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We adapt the post-Newtonian gravitational-radiation methods developed within general relativity by Epstein and Wagoner to the gravitation theory with torsion, recently proposed by Hehl et al., and show that the two theories predict in this approximation the same gravitational radiation losses. Since they agree also on the first post-Newtonian level, they are at the present time - observationally - indistinguishable., Published version: General Relativity and Gravitation, Vol. 12 (1980) 951-961 doi: 10.1007/BF00757366 arXiv-ed February 1980; LaTeX-ed May 1, 2023

Gravitacijski valovi poznat su fenomen otkriven općom teorijom relativnosti. Nakon prvog Einsteinovog izvoda u lineariziranoj teoriji, njihova fizikalnost bila je upitna više desetljeća. Bondi-Sachsov formalizam otklonio je sumnje i dao baždarno neovisne rezultate u punoj teoriji za asimptotski ravne prostore. Kako su opažanja pokazala da naš svemir nije asimptotski ravan, već ima malu pozitivnu kozmološku konstantu Λ > 0, pokrenuo se razvoj teorije za asimptotski de Sitterove prostore. Iznosimo glavne metode i rezultate za obje vrste prostora i razmatramo poteškoće u razvoju pune teorije u Λ > 0 slučaju. Gravitational waves are a well known phenomenon discovered by the means of general theory of relativity. After Einstein’s first derivation in linearized theory, their physicality was under question for multiple decades. Bondi-Sachs formalism resolved the suspicions and gave gauge independent results in full theory for asymptotically flat spaces. As observations have shown our universe not to be asymptotically flat, but to have a small positive cosmological constant Λ > 0, development of the theory in asymptotically de Sitter spaces began. We present the main methods and results in both cases and study the difficulties in development of the full theory in the Λ > 0 case.

We provide in this paper a first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime by using the conformal geometric approach. We will show that the existing decay results for the solutions of the Regge–Wheeler and Zerilli equations obtained recently by Anderson et al. (Ann. Henri Poincare 21:61–813, 2020) are sufficient to obtain the conformal scattering.

The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (S.A, T.B.) in (arXiv:1803.05341) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from (arXiv:1803.05341) with the first compatibility operator from that complex., 23 pages. Some remarks added

From the conformal transformation, a massless spin-2 field must be presented by a rank-3 mixed symmetric tensor field. A massless spin-2 rank-3 mixed symmetric tensor field in de Sitter ambient space formalism is studied in this paper, which may be regarded as the linearized gravity or its dual. Recalling the field equation, the possible physical solutions of the field equation are calculated. The solutions can be written in terms of a rank-2 symmetric tensor field and a scalar field. We discuss that under what conditions this tensor field can be associated with the de Sitter and conformal groups unitary representations. Finally, for the physical solution, the quantum field operator and the two-point function are presented.

We demonstrate that the linearized Einstein gravity in de Sitter (dS) spacetime besides the evident symmetries also possesses the additional (local) symmetry $h_{\mu\nu}\rightarrow h_{\mu\nu} + {\cal E}_{\mu\nu}\chi$, where ${\cal E}_{\mu\nu}$ is a spin-two projector tensor and $\chi$ is an arbitrary constant function. We argue that an anomalous symmetry associated with this hitherto `hidden' property of the existing physics is indeed at the origin of `dS breaking' in linearized quantum gravity., Comment: 6 pages, no figure, version accepted for publication in Physics Letters B

In this note, we prove decay for the spin ± 1 Teukolsky equations on the Schwarzschild spacetime. These equations are those satisfied by the extreme components ( $$\alpha $$ and $${\underline{\alpha }}$$ ) of the Maxwell field, when expressed with respect to a null frame. The subject has already been addressed in the literature, and the interest in the present approach lies in the connection with the recent work by Dafermos, Holzegel and Rodnianski on linearized gravity (Dafermos et al. in The linear stability of the Schwarzschild solution to gravitational perturbations, 2016. arXiv:1601.06467 ). In analogy with the spin $$\pm 2$$ case, it seems difficult to directly prove Morawetz estimates for solutions to the spin $$\pm 1$$ Teukolsky equations. By performing a differential transformation on the extreme components $$\alpha $$ and $${\underline{\alpha }}$$ , we obtain quantities which satisfy a Fackerell–Ipser Equation, which does admit a straightforward Morawetz estimate and is the key to the decay estimates. This approach is exactly analogous to the strategy appearing in the aforementioned work on linearized gravity. We achieve inverse polynomial decay estimates by a streamlined version of the physical space $$r^p$$ method of Dafermos and Rodnianski. Furthermore, we are also able to prove decay for all the components of the Maxwell system. The transformation that we use is a physical space version of a fixed-frequency transformation which appeared in the work of Chandrasekhar (Proc R Soc Lond Ser A 348(1652):39–55, 1976). The present note is a version of the author’s master thesis and also serves the “pedagogical” purpose to be as complete as possible in the presentation.

