Curved Background Spacetime Research Articles

Gravitational spinoptics in a curved space-time

In this paper we discuss propagation of the weak high-frequency gravitational waves in a curved spacetime background. We develop a so-called spinoptics approximation which takes into account interaction of the spin of the field with the curvature of the background metric. This is achieved by modifying the standard geometric optics approximation by including the helicity sensitive terms of the order 1/ω in the eikonal equation. The novelty of the approach developed in this paper is that instead of study of the high-frequency expansion of the equations for the gravitational field perturbations we construct the effective action for the gravitational spinoptics. The gravitational spinoptics equations derived by variation of the effective action correctly reproduce the earlier obtained results. However, the proposed effective action approach is technically more simple and transparent. It allows one to reduce the study of the high-frequency gravitational waves to study classical dynamics of massless particles with internal discrete degree of freedom (helicity). The formalism is covariant and it can be applied for arbitrary vacuum space-time background.

Yang Model Revisited

A long time ago, C.N. Yang proposed a generalization of the Snyder model to the case of a curved background spacetime, based on an algebra isomorphic to o(1, 5) which includes, as subalgebras both the Snyder and the de Sitter algebras. His proposal can, therefore, be interpreted as a model of noncommutative curved spacetime, and could be useful for relating physics on very small and very large scales. We review this model and some recent progress concerning its generalizations and its interpretation in the framework of Hopf algebras. We also report some possibilities to relate it to more phenomenological aspects.

Realizations and star-product of doubly κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-deformed Yang models

The Yang algebra was proposed a long time ago as a generalization of the Snyder algebra to the case of curved background spacetime. It includes as subalgebras both the Snyder and the de Sitter algebras and can therefore be viewed as a model of noncommutative curved spacetime. A peculiarity with respect to standard models of noncommutative geometry is that it includes translation and Lorentz generators, so that the definition of a Hopf algebra and the physical interpretation of the variables conjugated to the primary ones is not trivial. In this paper we consider the realizations of the Yang algebra and its κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-deformed generalization on an extended phase space and in this way we are able to define a Hopf structure and a twist.

Island formula from Wald-like entropy with backreaction

We propose a Lorentzian derivation of the generalized entropy associated with the island formula for black holes as a Wald-like entropy without reference to the exterior non-gravitating region or field-theoretic von Neumann entropy of Hawking radiation in a fixed curved spacetime background. We illustrate this idea by studying two-dimensional black holes in the Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model in which Hawking radiation is represented by conformal scalars. With some prescriptions assumed, we show that the generalized entropy for the island formula can be reproduced as the Wald-like entropy of the two-dimensional dilaton-gravity theories upon the inclusion of the backreaction from Hawking radiation described by conformal anomaly. We give a discussion on how a similar idea can be applied to higher-dimensional black holes. It is emphasized that the generalized entropy is obtained in a fully gravitational fashion, yet it yields the same Page curve as that of the half-gravitational set-up. We argue that the results in this paper exacerbate the issues raised in the work of massive islands and inconsistency of islands in theories of long-range gravity.

On Clifford multivector-valued actions, generalized Dirac equation and quantization of branes

We explore the construction of a generalized Dirac equation via the introduction of the notion of Clifford multivector-valued actions, which was inspired by the work of Kanatchikov [Kanatchikov IV. De Donder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory. Rept Math Phys. 1999;43:157–170; Kanatchikov IV. De Donder-Weyl Hamiltonian formulation and precanonical quantization of Vielbein gravity. J Phys Conf Ser. 2013;442:012041] on the De Donder-Weyl formulation of field theory. Crucial in this construction is the evaluation of the exponentials of multivectors associated with Clifford (hypercomplex) analysis. Exact matrix solutions (instead of spinors) of the generalized Dirac equation in D = 2 , 3 space–time dimensions are found. This formalism can be extended to curved space–time backgrounds. We conclude by proposing a wave-functional equation governing the quantum dynamics of branes living in C-spaces (Clifford spaces), and which is based on the De Donder–Weyl Hamiltonian formulation of field theory.

