead to dimensionless gravitational coupling (i.e., the gravitational constant is dimensionless) in the present gravitational gauge field theory. A low-energy effective Lagrangian density for the matter field can be obtained by integrating out the accompanying heavy field in generating functional of path integral formalism, and therefore, a dimensionful gravitational coupling coefficient (Einstein gravitational constant) emerges. Such a dimensionless coupling of gravity, where the dimensionful coupling is emergent at low energies, is considered for scalar and spinor fields, which serve as gravitating matter fields (gravitational source). Though there are higher derivatives (e.g., third- and fourth-order partial derivatives) of the scalar and spinor fields in the low-energy effective Lagrangian densities, the ordinary equations of motion of the scalar and spinor fields can also be emergent from the present gravitational gauge theory. Therefore, the Einstein gravity can be recovered from the present gravitational gauge theory. In addition to the gravitational Lagrangian of the spacetime-rotational gauge potential (i.e., spin–affine connection), the Lagrangian of a spacetime-translational gauge potential (i.e., vierbein) is also constructed. Thus, the present dimensionless gravitational gauge coupling preserves local rotational and translational gauge symmetries. Since the spin-connection gravitational gauge field equation is a third-order differential equation of metric (the Einstein field equation of gravity is a first-integral solution), it could provide a new route to the vacuum energy cosmological constant problem.

Republication of: Contributions to the theory of gravitational radiation fields. Exact solutions of the field equations of the general theory of relativity V

This is an English translation of a paper by Wolfgang Kundt and Manfred Trumper, first published in 1962 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was the last of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (All the other parts of the series have already been re-published as Golden Oldies.) This fifth contribution summarizes key points of the earlier papers and applies them, in particular results from papers II and IV in the series, in the context of the propagation of gravitational radiation when matter is present. 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 Malcolm A.H. MacCallum and by a brief autobiography of Manfred Trumper.

Editorial note to: Wolfgang Kundt and Manfred Trümper, Contributions to the theory of gravitational radiation fields. Exact solutions of the field equations of the general theory of relativity V

Editorial note to: Wolfgang Kundt and Manfred Trümper, Contributions to the theory of gravitational radiation fields. Exact solutions of the field equations of the general theory of relativity V

Effective field theory, past and future

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

The quantum gravitational field theory and the domains of its fix points for inflationary or low-redshift universe

We study a quantum field theory for the Einstein–Cartan gravity and the domain of its ultraviolet unstable (stable) fixed point [Formula: see text] [Formula: see text] of running gravitational constant [Formula: see text], where inflationary (low-redshift) universe can be realized as the basic space-time cutoff [Formula: see text] approaching to the Planck length [Formula: see text]. 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 [Formula: see text]. The correlation length [Formula: see text] characterizes an infrared size of a causally correlate patch of the universe. The quantitative description of low-redshift universe in the scaling-invariant region of fixed point [Formula: see text] is given, and its deviation from the [Formula: see text]CDM can be examined by recent cosmological observations, such as supernova Type Ia.

Improved routing strategy based on gravitational field theory**Project supported by the Technology and Development Research Project of China Railway Corporation (Grant No. 2012X007-D) and the Key Program of Technology and Development Research Foundation of China Railway Corporation (Grant No. 2012X003-A).

Routing and path selection are crucial for many communication and logistic applications. We study the interaction between nodes and packets and establish a simple model for describing the attraction of the node to the packet in transmission process by using the gravitational field theory, considering the real and potential congestion of the nodes. On the basis of this model, we propose a gravitational field routing strategy that considers the attractions of all of the nodes on the travel path to the packet. In order to illustrate the efficiency of proposed routing algorithm, we introduce the order parameter to measure the throughput of the network by the critical value of phase transition from a free flow phase to a congested phase, and study the distribution of betweenness centrality and traffic jam. Simulations show that, compared with the shortest path routing strategy, the gravitational field routing strategy considerably enhances the throughput of the network and balances the traffic load, and nearly all of the nodes are used efficiently.