The correct name of the second author is Martin Bonte. In the expression for the Pauli-Fierz Hamiltonian in equation (3.10), we missed two terms that vanish on the constraint surface., SCOPUS: er.j, info:eu-repo/semantics/published

We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Ra\~{n}ada-Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot perturbations are given and the geodesic equation as a function of two complex parameters of the GEM knots are calculated. Finally, the Landau--Lifshitz pseudo-tensor and a scalar invariant of the GEM knots are computed., Comment: 22 pages. Published in the Special Issue "Frame-Dragging and Gravitomagnetism"

This is an Open Access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License (http://creativecommons.org/licenses/by/4.0/)., One of the main problems that emergent-gravity approaches face is explaining how a system that does not contain gauge symmetries ab initio might develop them effectively in some regime. We review a mechanism introduced by some of the authors for the emergence of gauge symmetries in [JHEP 10 (2016) 084] and discuss how it works for interacting Lorentz-invariant vector field theories as a warm-up exercise for the more convoluted problem of gravity. Then, we apply this mechanism to the emergence of linear diffeomorphisms for the most general Lorentz-invariant linear theory of a two-index symmetric tensor field, which constitutes a generalization of the Fierz–Pauli theory describing linearized gravity. Finally we discuss two results, the well-known Weinberg–Witten theorem and a more recent theorem by Marolf, that are often invoked as no-go theorems for emergent gravity. Our analysis illustrates that, although these results pinpoint some of the particularities of gravity with respect to other gauge theories, they do not constitute an impediment for the emergent gravity program if gauge symmetries (diffeomorphisms) are emergent in the sense discussed in this paper. © 2021 by the authors., Financial support was provided by the Spanish Government through the projects FIS2017-86497-C2-1-P, FIS2017-86497-C2-2-P, PID2019-107847RB-C44, PID2020-118159GB-C43, PID2020-118159GB-C44, and by the Junta de Andalucia through the project FQM219. C.B. and G.G.M. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709). GGM acknowledges financial support from IPARCOS.

The Teukolsky Master Equation describes the dynamics of massless fields with spin on a Kerr black hole. Under separation of variables, spin-reversal for this equation is accomplished through the so-called Teukolsky--Starobinsky identities. These identities are associated to the so-called Teukolsky--Starobinsky constants, which are spin-dependent. We collect some properties of the Teukolsky--Starobinsky constants and dispel some myths present in the literature. We show that, contrary to popular belief, these constants can be negative for spin larger than 2. Such fields thus exhibit a novel form of energy amplification which occurs for non-superradiant frequencies., Comment: 17 pages, 4 figures

We study possibilities of creation and detection of oscillating gravitational fields from lab-scale high energy, relativistic sources. The sources considered are high energy laser beams in an optical cavity and the ultra-relativistic proton bunches circulating in the beam of the Large Hadron Collider (LHC) at CERN. These sources allow for signal frequencies much higher and far narrower in bandwidth than what most celestial sources produce. In addition, by modulating the beams, one can adjust the source frequency over a very broad range, from Hz to GHz. The gravitational field of these sources and responses of a variety of detectors are analyzed. We optimize a mechanical oscillator such as a pendulum or torsion balance as detector and find parameter regimes such that -- combined with the planned high-luminosity upgrade of the LHC as a source -- a signal-to-noise ratio substantially larger than 1 should be achievable at least in principle, neglecting all sources of technical noise. This opens new perspectives of studying general relativistic effects and possibly quantum-gravitational effects with ultra-relativistic, well-controlled terrestrial sources., Comment: Main Text: 23 pages, 1 figure. Appendix: 7 pages, 2 figures

Recent research show that the cosmological components of the Universe should influence on the propagation of Gravitational Waves (GWs) and even it has been proposed a new way to measure the cosmological constant using Pulsar Timing Arrays (PTAs). However, these results have considered very particular cases (e.g. a de Sitter Universe or a mixing with non-relativistic matter). In this work we propose an extension of these results, using the Hubble constant as the natural parameter that includes all the cosmological information and studying its effect on the propagation of GWs. Using linearized gravity we considered a mixture of perfect fluids permeating the spacetime and studied the propagation of GWs within the context of the LCDM model. We found from numerical simulations that the timing residual of local pulsars should present a distinguishable peak depending on the local value of the Hubble constant. As a consequence, when assuming the standard LCDM model, our result predicts that the region of maximum timing residual is determined by the redshift of the source. This framework represents a new test for the standard cosmological model, and it can be used to facilitate the measurements of gravitational wave by ongoing PTAs projects., Comment: 19 pages, 7 figures, 3 tables. Initially submitted to ApJ on March 5, 2019

Models of gravitational decoherence are not commonly applied to ultra-relativistic systems, including photons. As a result, few quantum optical tests of gravitational decoherence have been developed. In this paper, we generalize the gravitational decoherence model of Anastopoulos and Hu (arXiv:1305.5231) to photons. In this model, decoherence originates from a bath of stochastic gravitational perturbations, possibly of fundamental origin. We derive a master equation for general states of the electromagnetic (EM) field; the only free parameter is a noise temperature $\Theta$ of the gravitational fluctuations. We find that interference experiments with long baselines, accessible in near-future experiments, can, in principle, lead to strong constraints in $\Theta$., Comment: 24 pages, minor changes, references added, to be published in "Classical and Quantum Gravity"