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

The Dirac equation with /non--symmetric potentials in curved spacetime backgrounds

In this paper, we have presented the Dirac equation in the frame of position-dependent mass on two dimensional gravitational static background in the presence of /non--symmetric potential interactions. The exponential metric component have formed the reduced Dirac operator into the general supersymmetric model within mass changing with coordinates. We have obtained the eigenvalues of the Dirac operator for the complex Morse and trigonometric complex Scarf-II potentials SL(2, C) using Lie algebras and the supersymmetric quantum mechanical approaches. Moreover, after obtaining a general Sturm-Liouville type equation using a convenient mapping, the system have become available to be investigated within η- pseudo-Hermiticity. With this context, η operator is found for the examples of complex trigonometric Rosen-Morse potential and complex Morse potentials with real and complex parameters of the initial system and finally the solutions are obtained for each model with the graphics of energy values and probability densities.

Einstein-Dirac system in semiclassical gravity

We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple independent Dirac fields to preserve spherical symmetry. We canonically quantize a single Dirac field in a static spherically symmetric curved spacetime background. Using the semiclassical gravity approximation, in which the Einstein field equations are sourced by the expectation value of the stress-energy-momentum tensor, we derive a system of equations whose solutions describe static spherically symmetric self-gravitating configurations of identical quantum spin-$1/2$ particles. We self-consistently solve these equations and present example configurations. Although limiting cases of our semiclassical system of equations reproduce the multifield system of equations found in the literature, our system of equations is derived from the excitations of a single quantum field.

Hadamard tail from initial data on the light cone

Field perturbations of a curved background spacetime generally propagate not only at the speed of light but also at all smaller velocities. This so-called $Hadamard\,tail$ contribution to wave propagation is relevant in various settings, from classical self-force calculations to communication between quantum particle detectors. One method for calculating this tail contribution is by integrating the homogeneous wave equation using Characteristic Initial Data on the light cone. However, to the best of our knowledge, this method has never been implemented before except in flat or conformally-flat spacetimes, where null geodesics emanating from a point do not cross. In this work, we implement this method on the black hole toy model Pleba\'nski-Hacyan spacetime, $\mathbb{M}_2\times\mathbb{S}^2$. We obtain new results in this spacetime by calculating the Hadamard tail of a scalar field everywhere where it is defined (namely, in the maximal normal neighbourhood of an arbitrary point) and investigate how it varies for various values of the coupling constant. This serves as a proof-of-concept for the Characteristic Initial Data method on spacetimes where null geodesics emanating from a point $do$ cross.

Toward quantization of inhomogeneous field theory

We explore the quantization of a $$(1+1)$$ -dimensional inhomogeneous scalar field theory in which Poincaré symmetry is explicitly broken. We show the ‘classical equivalence’ between a scalar field theory on curved spacetime background and its corresponding inhomogeneous scalar field theory. This implies that a hidden connection may exist among some inhomogeneous field theories, which corresponds to general covariance in field theory on curved spacetime. Based on the classical equivalence, we propose how to quantize a specific field theory with broken Poincaré symmetry inspired by standard field theoretic approaches, canonical and algebraic methods, on curved spacetime. Consequently, we show that the Unruh effect can be realized in inhomogeneous field theory and propose that it may be tested by a condensed matter experiment. We suggest that an algebraic approach is appropriate for the quantization of a generic inhomogeneous field theory.

Studying Postmerger Outflows from Magnetized-neutrino-cooled Accretion Disks

Neutrino-cooled accretion flow around a spinning black hole, produced by a compact binary merger, is a promising scenario for jet formation and launching magnetically driven outflows. Based on GW170817 gravitational wave detection by LIGO and Virgo observatories, followed by electromagnetic counterparts, this model can explain the central engine of the short-duration gamma-ray bursts and kilonova radiations. Using the open-source general relativistic magnetohydrodynamic HARM-COOL code, we evolved several 2D magnetized accretion disk–black hole models with a realistic equation of state in the fixed curved spacetime background. We applied the particle tracer technique to measure the properties of the outflows. The disk and black hole's initial parameters are chosen in a way to represent different possible postmerger scenarios of the merging compact objects. Our simulations show a strong correlation between the black hole's spin and ejected mass. Generally, mergers producing massive disks and rapidly spinning black holes launch stronger outflows. We observed our models generate winds with moderate velocity (v/c ∼ 0.1–0.2) and a broad range of electron fractions. We use these results to estimate the luminosity and light curves of possible radioactively powered transients emitted by such systems. We found that the luminosity peaks within the range of 1040–1042 erg s−1, which agrees with previous studies for disk wind outflows.

