Background Gravitational Field Research Articles

Infrared structures of scattering on self-dual radiative backgrounds

The scattering of gluons and gravitons in trivial backgrounds is endowed with many surprising infrared features which have interesting conformal interpretations on the two-dimensional celestial sphere. However, the fate of these structures in more general asymptotically flat backgrounds is far from clear. In this paper, we consider holomorphic infrared structures in the presence of non-perturbative, self-dual background gauge and gravitational fields which are determined by freely specified radiative data. We make use of explicit formulae for tree-level gluon and graviton scattering in these self-dual radiative backgrounds, as well as chiral twistor sigma model descriptions of the classical dynamics. Remarkably, we find that the leading holomorphic part of tree-level collinear splitting functions — or celestial OPEs — and infinite-dimensional chiral soft algebras are undeformed by the background. We also compute all-order holomorphic celestial OPEs in the MHV sectors of gauge theory and gravity.

Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition

We formulate a model for quantum gravity based on the local Lorentz symmetry and general-coordinate invariance. A key idea is the irreversible vierbein postulate that a tree-level action for the model at a certain energy scale does not contain an inverse vierbein. Under this postulate, only the spinor becomes a dynamical field, and no gravitational background field is introduced in the tree-level action. In this paper, after explaining the transformation rules of the local Lorentz and general-coordinate transformations in detail, a tree-level action is defined. We show that fermionic fluctuations can induce a nonvanishing gravitational background field. Published by the American Physical Society 2024

Trace anomaly of weyl fermions via the path integral

We compute the trace, diffeomorphism and Lorentz anomalies of a free Weyl fermion in a gravitational background field by path integral methods. This is achieved by regularising the variation of the determinant of the Weyl operator building on earlier work by Leutwyler. The trace anomaly is found to be one half of the one of a Dirac fermion. Most importantly we establish that the potential parity-odd curvature term RR~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ R\\overset{\\sim }{R} $$\\end{document}, corresponding to the Pontryagin density, vanishes. This is to the contrary of some recent findings in the literature which gave rise to a controversy. We verify, that the regularisation does not lead to (spurious) anomalies in the Lorentz and diffeomorphism symmetries. We argue that in d = 2 (mod 4) P- and CP-odd terms cannot appear and that for d = 4 (mod 4) they are absent at least at leading order.

Generalized Newton–Cartan geometries for particles and strings

We discuss the generalized Newton–Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure group, we describe torsionful geometries with independent torsion tensors. A characteristic feature of the non-Lorentzian geometries we consider is that some of the torsion tensors are so-called ‘intrinsic torsion’ tensors. Setting some components of these intrinsic torsion tensors to zero leads to constraints on the geometry. For both particles and strings, we discuss various such constraints that can be imposed consistently with the structure group symmetries. In this way, we reproduce several results in the literature.

Photon propagation in a material medium on a curved spacetime

We consider a nonlinear dielectric medium surrounding a static, charged and spherically symmetric compact body which gravitational field is driven by general relativity. Considering the propagating waves on the dielectric medium, we describe the trajectory of light as geodesics on an effective geometry given by Hadamard’s discontinuities. We analyze some consequences of the effective geometry in the propagation of light, with relation to the predictions of the background gravitational field, that includes corrections on the geometrical redshift and on the gravitational deflection of light. We show that the background electromagnetic field polarize the material medium, such that different polarizations of light are distinguished by different corrections on these quantities. As a consequence, we have two possible paths for the trajectory of light in such configuration, that coincide if we turn off the electromagnetic field or if the permittivity is constant. We show that the effective metric associated to the negative polarization, for a given dependence of the dielectric permittivity, is conformally flat.

Energy-twisted boundary condition and response in one-dimensional quantum many-body systems

Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted-boundary-condition formalism for thermal transport in analogy to the U(1) twisted boundary condition for electrical transport. Specifically, using the transfer matrix formalism, we introduce what we call the energy-twisted boundary condition, and study the response of the system to the boundary condition. As specific examples, we obtain the thermal Meissner stiffness of (1+1)-dimensional CFT, the Ising model, and disordered fermion models. We also identify the boost deformation of integrable systems as a bulk counterpart of the energy-twisted boundary condition. We show that the boost deformation of the free fermion chain can be solved explicitly by solving the inviscid Burgers equation. We also discuss the boost deformation of the XXZ model, and its nonlinear thermal Drude weights, by studying the boost-deformed Bethe ansatz equations.

