Background Spacetime Research Articles

Background Independence and Gauge Invariance in General Relativity Part 2—Covariant Quantum Gravity

Background independence is often being claimed as the characteristic property of several current and past models of Quantum Gravity. In actual fact, such a notion has a wider connotation and must be rooted into the validity of the general covariance principle, demanding its logical connection with the notions of manifest covariance and (quantum) gauge invariance. In fact, as we intend to show here, it involves (a) the existence of a well-defined, albeit arbitrary, classical background space-time; and (b) the suitable realization of a dynamical equation for the related background metric field tensor, referred to as quantum-modified Einstein tensor field equation, which actually determines it in a suitable functional setting. Remarkably, it is proved that in the context of the theory of Covariant Quantum Gravity (CQG-theory), recently developed by Cremaschini and Tessarotto (2015–2022), background independence implies that such an equation “emerges” rigorously from the same CQG-theory. This follows in terms of a stochastic quantum expectation value evaluated with respect to the corresponding characteristic quantum PDE. It is shown that an analogous emergence property applies also to the background metric field tensor in terms of stochastic fluctuations of the corresponding underlying quantum tensor of gravitational field. These results warrant the consistent validity of background independence for the prescription of the space-time metric tensor in CQG-theory.

Spin 2 Particle with Anomalous Magnetic Moment in Riemann Space−Time: A Massless Case with the Gauge Symmetry

The most of studies in the theory of spin 2 field were performed with the use of the 2-nd order equations. The spin 2 particle theory proposed by F.I. Fedorov is based on the first order equations requires a 30-component set of tensors. Besides, by him and coauthors was elaborated a more general theory, which is based on 50-component set of tensors. In the present paper, we consider this more general theory in presence of arbitrary electromagnetic fields and Riemannian space-time backgrounds. First we study the 50-component theory for a massive particle. In this case, there arises the non-minimal interaction with the curved space-time background through the Ricci and Riemann tensors. It is important that the theory under consideration allows for a new massless limit for the spin 2 field. This fact is of special interest, because the conventional Pauli - Fierz theory for the massless field does not possess gauge symmetry in the curved space-time, in particular, in models with the vanishing Ricci tensor. We show that the generalized theory possesses such a gauge symmetry in all space-time models for which the Ricci tensor vanishes.

Milne spacetime with conical defect: Some holographic studies

We initiate a holographic study of field theory in a time-dependent background with a conical defect. We focus on the Milne spacetime to which, in the absence of cosmological constant, at late time any hyperbolic Friedmann-Robertson-Walker metric flows. When the Milne vacuum is represented by the adiabatic one, we are able to compute the two point correlators of operators which are dual to the massive scalars in the bulk AdS-Milne spacetime background with a defect. We find, for both twisted and untwisted operators, the correlators can be represented as the sum over images. This sum can be carried out explicitly to write the results in compact forms.

Internal structures and circular orbits for test particles

We explore how the internal structure of a test particle affects its equatorial stable circular orbits around the Kerr black hole with or without a cosmological constant. To this end, we first explicitly write equations of motion for a test particle in the pole-dipole-quadrupole approximation specifying the quadrupole momentum tensor to a spin-induced model. Then we calculate characteristic quantities – radius, angular momentum, energy, angular velocity, and impact parameter – for the particles on the stable circular orbits. Once the pole-dipole-quadrupole approximation is taken, we find that for a particle on an innermost stable circular orbit, all characteristic quantities, except the angular velocity, become greater relative to the pole-dipole case. In contrast, for a particle on an outermost stable circular orbit, which only exists in the case of the spacetime background being asymptotically de Sitter, it is the radius that becomes smaller while all other quantities become greater.

Closed string radiation from the interacting fractional-dressed Dp-branes with the transverse motions

We determine the boundary states, associated with a fractional Dp-brane in the presence of the Kalb–Ramond field and a U(1) gauge potential. The background spacetime is the non-compact orbifold {mathbb {R}}^{1, 21} otimes {mathbb {R}}^4/ {mathbb {Z}}_2. Besides, the brane has a transverse velocity. We compute the radiation amplitude of a massless closed string from the interaction of two fractional Dp-branes with the previous background fields. The branes have been dressed by different fields and have transverse motions. The total radiation amplitude will be investigated for large inter-brane separation. Finally, the graviton, Kalb–Ramond (axion) and dilaton emissions will be distinctly studied. Our calculations are in the context of the bosonic string theory.

