We study the retarded field sourced by a uniformly accelerated particle in a nonlocal scalar field theory. While the presence of nonlocality regularizes the field at the location of the source, we ...also show that Lorentz-invariant nonlocal field theories are particularly sensitive to the somewhat unphysical assumption of uniform acceleration, leading to logarithmic divergences on the acceleration horizon. Analytic properties of the nonlocal retarded Green function indicate that the divergences can be removed by placing appropriate sources on the acceleration horizon in the asymptotic past.
Theories with an infinite number of derivatives are described by nonlocal Lagrangians for which the standard Hamiltonian formalism cannot be applied. Hamiltonians of special types of nonlocal ...theories can be constructed by means of the ( 1 + 1 )-dimensional Hamiltonian formalism. In this paper, we consider a simple scalar field model inspired by the infinite derivative gravity and study its reduced phase space by using this formalism. Assuming the expansion of the solutions in the coupling constant, we compute the perturbative Hamiltonian and the symplectic 2-form. We also discuss an example of a theory leading to an infinite-dimensional reduced phase space for a different choice of the form factor.
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 Bab constructed from the Riemann tensor and its covariant derivatives have traceless part of type N of the form B(□)Sab and the trace part constantly proportional to the metric. Here, B(□) is an analytic operator and Sab 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 exp(−ℓ2Δ) (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.
We study fixed points of isometries of the higher-dimensional Kerr-NUT-(A)dS spacetimes that form generalizations of symmetry axes. It turns out that, in the presence of nonzero NUT charges, some ...parts of the symmetry axes are necessarily singular and their intersections are surrounded by regions with closed timelike curves. Motivated by similarities with the spacetime of a spinning cosmic string, we introduce geometric quantities that characterize various types of singularities on symmetry axes. Expanding the Kerr-NUT-(A)dS spacetimes around candidates for possible fixed points, we find the Killing vectors associated with generalized symmetry axes. By means of these Killing vectors, we calculate the introduced geometric quantities describing axial singularities and show their relation to the parameters of the Kerr-NUT-(A)dS spacetimes. In addition, we identify the Killing coordinates that may be regarded as generalization of the Boyer-Lindquist coordinates.
In this paper, we obtain a complete list of stationary and axisymmetric spacetimes, generated from a Minkowski spacetime using the Ernst technique. We do so by operating on the associated seed ...potentials with a composition of Ehlers and Harrison transformations. In particular, assigning an additional “electric” or “magnetic” tag to the transformations, we investigate the new spacetimes obtained either via a composition of magnetic Ehlers and Harrison transformations (first part) or via a magnetic-electric combination (second part). In the first part, the resulting type D spacetime, dubbed electromagnetic swirling universe, features key properties, separately found in swirling and (Bonnor–)Melvin spacetimes, the latter recovered in appropriate limits. A detailed analysis of the geometry is included, and subtle issues are addressed. A detailed proof that the spacetime belongs to the Kundt family, is included, and a notable relation to the5 planar-Reissner–Nordström-NUT black hole is also meticulously worked out. This relation is further exploited to reverse-engineer the form of the solution in the presence of a nontrivial cosmological constant. A Schwarzschild black hole embedded into the new background is also discussed. In the second part, we present four novel stationary and axisymmetric asymptotically nonflat type I spacetimes, which are naively expected to be extensions of the Melvin or swirling solution including a NUT parameter or electromagnetic charges. We actually find that they are, under conditions, free of curvature and topological singularities, with the physical meaning of the electric transformation parameters in these backgrounds requiring further investigation.
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