Stationary Structures in a Four Component Dense Magnetoplasma With Lateral Perturbations

We considered a dense plasma containing electrons, positrons, ions and dust particles in background magnetic and gravitational fields alongside collisional effects for the heavier species (ions and dust particles). Such plasmas are found in magnetars, black hole accretion disks, and so on. The quantum hydrodynamic (QHD) model was used to construct the governing equations of the plasma. Relativistic degeneracy pressure is taken as the equation of state for the electrons and positrons. Effects of exchange-correlation potential were also considered for the lighter species. We employed the reductive perturbation method (RPM) in order to obtain the Zakharov–Kuznetsov (ZK) equation describing 3-D ion acoustic waves (IAWs) with minimal lateral perturbations. Low order analytical solutions allow us to understand the parametric dependence of said structures. Our newly developed numerical technique: homotopy assisted symbolic simulation (HASS) sheds light on the gradual evolution of higher order stationary formations in the system. The results thus obtained can potentially explain certain astrophysical phenomena as well as dense laboratory plasmas.

Pinball spring model

In general relativity it is difficult to work with the concept of a classical phenomenological spring model since it involves action at a distance. We propose a toy relativistic model exhibiting oscillatory behavior and investigate its motion in selected gravitational fields. The simple model can be used to study the behavior of extended objects falling freely in a background gravitational field. Unlike previous glider-type models, the present system only involves local interaction, avoiding thus the pitfalls of superluminal motion. Moreover, it locally satisfies energy-momentum conservation.

A Conceptual Model to Explain Dark Matter and Dark Energy

This paper considers a conceptual model that attempts to explain ‘Dark Matter’ and ‘Dark Energy’. The model is based on considering a gravitational field to be the result of a mass (a Higgs field) scattering pre-existing cosmic background space-time waves or ‘Uber-waves’. The term ‘Uber’ is used to denote an outstanding or supreme example of a particular kind of gravitational wave with cosmic-scale wavelengths that are far in excess of those associated with the gravitational waves generated by accelerating masses. Such waves are taken to be the very lowest frequency components associated with the spectrum of space-time waves generated by the ‘Big Bang’ and are supported by the expanding fabric of space-time produced at the point of the big bang, i.e. the lowest frequency components of a cosmological spectrum whose bandwidth is the a Planck frequency (～10∧43 Hz). Like electromagnetic waves, Uber waves are taken to propagate with an upper velocity consistent with the speed of light and interact with, and are scattered by, a Higgs field. This interaction produces the effect of a mass locally curving space-time, an idea that is contrary to the conventional model associated with General Relativity where mass is taken to curve space-time directly which otherwise remains ‘flat’. By assuming the pre-existence of background Uber waves, we consider the concave curvature of such waves to generate an apparent attractive gravitational force. This interaction produces the effect of a mass locally curving space-time, an idea that is contrary to the conventional model associated with General Relativity where mass is taken to curve space-time directly which otherwise remains ‘flat’. By assuming the pre-existence of background Uber waves, we consider the concave curvature of such waves to generate an apparent attractive gravitational force. This attractive force is taken to govern the formation of large scale structures of matter (galaxies and super-clusters of galaxies, for example) in the conventional sense but surrounded by a residual background gravitational field. It is this residual field that gives rise to the effect known as dark matter where more gravity (as an attractive only force) appears to be available than that which can be accounted for by the observed (luminous) mass, a luminosity that is generated primarily by nuclear fusion in stars. The convex curvature of Uber waves is considered to account for cosmic voids within which gravity is a repulsive force and where large scale structures of matter can therefore not be formed. This is considered to explain the super-large cosmic voids or super voids that are observed. These are regions of the universe where there is an absence of rich super clusters of matter. In these anti-gravity zones, only relatively small structures of matter can be formed by electrostatic forces alone which are then repelled from each other when their mass becomes significant enough for the force of anti-gravity to become significant. In such regions of an Uber wave, the matter generated from electrostatic forces builds up to produce a weak gravitational repulsive field due to the low mass density within a void. However, due to the immense size of these cosmic voids, they are taken to generate a net repulsive force which is considered to be the reason for the acceleration associated with the expansion of the universe; the effect of dark energy. This effect also accounts for the cosmic web structure in which luminescent matter appears to exist in relatively thin connective filaments. The purpose of this paper is to provide a conceptual model and not to investigate the ideas proposed in any significant mathematical detail. This is accomplished by building up the ideas on a case-by-case basis, coupled with a series of thought experiments but without resorting to specific physical scales or the physical parameters associated with these scales other than, by default, the speed of light and Newton’s gravitational constant.

