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Potentials arising in ultraviolet-completed field theories can be devoid of singularities, and hence render spacetimes simply connected. This challenges the notion of topological invariants considered in such scenarios. We explore the classical implications for (i) electrodynamics in flat spacetime, (ii) ultrarelativistic gyratonic solutions of weak-field gravity, and (iii) exact electro-vacuum black hole solutions in general relativity. In linear theories, regularity spoils the character of topological invariants and leads to radius-dependent Aharanov--Bohm phases, which are potentially observable for large winding numbers. In general relativity, the physics is richer: The electromagnetic field can be regular and maintain its usual topological invariants, and the resulting geometry is a Reissner--Nordstr\"om black hole with a spacetime region of coordinate radius $\sim q^2/(GM)$ cut out. This guarantees the regularity of linear and quadratic curvature invariants ($\mathcal{R}$ and $\mathcal{R}^2$), but does not resolve singularities in invariants such as $\mathcal{R}^p\Box^n \mathcal{R}^q$, reflected by conical or solid angle defects. This motivates that gravitational models beyond general relativity need to be considered. These connections between regularity (= UV properties of field theories) and topological invariants (= IR observables) may hence present an intriguing avenue to search for traces of new physics and identify promising modified gravity theories., Comment: 13 pages, 3 figures, comments welcome!

Regular black hole metrics involve a universal, mass-independent regulator that can be up to O(700) km while remaining consistent with terrestrial tests of Newtonian gravity and astrophysical tests of general relativistic orbits. However, for such large values of the regulator scale, the metric describes a compact, astrophysical-mass object with no horizon rather than a black hole. We note that allowing the regulator to have a nontrivial mass dependence preserves the horizon, while allowing large, percent-level effects in black hole observables. By considering the deflection angle of light and the black hole shadow, we demonstrate this possibility explicitly., Comment: 7 pages LaTeX, 3 figures. v3: revised throughout, including the title and abstract, for improved presentation

Within the asymptotic safety program, it is possible to construct renormalization group (RG) improved spacetimes by replacing the gravitational coupling $G$ by its running counterpart $G(k)$, and subsequently identifying the RG scale $k$ with a physical distance scale. This procedure has been used to construct a regular Schwarzschild geometry, but it fails in the presence of a cosmological constant. This can only be avoided if the dimensionless cosmological constant has a trivial ultraviolet fixed point, but so far no such scenario has been encountered in quantum general relativity (with or without matter). In this Letter we provide a possible solution to this problem. In Poincare gauge gravity an effective cosmological constant arises naturally, and if the non-Abelian Lorentz spin connection is asymptotically free, it generates a trivial ultraviolet fixed point for this cosmological constant. We thereby tentatively propose a nonsingular black hole consistent with the principles of asymptotic safety, embedded in Poincare gauge gravity., Comment: 7 pages

The entropy of a Schwarzschild black hole, as computed via the semiclassical Euclidean path integral in a stationary phase approximation, is determined not by the on-shell value of the action (which vanishes), but by the Gibbons--Hawking--York boundary term evaluated on a suitable hypersurface, which can be chosen arbitrarily far away from the horizon. For this reason, the black hole singularity seemingly has no influence on the Bekenstein--Hawking area law. In this Essay we estimate how a regular black hole core, deep inside a Euclidean black hole of mass $M$ and generated via a UV regulator length scale $\ell > 0$, affects the black hole entropy. The contributions are suppressed by factors of $\ell/(2GM)$; demanding exact agreement with the area law as well as a self-consistent first law of black hole thermodynamics at all orders, however, demands that these contributions vanish identically via uniformly bounded curvature. This links the limiting curvature hypothesis to black hole thermodynamics., Comment: Essay written for the Gravity Research Foundation 2023 Awards for Essays on Gravitation; awarded an Honorable Mention; 7 pages

Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymptotically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regulator scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity., Comment: 18 pages LaTeX, 1 Figure. v2: references added. v3: Discussion clarified and references added