Spin Optics for Gravitational Waves

We present the geometric optics expansion for circularly polarized gravitational waves on a curved spacetime background, to subleading order. We call spin optics to the subleading order geometric optics expansion, which involves modifying the standard eikonal function by including a specially chosen helicity-dependent correction. We show that the techniques developed for the propagation of electromagnetic waves can also be applied to gravitational waves in the limit of spin optics. However, one needs to account for the difference in the photon and graviton helicity, which we do here.

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.

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.

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.

Fractons in curved space

We consistently couple simple continuum field theories with fracton excitations to curved spacetime backgrounds. We consider homogeneous and isotropic fracton field theories, with a conserved U(1) charge and dipole moment. Coupling to background fields allows us to consistently define a stress-energy tensor for these theories and obtain the respective Ward identities. Along the way, we find evidence for a mixed gauge-gravitational anomaly in the symmetric tensor gauge theory which naturally couples to conserved dipoles. Our results generalise to systems with arbitrarily higher conserved moments, in particular, a conserved quadrupole moment.

Neutrino Dynamics in a Quantum-Corrected Schwarzschild Spacetime

We study neutrino propagation in a curved spacetime background described by the Schwarzschild solution with the addition of quantum corrections evaluated in the framework of perturbative quantum gravity at lowest order. In particular, we investigate neutrino oscillations and decoherence within the Gaussian wave packet description, finding that quantum gravity corrections significantly affect the intrinsic features of mixed particles and induce potentially measurable physical effects.

Analogue Metric in a Black-Bounce Background

The conventional approach of embedding an effective acoustic metric for sound motion in a background flat Minkowski space-time has recently been extended to incorporate more general curved background metrics, which might contain a black hole. Though the observational aspects of these kinds of acoustics horizons, including the sonic shadow structure and quasi normal modes, have received significant attention in the literature, there is room left for discussions about embedding more general classes of curved background space-times without optical horizons. Here, we propose and study a new class of acoustic metrics that is embedded in a black-bounce space-time, thereby giving a suitable tuneable system to understand possible observational effects of the presence or absence of acoustic horizons. After showing that the metric can represent five types of different effective backgrounds for sound motion, including a novel “acoustic wormhole–optical wormhole” branch, we discuss how the distinctive features of sonic shadows can appear even in the absence of any acoustic horizon due to the wormhole throat present in the acoustic metric.

Covariant higher order perturbations of branes in curved spacetime

The treatment of higher order perturbations of branes is considered using a covariant variational approach. This covariant variational approach brings to the forefront the geometric structure of the underlying perturbation theory, as opposed to a more commonly used ``direct approach,'' that ignores the variational origin. In addition, it offers a clear calculational advantage with respect to so-called ``gauge fixed'' treatments that distinguish tangential and normal modes, as it emphasizes the symmetries of the geometric models that describe the brane dynamics. We restrict our attention to a brane action that depends at most on first derivatives of the embedding functions of the world volume spanned by the brane in its evolution. We consider first and second variations of the action that describes the brane dynamics. The first variation produces the equations of motion, as is well known. In the second variation we derive the Jacobi equations for these kind of models, and we emphasize the role of the Hessian matrix. This is extended to third order in variations, first in a flat and then in a curved spacetime background. Further, we specialize to the relevant case of the Dirac-Nambu-Goto action that describes extremal branes. The proper setting of a covariant variational approach allows to go in principle to geometric models that depend on higher derivatives of the embedding functions, and higher order perturbations, with the due complications involved, but with a solid framework in place.

On the renormalization of entanglement entropy

The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.