Gravity-Induced Geometric Phases and Entanglement in Spinors and Neutrinos: Gravitational Zeeman Effect

We show Zeeman-like splitting in the energy of spinors propagating in a background gravitational field, analogous to the spinors in an electromagnetic field, otherwise termed the Gravitational Zeeman Effect. These spinors are also found to acquire a geometric phase, in a similar way as they do in the presence of magnetic fields. However, in a gravitational background, the Aharonov-Bohm type effect, in addition to Berry-like phase, arises. Based on this result, we investigate geometric phases acquired by neutrinos propagating in a strong gravitational field. We also explore entanglement of neutrino states due to gravity, which could induce neutrino-antineutrino oscillation in the first place. We show that entangled states also acquire geometric phases which are determined by the relative strength between gravitational field and neutrino masses.

CFT in conformally flat spacetimes

A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal isometry group is of maximal rank and the conformal Killing vectors in conformally flat coordinates are {\em exactly} the same as the ones of flat spacetime. In this work, a new concept of distance is introduced, the {\em conformal distance}, which transforms covariantly under all conformal isometries of the CF space. It is shown that precisely for CF spacetimes, an adequate power of the said conformal distance is a solution of the non-minimal d'Alembert equation.

Acoustic ray method derived with the concept of analogue gravity for the calculation of the sound field due to rotating sound sources

Acoustics in a moving fluid is a simple model of an analogue space–time. The analysis shows that the null geodesics of the metric gμν in that space–time correspond to the rays in the eikonal approximation of geometrical acoustics. The physical connection to general relativity is the propagation of sound along the null geodesics that corresponds to the propagation of a scalar field in a background gravitational field. In this framework, we derive a three-dimensional acoustic ray method in a rotating frame of reference and calculate an acoustic metric, acoustic rays, travel times, and amplitudes for the fluctuating part of the pressure. Further the application to rotating beamforming, i.e., localization and estimation of the strength of rotating sound sources with a microphone array, is presented. Analytical calculations are compared with the spherical harmonic series expansion method for the sound propagation in the rotating frame of reference. Two benchmark cases on rotating sound sources with generic time-data and measured time-data of an axial fan demonstrate its applicability to rotating beamforming.

Effective gravitational couplings of four-dimensional mathcal{N} = 2 supersymmetric gauge theories

The low energy effective couplings of a four-dimensional mathcal{N} = 2 supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions A and B. These two functions play an important role in the study of topo- logically twisted four-dimensional mathcal{N} = 2 supersymmetric gauge theories and in the computation of central charges of mathcal{N} = 2 superconformal theories. In this paper, we compute A and B from the partition function in the Ω-background for SU(2) gauge theories. Our results not only confirm the predicted expressions of the effective gravitational couplings, but also give the previously undetermined overall multiplicative factors. We also analyze A and B for the SU(N ) super-Yang-Mills theory, and confirm all the previous predictions.