Observational constraints on anisotropies for bouncing alternatives to inflation

We calculate how primordial anisotropies in the background space-time affect the evolution of cosmological perturbations for bouncing alternatives to inflation, like ekpyrosis and the matter bounce scenario. We find that the leading order effect of anisotropies in the contracting phase of the universe is to induce anisotropies in the cosmic microwave background with a very concrete form: a scale-invariant quadrupolar angular distribution. Sub-leading effects are the generation of higher-order moments in the angular distribution, as well as cross-correlations between scalar and tensor modes. We also find that observational constraints from the cosmic microwave background on the quadrupole moment provide strong bounds on allowed anisotropies for bouncing alternatives to inflation that are significantly more constraining than the bounds previously obtained using scaling arguments based on the conjectured Belinski-Khalatnikov-Lifshitz instability.

Regularization of a scalar charged particle for generic orbits in Kerr spacetime

A scalar charged particle moving in a curved background spacetime will emit a field affecting its own motion; the resolving of this resulting motion is often referred to as the self-force problem. This also serves as a toy model for the astrophysically interesting compact body binaries, extreme mass ratio inspirals, targets for the future space-based gravitational wave detector, LISA. In the modelling of such systems, a point-particle assumption leads to problematic singularities which need to be safely removed to solve for the motion of the particle regardless of the scenario: scalar, electromagnetic or gravitational. Here, we concentrate on a scalar charged particle and calculate the next order of the Detweiler-Whiting singular field and its resulting regularisation parameter when employing the mode-sum method of regularisation. This enables sufficiently faster self-force calculations giving the same level of accuracy with significantly less $\ell$ modes. Due to the similarity of the governing equations, this also lays the groundwork for similar calculations for an electromagnetic or mass charged particle in Kerr spacetime and has applications in other regularisation schemes like the effective source and matched expansion.

A proposal for a metaphysics of self-subsisting structures. I. Classical physics

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered—and is thus susceptible to scientific progress—the empirically successful structural features of the framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space.

Chiral gravitational waves from thermalized neutrinos in the early Universe

We investigate polarized gravitational waves generated by chiral fermions in the early Universe. In particular, we focus on the contribution from left-handed neutrinos in thermal equilibrium with finite temperature and chemical potential in the radiation dominated era. We compute the correlation functions of gravitational fields pertinent to the Stokes parameter V characterizing the circular polarization of gravitational waves in the Minkowski and expanding spacetime backgrounds. In the expanding universe, we find that the thermalized neutrinos induce a non-vanishing V linear to the neutrino degeneracy parameter and wavenumber of gravitational waves in the long wavelength region. While the magnitude of the gravitational waves generated by thermal neutrinos is too small to be detectable by current and planned third generation gravitational wave detectors, their observations by future generation detectors for ultra-high frequency regimes could provide information on the neutrino degeneracy parameter in the early Universe.

On Graviton Propagation in Curved Space-Time Background

Equation describing propagation of gravitational waves (GW) over arbitrary curved space-time background is analyzed. New terms, which are absent in the conventional homogeneous and isotropic Friedmann cosmology, are found. Some examples of realistic metric, where these new terms manifest themselves, are presented. Possible implications to very low frequency GW are briefly discussed.

영화 <국두(菊豆)>에서 나타나는 욕망과 금기

Zhang Yimou(张艺谋)’s movie <Judou> is the one that was made by adapting Liu Heng’s novel 『Fuxi Fuxi』. This writing is aimed to inquire into the narrative structure of a movie through comparing two works. What examines <Judou>, which is positioned in the middle of the period that <Red Sorghum(红高粱)> and <Raise The Red Lantern(大紅燈籠高高掛)> were produced, is an important point available for checking an aesthetic flow in Zhang Yimou’s movie. With paying attention to this point, this study shed light on the cinematic value that Judou> has. To this end, the thematic consciousness in the movie <Judou> was explored through the narrative comparison between original novel and movie, namely, through the setting of space-time backgrounds and characters, a variation of the narrative, and the cinematic techniques and devices. First, a character who leads a narrative in the novel is Tianqing, but is Judou in the movie. This movement of the central figure is associated with the thematic consciousness of the movie. It took a look at how Tianqing’s sexual awareness and sexual desire of being seen in the novel are changed in the movie. Second, it analyzed the closed space in a dyeing factory, Tianqing’s sneaking a look at Judou, and the meaning of sunlight and backlight. Third, a narrative on feudal violence was inspected. Through ancestral shrine(祠堂) and color, the image of feudalism was searched. Through dyeing cloth, ‘coloring’ was clarified to metaphorize the injection of feudalism. Especially through a few devices that appear in the movie, Tianbai was confirmed to be a successor of feudalism. Fourth, it dealt with the violation of taboos, namely, incest and killing father(殺父). It examined what the meaning of killing father is that was committed by Tianbai, along with a taboo violation by Judou and Tianqing.