In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, remain uniformly bounded and decay to a linearized Kerr metric on the exterior region. We employ Hodge decomposition to split the solution into closed and co-closed portions, respectively identified with even-parity and odd-parity solutions in the physics literature. For the co-closed portion, we extend previous results by the first two authors, deriving Regge-Wheeler type equations for two gauge-invariant master quantities without the earlier paper's need of axisymmetry. For the closed portion, we build upon earlier work of Zerilli and Moncrief, wherein the authors derive an equation for a gauge-invariant master quantity in a spherical harmonic decomposition. We work with gauge-invariant quantities at the level of perturbed connection coefficients, with the initial value problem formulated on Cauchy data sets. With the choice of an appropriate gauge in each of the two portions, decay estimates on these decoupled quantities are used to establish decay of the metric coefficients of the solution, completing the proof of linear stability. Our result differs from that of Dafermos-Holzegel-Rodnianski, both in our choice of gauge and in our identification and utilization of lower-level gauge-invariant master quantities., v3: 62 pages, to appear in J. Differential Geom.; v2: 47 pages, estimates near the horizon corrected, allowing for metric-level decay

It is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.

Gauge invariant, Hamiltonian formulation of field dynamics within a compact region $\Sigma$ with boundary $\partial \Sigma$ is given for the gravitational field linearized over a Kottler metric. The boundary conditions which make the system autonomous are discussed and the corresponding Hamiltonian functional $\mathcal{H}_\text{Invariant}$ is calculated. It is shown that, under specific boundary conditions, the quasi-local Geroch--Hawking mass $\mathcal{H}_\text{Hawking}$ reduces to $\mathcal{H}_\text{Invariant}$ in the weak field approximation. This observation is a quasi-local version of the classical Brill--Deser result., Comment: 10 pages

We construct a class of conserved currents for linearized gravity on a Kerr background. Our procedure, motivated by the current for scalar fields discovered by Carter (1977), is given by taking the symplectic product of solutions to the linearized Einstein equations that are defined by symmetry operators. We consider symmetry operators that are associated with separation of variables in the Teukolsky equation, as well as those arising due the self-adjoint nature of the Einstein equations. In the geometric optics limit, the charges associated with these currents reduce to sums over gravitons of positive powers of their Carter constants, much like the conserved current for scalar fields. We furthermore compute the fluxes of these conserved currents through null infinity and the horizon and identify which are finite., Comment: 37 pages; v2: added clarifications and references, fixed typos; v3: matches published version

We consider the gravitational radiation in conformal gravity theory. We perturb the metric from flat Mikowski space and obtain the wave equation after introducing the appropriate transformation for perturbation. We derive the effective energy-momentum tensor for the gravitational radiation, which can be used to determine the energy carried by gravitational waves., Comment: 8 pages, no figures, some errors are corrected

Using the linearized gravity in the weak field regime and applying the quantum field theory prescription, the study of the gravitational interactions of massless fermions (neutrinos) in tree-level and through the u- and t-channels has been investigated before, but the gravitational interaction through the s-channel has not taken into account yet. In this paper, we calculate the cross section for the gravitational interaction of a fermion-anti-fermion pair to another pair of fermion-anti-fermion in tree level, that is purely an s-channel interaction, and compare it with the electromagnetic analogous.

Lorentz and diffeomorphism violations are studied in linearized gravity using effective field theory. A classification of all gauge-invariant and gauge-violating terms is given. The exact covariant dispersion relation for gravitational modes involving operators of arbitrary mass dimension is constructed, and various special limits are discussed., 17 pages

We consider the dynamics of a charged particle (e.g., an electron) oscillating in a laser field in flat spacetime and describe it in terms of the variable mass metric. By applying Einstein's equivalence principle, we show that, after representing the electron motion in a time-dependent manner, the variable mass metric takes the form of the Friedmann–Lemaitre–Robertson–Walker metric. We quantize a pseudo-scalar field in this spacetime and derive the production rate of electrically neutral, spinless particles. We show that this approach can provide an alternative experimental method to axion searches.

I discuss the recent claims made by Mario Bunge on the philosophical implications of the discovery of gravitational waves. I think that Bunge is right when he points out that the detection implies the materiality of spacetime, but I reject his identification of spacetime with the gravitational field. I show that Bunge’s analysis of the spacetime inside a hollow sphere is defective, but this in no way affects his main claim. Fil: Romero, Gustavo Esteban. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina

The genesis of Einstein’s theory of general relativity is briefly reviewed. The “three acts” of the “drama” are described in their historical and scientific aspects: the first act, from 1907 to 1911, when Einstein formulates the equivalence principle and predicts on its basis various gravitational phenomena: the second act, in 1912, when he guesses the geometrical nature of gravity; the third act, in 1915, when he completes the theory and obtains the equation of the gravitational field. The most important tests of theory are also discussed, from the deflection of light to the recent direct detection of gravitational waves.