We consider the inclusion of TeV-scale, fermionic dark matter in an asymptotically safe model of gauged baryon number that has been recently proposed [Phys. Rev. D 106, no. 3, 035015 (2022)]. The new gauge boson serves as a portal between the dark and the visible sectors. The range of the baryon number gauge coupling and the kinetic mixing between baryon number and hypercharge are constrained by the requirement that nontrivial ultraviolet fixed points are reached. We show that this asymptotically safe dark matter model can achieve the correct dark matter relic density while remaining consistent with direct detection bounds., Comment: 14 pages, LaTeX, 3 figures. v2: references added

We consider a model with gauged baryon number that may be rendered asymptotically safe when gravitational effects above the Planck scale are taken into account. We study the ultraviolet fixed points in this theory and determine the restrictions on the parameter space of the model at the TeV scale following from the requirement that the asymptotic fixed points are reached. Assuming that the new gauge symmetry is broken at the TeV scale, we comment on the phenomenological implications of these restrictions., Comment: 28 pages LaTeX, 5 figures, 1 appendix. v3: matches the published version, discussion and 2 figures added

Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here, we extend previous work on pure scalar and Abelian gauge theories to asymptotically nonlocal non-Abelian theories. In particular, we confirm that there is a limit in which the Lee-Wick spectrum can be decoupled, but where the hierarchy problem is resolved via an emergent nonlocal scale that regulates loop diagrams and that is hierarchically smaller than the lightest Lee-Wick resonance., Comment: 18 pages, 1 figure, matches the published version; v1: 17 pages, 1 figure

Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here we extend this framework, developed previously in a theory of real scalar fields, to gauge theories. We focus primarily on asymptotically nonlocal scalar electrodynamics, first identifying equivalent gauge-invariant formulations of the Lagrangian, one with higher-derivative terms and the other with auxiliary fields instead. We then study mass renormalization of the complex scalar field in each formulation, showing that an emergent nonlocal scale (i.e., one that does not appear as a fundamental parameter in the Lagrangian of the finite-derivative theories) regulates loop integrals as the limiting theory is approached, so that quadratic divergences can be hierarchically smaller than the lightest Lee-Wick partner. We conclude by making preliminary remarks on the generalization of our approach to non-Abelian theories, including an asymptotically nonlocal standard model., Comment: Minor errors corrected. 30 pages LaTeX, 3 figures

We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with $N$ propagator poles, including $N-1$ Lee-Wick partners, and a nonlocal infinite-derivative theory with kinetic terms modified by an entire function of derivatives with only one propagator pole. Since the latter description arises when taking the $N\rightarrow\infty$ limit, we refer to the theory as "asymptotically nonlocal." Introducing an auxiliary-field formulation of the theory allows one to recover either the higher-derivative form (for any $N$) or the Lee-Wick form of the Lagrangian, depending on which auxiliary fields are integrated out. The effective scale that regulates quadratic divergences in the large-$N$ theory is the would-be nonlocal scale, which can be hierarchically lower than the mass of the lightest Lee-Wick resonance. We comment on the possible utility of this construction in addressing the hierarchy problem., Comment: 21 pages LaTeX, 3 figures. Discussion added; $m_1$ now consistently refers to the lightest Lee--Wick mass, with Fig. 1 updated accordingly; v1: 20 pages LaTeX, 3 figures

Cutting out an infinite tube around $r=0$ formally removes the Schwarzschild singularity, but without a physical mechanism this procedure seems ad hoc and artificial. In this Essay we provide such a mechanism by means of non-locality. Motivated by the Gauss law we define a suitable radius variable as the inverse of a regular non-local potential, and use this variable to model a non-singular black hole. The resulting geometry has a de Sitter core, but for generic values of the regulator there is no inner horizon, saving this model from potential issues via mass inflation. An outer horizon only exists for masses above a critical threshold, thereby reproducing the conjectured "mass gap" for black holes in non-local theories. The geometry's density and pressure terms decrease exponentially, thereby rendering it an almost-exact vacuum solution of the Einstein equations outside of astrophysical black holes., Comment: 11 pages, 2 figures; fixed a typo in Eq.(4), added references and additional discussion. Extended version of an Essay written for the Gravity Research Foundation 2021 Awards for Essays on Gravitation

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 non-locality 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 non-locality. We restore an exact non-local gravitoelectromagnetic duality everywhere via a manifestly dual modification of the linearized non-local field equations. In the limit of vanishing non-locality we recover the well-known results from weak-field general relativity., Comment: 8 pages, comments welcome!