Eikonal amplitudes from curved backgrounds

Eikonal exponentiation in QFT describes the emergence of classical physics at long distances in terms of a non-trivial resummation of infinitely many diagrams. Long ago, 't~Hooft proposed a beautiful correspondence between ultra-relativistic scalar eikonal scattering and one-to-one scattering in a background shockwave space-time, bypassing the need to resum. In this spirit, we propose a covariant method for computing one-to-one amplitudes in curved background space-times which gives rise what we conjecture to be a general expression for the eikonal amplitude. We show how the one-to-one scattering amplitude for scalars on any stationary space-time reduces to a boundary term that captures the long-distance behavior of the background and has the structure of an exponentiated eikonal amplitude. In the case of scalar scattering on Schwarzschild, we recover the known results for gravitational scattering of massive scalars in the eikonal regime. For Kerr, we find a remarkable exponentiation of the tree-level amplitude for gravitational scattering between a massive scalar and a massive particle of infinite spin. This amplitude exhibits a Kawai-Lewellen-Tye-like factorization, which we use to evaluate the eikonal amplitude in momentum space, and study its analytic properties.

Graviton non-gaussianity in α-vacuum

We compute the leading order non-Gaussianity, i.e., the bispectrum, of the tensor perturbation in the general α-vacuum on de Sitter space in general relativity. In addition to the well-known Bunch-Davies (BD) vacuum, there exits an infinite number of de Sitter invariant vacua represented by a real parameter α and a phase ϕ, with α = 0 being the BD vacuum. They are called α-vacua. In the standard slow-roll inflation, as de Sitter invariance no longer applies, the α-vacua lose its relevance in the rigorous sense. Nevertheless, if we assume that the parameter α is only weakly dependent on the wavenumber with an appropriate UV cutoff, we may consider pseudo-α-vacua. In the case of false vacuum inflation where the background spacetime is pure de Sitter, a non-trivial (non-BD) α-vacuum could indeed be realized. We find an intriguing result that the bispectrum may be exponentially enhanced to be detectable by observation even if the spectrum is too small to be detected.

The cosmological constant as a boundary term

We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general relativity the cosmological constant is a parameter of the action. Unimodular gravity with a nondynamical background spacetime volume element has a time variable that is canonically conjugate to the cosmological constant. Wave functions depend on time and satisfy a Schrödinger equation. On the contrary, in the covariant version of unimodular gravity with a 3-form gauge field, proposed by Henneaux and Teitelboim, wave functions are time independent and satisfy a Wheeler-DeWitt equation, as in general relativity. The 3-form gauge field integrated over spacelike hypersurfaces becomes a “cosmic time” only in the semiclassical approximation. In unimodular gravity the smallness of the observed cosmological constant has to be explained as a property of the initial state.

Gravitational waves in gauge theory gravity with a negative cosmological constant

In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacement and rotation. Similar to the electromagnetism, the gauge formulation enables us to interpret the gravitational force as a gauge force on the background flat spacetime. The dynamical fields that describe the gravitational interactions are those position and rotation gauge fields introduced as the requirement of the gauge covariance. The gravitational field equations can be derived from the least action principle with the action as a gauge invariant quantity built from the covariant field strength. We discuss the gravitational wave solutions of the field equations with a negative cosmological constant, and show that these solutions are of Petrov type-N. We also discuss the velocity memory effect by calculating the velocity change of an initially free falling massive particle due to the presence of the gravitational waves.

Spacetime evolution during moduli stabilization in radiation dominated era beyond 4D effective theory

We investigate the time evolution of the background spacetime during the moduli stabilization process, which is assumed to occur in the radiation dominated era. The setup is basically the Salam-Sezgin model, but we add a potential term for the dilaton in order to stabilize the moduli completely. We numerically solve the higher-dimensional background field equations, including a case that the stabilization process cannot be described within the 4D effective theory. In contrast to the conventional 4D effective theory analysis, we find that when the mass scale of the stabilization is larger than the compactification scale, the radiation contribution to the total energy density remains to be non-negligible for a much longer time than the stabilization time scale. As a result, the non-compact 3D space expands slower than the matter dominated universe. We also find the equation of state for the radiation wrad remains to be smaller than 1/3 for a long time, which indicates that the radiation still feels the extra dimensions for a while even after the moduli are stabilized.

