Retarded field of a uniformly accelerated source in nonlocal scalar field theory

Kolář, Ivan; Boos, Jens

doi:10.1103/physrevd.103.105004

Cited by 18 publications

(26 citation statements)

References 43 publications

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“…There are many examples where IDG shows that regularisation of the gravitational field is possible, for instance, the well-known gravitational potential 1/r of pointlike sources at the linearized level [11]. A similar property remains true for other types of sources, for example: electromagnetic and NUT charges [14][15][16], accelerated particles [17], models of mini-black-hole production [18], scalar lumps [19], spinning ring distributions [20] and other objects associated with topological defects such as p-branes, cosmic strings and gyratons [21][22][23]. Furthermore, it was shown that IDG also provides solutions for bouncing cosmology [24][25][26][27][28][29] and gravitational waves [30][31][32][33].…”

Section: Introductionmentioning

confidence: 85%

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Infinite-derivative linearized gravity in convolutional form

Heredia,

Kolář,

Llosa

et al. 2021

Preprint

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This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions S ′ . We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all R 3 and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in S ′ .

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Section: Introductionmentioning

confidence: 85%

“…There is an interesting line of research where even powers of the ✷ operator are considered, see for instance[17] 7. In fact, they are the heat kernels in 1-dimension and 3-dimension space where ℓ 2 plays the role of evolution parameter of the heat equation.…”

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confidence: 99%

Infinite-derivative linearized gravity in convolutional form

Heredia,

Kolář,

Llosa

et al. 2021

Preprint

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“…The inverse operator a −1 ð□Þ always exists in nonlocal theories of this class since að□Þ has no zeroes. In the literature it has been shown that this inverse operator can act as a smearing operator on sharply localized objects, mostly in the static case but also in the time-dependent case [45,53]. This allows for the tentative interpretation of the Ricci curvature as the "smeared out matter curvature" in this class of nonlocal theories.…”

Section: B Ricci Curvaturementioning

confidence: 98%

“…While a few exact classical solutions have been found in the context of gravitational waves [37,38] and cosmology [39,40], the complexity of the nonlocal gravitational field equations has so far prohibited a deeper study of the nonlinear regime; a notable exception is the recent work on almost universal spacetimes [41]. At the weak-field level, however, a plethora of solutions has been constructed in the past years [42][43][44][45][46][47][48][49][50][51][52][53]. The common feature of these linearized solutions lies in two main aspects:…”

Section: Introductionmentioning

confidence: 99%

Nonlocality and gravitoelectromagnetic duality

Boos

Kolář

2021

Phys. Rev. D

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The weak-field Schwarzschild and NUT solutions of general relativity are gravitoelectromagnetically dual to each other, except on the positive z-axis. The presence of nonlocality weakens this duality and violates it within a smeared region around the positive z-axis, whose typical transverse size is given by the scale of nonlocality. We restore an exact nonlocal gravitoelectromagnetic duality everywhere via a manifestly dual modification of the linearized nonlocal field equations. In the limit of vanishing nonlocality we recover the well-known results from weak-field general relativity. Nonlocality, as a possible ultraviolet completion of gravity, does not pose a fundamental impediment to duality structures at the linear level.

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“…Due to the complicated nature of the theory, most of the research has focused on the weak field regime of IDG. At the linearized level, it was shown that IDG can avoid various spacetime singularities: (i) diverging Newton's potential is mollified by the error function [11,[19][20][21]; (ii) there exists a mass gap for a mini-black-hole production in a collision of null sources [22][23][24]; (iii) solutions corresponding to topological defects such as the conical deficits [25] and the Misner strings of NUT charges [26] are regularized at the axis; (iv) fields of time-dependent [27] and uniformly accelerated sources [28] are finite at the location of the source.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of nonlocal gravity in a class of almost universal spacetimes

2021

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We study exact solutions of the infinite derivative gravity with null radiation which belong to the class of almost universal Weyl type III/N Kundt spacetimes. This class is defined by the property that all rank-2 tensors B ab constructed from the Riemann tensor and its covariant derivatives have traceless part of type N of the form Bð□ÞS ab and the trace part constantly proportional to the metric. Here, Bð□Þ is an analytic operator and S ab is the traceless Ricci tensor. We show that the convoluted field equations reduce to a single nonlocal but linear equation, which contains only the Laplace operator Δ on 2-dimensional spaces of constant curvature. Such a nonlocal linear equation is always exactly solvable by eigenfunction expansion or using the heat kernel method for the nonlocal form factor expð−l 2 ΔÞ (with l being the length scale of nonlocality) as we demonstrate on several examples. We find the nonlocal analogues of the Aichelburg-Sexl and the Hotta-Tanaka solutions, which describe gravitational waves generated by null sources propagating in Minkowski, de Sitter, and anti-de Sitter spacetimes. They reduce to the solutions of the local theory far from the sources or in the local limit, l → 0. In the limit l → ∞, they become conformally flat. We also discuss possible hints suggesting that the nonlocal solutions are regular at the locations of the sources in contrast to the local solutions; all curvature components in the natural null frame are finite and specifically the Weyl components vanish.

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Retarded field of a uniformly accelerated source in nonlocal scalar field theory

Cited by 18 publications

References 43 publications

Infinite-derivative linearized gravity in convolutional form

Infinite-derivative linearized gravity in convolutional form

Nonlocality and gravitoelectromagnetic duality

Exact solutions of nonlocal gravity in a class of almost universal spacetimes

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