We study the retarded field sourced by a uniformly accelerated particle in a non-local scalar field theory. While the presence of non-locality regularizes the field at the location of the source, we also show that Lorentz-invariant non-local 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 non-local retarded Green function indicate that the divergences can be removed by placing appropriate sources on the acceleration horizon in the asymptotic past., Comment: 15 pages, 5 figures, comments welcome!

We study a non-local ghost-free Lorentz invariant modification of the Maxwell equations in four- and higher-dimensional flat spacetimes. We construct solutions of these equations for stationary charged and magnetized objects and use them to find the field created by such objects moving with the speed of light., Comment: 10 pages, 1 figure, comments welcome!

Considering an exactly solvable local quantum theory of a scalar field interacting with a $\delta$-shaped time-dependent potential we calculate the Bogoliubov coefficients analytically and determine the spectrum of created particles. We then show how these considerations, when suitably generalized to a specific nonlocal "infinite-derivative" quantum theory, are impacted by the presence of nonlocality. In this model, nonlocality leads to a significant resonant amplification of certain modes, leaving its imprint not only in the particle spectrum but also in the total number density of created particles., Comment: 6 pages, 1 figure, matches the published version. v1: 5 pages, 1 figure. Comments welcome!

Spacetime---the union of space and time---is both the actor and the stage during physical processes in our fascinating Universe. In Lorentz invariant local theories, the existence of a maximum signalling speed (the "speed of light") determines a notion of causality in spacetime, distinguishing the past from the future, and the cause from the effect. This thesis is dedicated to the study of \emph{deviations} from locality. Focussing on a particular class of \emph{non-local} theories that is both Lorentz invariant and free of ghosts, we aim to understand the effects of such non-local physics in both gravity and quantum theory. Non-local ghost-free theories are accompanied by a parameter $\ell$ of dimension length that parametrizes the scale of non-locality, and for that reason we strive to express all effects of non-locality in terms of this symbol. In the limiting case of $\ell=0$ one recovers the local theory, and the effects of non-locality vanish. In order to address these questions we develop the notion of non-local Green functions [...]. The results presented in this thesis establish several effects of a Lorentz invariant, ghost-free non-locality in the areas of both gravitational and quantum physics. (Full abstract in document.), Comment: Comments welcome! Includes a didactic introduction into non-local infinite-derivative "ghost-free" field theory. Ph.D. thesis, University of Alberta. Supervisor: Prof. Valeri P. Frolov. 234 pages, 36 figures

We study the gravitational field of ultrarelativistic spinning objects (gyratons) in a modified gravity theory with higher derivatives. In particular, we focus on a special class of such theories with an infinite number of derivatives known as "ghost-free gravity" that include a non-local form factor such as $\exp(-\Box\ell^2)$, where $\ell$ is the scale of non-locality. First, we obtain solutions of the linearized ghost-free equations for stationary spinning objects. To obtain gyraton solutions we boost these metrics and take their Penrose limit. This approach allows us to perform calculations for any number of spacetime dimensions. All solutions are regular at the gyraton axis. In four dimensions, when the scale non-locality $\ell$ tends to zero, the obtained gyraton solutions correctly reproduce the Aichelburg--Sexl metric and its generalization to spinning sources found earlier by Bonnor. We also study the properties of the obtained four-dimensional and higher-dimensional ghost-free gyraton metrics and briefly discuss their possible applications., Comment: v2: 13 pages, 2 figures, matches published version, title changed slightly and references added; v1: 13 pages, 2 figures, computer algebra code available at http://spintwo.net/static/2020.04.14/