Scalar perturbations in f(T) gravity using the 1 + 3 covariant approach

The cosmological scalar perturbations of standard matter are investigated in the context of extended teleparallel f(T) gravity theories using the 1+3 covariant formalism. After a review of the background gravitational field equations of f(T) gravity and the introduction of the covariant perturbation variables, the usual scalar and harmonic decomposition have been performed, and the analysis of the growth of the density contrasts in the quasi-static approximation for two non-interacting fluids scenarios, namely torsion-dust and torsion-radiation mixtures is presented for the generic f(T) gravity theory. Special applications to two classes of f(T) gravity toy models, namely f(T) = mu T_0 Big (frac{T}{T_0}Big )^n and f(T) = T+ mu T_0 Big (-frac{T}{T_0}Big )^n, have then been made within the observationally viable regions of their respective parameter spaces, and the growth of the matter density contrast for both torsion-dust and torsion-radiation epochs of the Universe has been examined. The exact solutions of the dust perturbations, with growing amplitudes in cosmic time, are obtained for some limiting cases of n. Similarly, the long- and short-wavelength modes in the torsion-radiation case are treated, with the amplitudes either oscillating or monotonically growing with time. Overall, it is noted that f(T) models contain a richer set of observationally viable structure growth scenarios that can be tested against up-and-coming observational data and can accommodate currently known features of the large-scale structure power spectrum in the general relativistic and varLambda CDM limits.

Incorporating physical constraints in braneworld black-string solutions for a Minkowski brane in scalar-tensor gravity

In the framework of a general scalar-tensor theory, where the scalar field is non-minimally coupled to the five-dimensional Ricci scalar curvature, we investigate the emergence of complete brane-world solutions. By assuming a variety of forms for the coupling function, we solve the field equations in the bulk, and determine in an analytic way the form of the gravitational background and scalar field in each case. The solutions are always characterized by a regular scalar field, a finite energy-momentum tensor, and an exponentially decaying warp factor even in the absence of a negative bulk cosmological constant. The space-time on the brane is described by the Schwarzschild solution leading to either a non-homogeneous black-string solution in the bulk, when the mass parameter $M$ is non-zero, or a regular anti-de Sitter space-time, when $M=0$. We construct physically-acceptable solutions by demanding in addition a positive effective gravitational constant on our brane, a positive total energy-density for our brane and the validity of the weak energy condition in the bulk. We find that, although the theory does not allow for all three conditions to be simultaneously satisfied, a plethora of solutions emerge which satisfy the first two, and most fundamental, conditions.

Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak post-Newtonian gravitational background field, described by the Eddington--Robertson parametrised post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows to systematically derive the coupling of the model system to gravity, instead of `guessing' it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

General Assertions on the Gravitational Waves Polarization Modes from an f(R) Model of Gravity

Detailed analysis of an f( R) theory is emphasized in a Minkowski and non trivial background. It is shown that the polarization modes depend strongly on the metric or Palatini formalism, Einstein or Jordan frame, function f (R ), background gravitational field and the observer.

Neutrino spin oscillations in external fields in curved spacetime

We study spin oscillations of massive Dirac neutrinos in background matter, electromagnetic and gravitational fields. First, using the Dirac equation for a neutrino interacting with the external fields in curved spacetime, we rederive the quasiclassical equation for the neutrino spin evolution, which was proposed previously basing on principles of the general covariance. Then, we apply this result for the description of neutrino spin oscillations in nonmoving and unpolarized matter under the influence of a constant transverse magnetic field and a gravitational wave. We derive the effective Schr\"odinger equation for neutrino oscillations in these external fields and solve it numerically. Choosing realistic parameters of external fields, we show that the parametric resonance can take place in spin oscillations of low energy neutrinos. Some astrophysical applications are briefly discussed.

On a Relation Between Twistors and Killing Spinors

Inspiring from the consequence of constructing conformal Killing-Yano forms out of Killing-Yano forms and closed conformal Killing-Yano forms, this work includes a method for building up twistors from Killing spinors which can be analogously interpreted as the quantum electrodynamical pair annihilation process in background gravitational fields. The former consequence is easily verified if one introduces a new defining differential equation for (possibly inhomogeneous) Killing-Yano forms which is free from auxiliary vector fields, as is done in this text. From this point of view a neat relation between the symmetry operators of massive and massless Dirac equation is also introduced. Some other physical interpretations are also included.

High-energy hyperbolic scattering by neutron stars and black holes

We investigate the hyperbolic scattering of test particles, spinning test particles and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.