Electromagnetic, Gravitational, and Plasma-Related Perturbations of Locally Rotationally Symmetric Class II Spacetimes

We investigate electromagnetic, gravitational, and plasma-related perturbations to the first order on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II spacetimes. Due to the anisotropic nature of the studied backgrounds, we are able to include a non-zero magnetic field to the zeroth order. As a result of this inclusion, we find interesting interactions between the electromagnetic and gravitational variables already of the first order in the perturbations. The equations governing these perturbations are found by using the Ricci identities, the Bianchi identities, Einstein’s field equations, Maxwell’s equations, particle conservation, and a form of energy-momentum conservation for the plasma components. Using a 1+1+2 covariant split of spacetime, the studied quantities and equations are decomposed with respect to the preferred directions on the background spacetimes. After linearizing the decomposed equations around an LRS background, performing a harmonic decomposition, and imposing the cold magnetohydrodynamic (MHD) limit with a finite electrical resistivity, the system is then reduced to a set of ordinary differential equations in time and some constraints. On solving for some of the harmonic coefficients in terms of the others, the system is found to decouple into two closed and independent subsectors. Through numerical calculations, we then observe some mechanisms for generating magnetic field perturbations, showing some traits similar to previous works using Friedmann–Lemaître–Robertson–Walker (FLRW) backgrounds. Furthermore, beat-like patterns are observed in the short wave length limit due to interference between gravitational waves and plasmonic modes.

Testing black holes in non-linear electrodynamics from the observed quasi-periodic oscillations

Quasi-periodic oscillations (QPOs), in particular, the ones with high frequencies, often observed in the power spectrum of black holes, are useful in understanding the nature of strong gravity since they are associated with the motion of matter in the vicinity of the black hole horizon. Interestingly, these high frequency QPOs (HFQPOs) are observed in commensurable pairs, the most common ratio being 3:2. Several theoretical models are proposed in the literature which explain the HFQPOs in terms of the orbital and epicyclic frequencies of matter rotating around the central object. Since these frequencies are sensitive to the background spacetime, the observed HFQPOs can potentially extract useful information regarding the nature of the same. In this work, we investigate the role of regular black holes with a Minkowski core, which arise in gravity coupled to non-linear electrodynamics, in explaining the HFQPOs. Regular black holes are particularly interesting as they provide a possible resolution to the singularity problem in general relativity. We compare the model dependent QPO frequencies with the available observations of the quasi-periodic oscillations from black hole sources and perform a χ2 analysis. Our study reveals that most QPO models favor small but non-trivial values of the non-linear electrodynamics charge parameter. In particular, black holes with large values of non-linear electrodynamics charge parameter are generically disfavored by present observations related to QPOs.

Noncommutative D=5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly

Actions for noncommutative (NC) gauge field theories can be expanded perturbatively in powers of the noncommutativity parameter theta using the Seiberg–Witten map between ordinary classical fields and their NC counterparts. The leading order term represents classical (theta =0) action while higher-order terms give us theta -dependent NC corrections that ought to capture some aspects of quantum gravity. Building on previous work of Aschieri and Castellani on NC Chern–Simons (CS) gauge and gravity theories, showing that non-trivial theta -dependence exists only for spacetime dimensions Dge 5, we investigate a correlated effect of these extra spatial dimensions and noncommutativity on four-dimensional physics, up to first-order in theta . Assuming that one spatial dimension is compactified into a circle, we apply the Kaluza–Klein reduction procedure on the NC D=5 CS theory for the conformal gauge group SO(4, 2), to obtain an effective, theta -dependent four-dimensional theory of gravity that has Einstein–Hilbert gravity with negative cosmological constant as its commutative limit. We derive field equations for this modified theory of gravity and study the effect of NC interactions on some classical geometries, such as the AdS-Schwarzschild black hole. We find that this NC background spacetime gives rise to chiral gravitational anomaly due to the nonvanishing theta -dependent Pontryagin density.

Generalizations of Snyder model to curved spaces

We consider generalizations of the Snyder algebra to a curved spacetime background with de Sitter symmetry. As special cases, we obtain the algebras of the Yang model and of triply special relativity. We discuss the realizations of these algebras in terms of canonical phase space coordinates, up to fourth order in the deformation parameters. In the case of triply special relativity we also find exact realization, exploiting its algebraic relation with the Snyder model.