Cosmic strings, as remnants of the symmetry breaking phase in the Early Universe, may be susceptible to non-local physics. Here we show that the presence of a Poincar\'e-invariant non-locality -- parametrized by a factor $\exp(-\Box\ell^2)$ -- regularizes the gravitational field and thereby changes the properties of spacetime: it is now simply connected and the angle deficit around the cosmic string becomes a function of the radial distance. Similar changes occur for the non-local gravitomagnetic field of a rotating cosmic string, and we translate these mathematical facts into the language of non-local gravitoelectromagnetism and thereby provide a physical interpretation. We hope that these insights might prove helpful in the search for traces of non-local physics in our Universe., Comment: v2: Matches published version, 10 pages, 1 figure. v1: 9 pages, 1 figure. Essay written for the Gravity Research Foundation 2020 Awards for Essays on Gravitation, awarded an Honorable Mention

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study., Comment: 14 pages, 3 figures, references added, typo corrected

We study the response of a scalar thermal field to a $\delta$-probe in the context of non-local ghost-free theories. In these theories a non-local form factor is inserted into the kinetic part of the action which does not introduce new poles. For the case of a static $\delta$-potential we obtain an explicit expression for the thermal Hadamard function and use it for the calculation of the thermal fluctuations. We then demonstrate how the presence of non-locality modifies the amplitude of these fluctuations. Finally, we also discuss the fluctuation-dissipation theorem in the context of ghost-free quantum field theories at finite temperature., Comment: 8 pages, 4 figures, computer algebra code available at http://spintwo.net/static/2019.04.16/ , v2: matches the published version

We discuss the response of vacuum fluctuations to a static potential in the context of massive, ghost-free infinite-derivative scalar field theories in two dimensions. For the special case of a $\delta$-like potential, $V=\lambda \delta(x)$, the problem is exactly solvable and we calculate the corresponding Hadamard function for this quantum field. Using this exact result we determine the renormalized value of the vacuum polarization $\langle \hat{\varphi}^2(x)\rangle_\text{ren}$ as a function of the distance $x$ from the position of the potential. This expression depends on the amplitude of the potential as well as the scale of non-locality $\ell$; for distances $x\gg\ell$ the non-local and local results agree, whereas for distances $x < \ell$ there is a difference., Comment: 17 pages, 7 figures, computer algebra code available at http://spintwo.net/static/2019.01.21/ , v2: matches the published version

We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein's general relativity., Comment: 54 pages, 2 figures, Latex

We discuss the quantum-mechanical scattering of a massless scalar field on a $\delta$-potential in a ghost-free theory and obtain analytic solutions for the scattering coefficients. Due to the non-locality of the ghost-free theory the transmission coefficient tends to unity for frequencies much larger than the inverse scale of non-locality, even for infinitely strong potentials. At the same time there exists a critical strength of the $\delta$-potential barrier below which there is always a frequency that is totally reflected. These scattering properties in ghost-free theories are quite generic and distinguish them from local field theories. Moreover, we study quasi-normal states that are present for the $\delta$-potential well. In the limit of vanishing non-locality, we recover the standard results of local field theory., Comment: v2: 7 pages, 2 figures, matches published version; v1: 6 pages, 2 figures

Analysis of the highest temperature in the machining processes, namely the flash temperature, helps to understand the physics of the process, to improve cutting tool geometry, and to achieve high performance machining. In the present work, the interaction between cutting grain and workpiece material in grinding process is analyzed. Single diamonds are considered for machining, which operates in comparison to other measurements in the range of grinding speed. The highest temperature in the grain-material interaction and cutting forces are measured. In order to measure the flash temperature, an innovative method to measure and analyze the temperature through the diamond grain in the cutting zone by a two-color pyrometer is proposed. Furthermore, cutting forces are measured simultaneously. In order to measure the temperature in the cutting zone, an accurate connection between diamond and pyrometer fiber is required. Thus, the diamond tool holders are manufactured by electrical discharge machining (EDM) milling in deionized water. A 0.5-mm-diameter hole is drilled in each holder to connect the diamond precisely to the pyrometer fiber. Machining processes are performed with 30 {\mu}m depth of cut, cutting length of 20 mm, and cutting speed of 65 m/s on Ti6Al4V. The cutting tool is fixed, and the shape of the rotating workpiece is optimized. The diamond holder with the specific shape is designed and manufactured. Quasi-static, dynamic, modal, and harmonic response analyses are performed in order to reduce vibrations and chattering. The measured flash temperature is 1380 {\deg}C and cutting normal, tangential, and axial forces are measured., Comment: 13 pages

When a positively charged impurity is placed inside a cold metal, the resulting charge density around that object exhibits characteristic ripples to negative values, known as Friedel oscillations. In this essay, we describe a somewhat analogous effect in (i) linearized higher-derivative gravity and (ii) linearized infinite-derivative "ghost-free" gravity: when a gravitational impurity (point particle) is placed in Minkowski vacuum, the local energy density $\rho \equiv G{}_{\mu\nu}\xi{}^\mu \xi{}^\nu$ (with $\xi=\partial_t$) exhibits oscillations to negative values. The wavelength of these oscillations is roughly given by (i) the Pauli--Villars regularization scale and (ii) the scale of non-locality. We hence dub this phenomenon gravitational Friedel oscillations., Comment: 10 pages, 3 figures, matches the published version. Essay received an Honorable Mention in the 2018 Essay Competition of the Gravity Research Foundation

We study the gravitational field of static p-branes in D-dimensional Minkowski space in the framework of linearized ghost-free (GF) gravity. The concrete models of GF gravity we consider are parametrized by the non-local form factors $\exp(-\Box/\mu^2)$ and $\exp(\Box^2/\mu^4)$, where $\mu^{-1}$ is the scale of non-locality. We show that the singular behavior of the gravitational field of p-branes in General Relativity is cured by short-range modifications introduced by the non-localities, and we derive exact expressions of the regularized gravitational fields, whose geometry can be written as a warped metric. For large distances compared to the scale of non-locality, $\mu r\rightarrow\infty$, our solutions approach those found in linearized General Relativity., Comment: 11 pages, 4 figures, matches the published version

We construct special solutions of the Nambu-Goto equations for stationary strings in a general Kerr-NUT-(A)dS spacetime in any number of dimensions. This construction is based on the existence of explicit and hidden symmetries generated by the principal tensor which exists for these metrics. The characteristic property of these string configurations, which we call "principal Killing strings," is that they are stretched out from "infinity" to the horizon of the Kerr-NUT-(A)dS black hole and remain regular at the latter. We also demonstrate that principal Killing strings extract angular momentum from higher-dimensional rotating black holes and interpret this as the action of an asymptotic torque., Comment: 14 pages, 1 figure, matches the published version

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without cosmological constant. This solution is a warped product of two metrics. One of them is a deformed two-sphere whose Gaussian curvature is determined by the energy-density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(A)dS generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed., Comment: 10 pages, 3 figures, matches the published version

In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter fields. Moreover, we demonstrate that the principal null directions of the Kerr geometry can be obtained by projections involving either the Bel--Robinson or the Kummer tensor. We conjecture that this is also possible in more general settings., Comment: 4 pages, 10 figures. Essay written for the Gravity Research Foundation 2017 Awards for Essays on Gravitation

Coupling fermions to gravity necessarily leads to a non-renormalizable, gravitational four-fermion contact interaction. In this essay, we argue that augmenting the Einstein-Cartan Lagrangian with suitable kinetic terms quadratic in the gravitational gauge field strengths (torsion and curvature) gives rise to new, massive propagating gravitational degrees of freedom. This is to be seen in close analogy to Fermi's effective four-fermion interaction and its emergent W and Z bosons., Comment: title changed, matches published version, 7 pages

Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution---the exact seven parameter solution of Pleba\'nski--Demia\'nski (PD)---to demonstrate these analogies for a physically meaningful spacetime: The two quadratic curvature invariants $\bf{B}^2-\bf{E}^2$ and $\bf{E}\cdot\bf{B}$ are evaluated analytically. In the asymptotically flat case, the leading terms of $\bf{E}$ and $\bf{B}$ can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel--Robinson tensor reads $(\mathbf{B}^2+\mathbf{E}^2)^2$ for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy-momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel--Robinson 3-form, from which the Bel--Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition. The calculations are carried out in two coordinate systems: in the original polynomial PD coordinates, and in a modified Boyer--Lindquist-like version introduced by Griffiths and Podolsk\'y (GP) allowing for a more straightforward physical interpretation of the free parameters., Comment: 52 pages, 11 listings of computer algebra code; typos removed, and journal reference added