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The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use our results to check the changes, during scattering, of the individual momenta, as well as of the total angular momentum. High post-Newtonian order values of the $O(G^2)$ radiation-reaction acceleration components are provided for checks of future post-Newtonian computations., Comment: 14 pages, revtex macros used

We discuss the dynamics of a (neutral) test particle in Topological Star spacetime undergoing scattering processes by a superposed test radiation field, a situation that in a 4D black hole spacetime is known as relativistic Poynting-Robertson effect, paving the way for future studies involving radiation-reaction effects. Furthermore, we study self-force-driven evolution of a scalar field, perturbing the Top-Star spacetime with a scalar charge current. The latter for simplicity is taken to be circular, equatorial and geodetic. To perform this study, besides solving all the self-force related problem (regularization of all divergences due to the self-field, mode sum regularization, etc.), we had to adapt the 4D Mano-Suzuki-Takasugi formalism to the present 5D situation. Finally, we have compared this formalism with the (quantum) Seiberg-Witten formalism, both related to the solutions of a Heun Confluent Equation, but appearing in different contexts in the literature, black hole perturbation theory the first, quantum curves in super-Yang-Mills theories the second., Comment: 31 pages, 3 figures for 8 eps files, revtex macros used

Using the Multipolar Post-Minkowskian formalism, we compute the frequency-domain waveform generated by the gravitational scattering of two nonspinning bodies at the fourth post-Minkowskian order ($O(G^4)$, or two-loop order), and at the fractional second Post-Newtonian accuracy ($O(v^4/c^4)$). The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, $U_{\ell m}(\omega), V_{\ell m}(\omega)$, are explicitly expressed in terms of a small number of master integrals. The basis of master integrals contains both (modified) Bessel functions, and solutions of inhomogeneous Bessel equations with Bessel-function sources. We show how to express the latter in terms of Meijer G functions. The low-frequency expansion of our results is checked againg existing classical soft theorems. We also complete our previous results on the $O(G^2)$ bremsstrahlung waveform by computing the $O(G^3)$ spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity., Comment: 22 pages, revtex macros used

In this paper we present an approach to compute analytical post-Minkowskian corrections to unbound two-body scattering in the self-force formalism. Our method relies on a further low-velocity (post-Newtonian) expansion of the motion. We present a general strategy valid for gravitational and non-gravitational self-force, and we explicitly demonstrate our approach for a scalar charge scattering off a Schwarzschild black hole. We compare our results with recent calculations in [Barack et al., PRD 108, 024025 (2023)], showing complete agreement where appropriate and fixing undetermined scale factors in their calculation. Our results also extend their results by including in our dissipative sector the contributions from the flux into the black hole horizon., Comment: 24 pages

We compute the purely local-in-time (scale-free and logarithm-free) part of the conservative dynamics of gravitationally interacting two-body systems at the fourth post-Minkowskian order, and at the thirtiest order in velocity. The gauge-invariant content of this fourth post-Minkowskian local dynamics is given in two ways: (i) its contribution to the on-shell action (for both hyperboliclike and ellipticlike motions); and (ii) its contribution to the Effective One Body Hamiltonian (in energy gauge). Our computation capitalizes on the Tutti Frutti approach [Phys. Rev. Lett. \textbf{123}, no.23, 231104 (2019)], and on recent post-Minkowskian advances [Phys. Rev. Lett. \textbf{128}, no.16, 161103 (2022)], [Phys. Rev. Lett. \textbf{128}, no.16, 161104 (2022)], and [Phys. Rev. Lett. \textbf{132}, no.22, 221401 (2024)]., Comment: 19 pages, revtex macros used

This paper proves that, in a four-dimensional spherically symmetric spacetime manifold, one can consider coordinate transformations expressed by fractional linear maps which give rise to isometries and make it possible to bring infinity down to a finite distance. The projective boundary of spherically symmetric spacetimes here studied is the disjoint union of three points: future timelike infinity, past timelike infinity, spacelike infinity, and the three-dimensional products of half-lines with a 2-sphere. Geodesics are then studied in the projectively transformed (t',r',theta',phi') coordinates for Schwarzschild spacetime, with special interest in their way of approaching our points at infinity. Next, Nariai, de Sitter and Godel spacetimes are studied with our projective method. Since the kinds of infinity here defined depend only on the symmetry of interest in a spacetime manifold, they have a broad range of applications, which motivate the innovative analysis of Schwarzschild, Nariai, de Sitter and Godel spacetimes., Comment: 17 pages in double-column format; 11 figures. Section II has been substantially improved, and new references have been added

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton's constant, $h \sim G+G^2+G^3$ (one-loop level), and correspondingly update its comparison with its classically-derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452 [hep-th]], the term quadratic in the amplitude in the observable-based formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order $h \sim G^1$ and at order $h \sim G^3$ when including disconnected diagrams in the observable-based formalism., Comment: 29 pages; v2: published version

We investigate the geometrical properties, spectral classification, geodesics, and causal structure of the Bonnor's spacetime [Journal of Physics A Math. Gen., \textbf{10}, 1673 (1977)], i.e., a stationary axisymmetric solution with a rotating dust as a source. This spacetime has a directional singularity at the origin of the coordinates (related to the diverging vorticity field of the fluid there), which is surrounded by a toroidal region where closed timelike curves (CTCs) are allowed, leading to chronology violations. We use the effective potential approach to provide a classification of the different kind of geodesic orbits on the symmetry plane as well as to study the helical-like motion aroud the symmetry axis on a cylinder with constant radius. In the former case we find that as a general feature for positive values of the angular momentum test particles released from a fixed space point and directed towards the singularity are repelled and scattered back as soon as they approach the CTC boundary, without reaching the central singularity. In contrast, for negative values of the angular momentum there exist conditions in the parameter space for which particles are allowed to enter the pathological region. Finally, as a more realistic mechanism, we study accelerated orbits undergoing friction forces due to the interaction with the background fluid, which may also act in order to prevent particles from approaching the CTC region., Comment: 11 pages, 5 figures (10 eps files); v2: new Section IV added

We compare recent one-loop-level, scattering-amplitude-based, computations of the classical part of the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding Multipolar-Post-Minkowskian waveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$, the two waveforms are found to agree at the Newtonian and first post-Newtonian levels, as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail. However, we find that there are significant differences at the second-and-a-half post-Newtonian level, $O\left( \frac{G^2}{c^5} \right)$, i.e. when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tails of higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines; and (iv) various contributions of cubically nonlinear origin (notably linked to the quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone). These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim \omega \ln \omega $, i.e. $O\left(\frac{1}{t^2} \right)$ in the time domain. Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checked that they agree with the corresponding existing classical soft graviton results., Comment: 23 pages, 2 figures; V2: new Sec. 9 and new references added, minor text modifications; V3: corrected Eqs 8.11, 8.12, 8.13 (and consequently Eq. 9.14), one reference added

We compute the leading order contribution to radiative losses in the case of spinning binaries with aligned spins due to their spin-orbit interaction. The orbital average along hyperboliclike orbits is taken through an appropriate spin-orbit modification to the quasi-Keplerian parametrization for nonspinning bodies, which maintains the same functional form, but with spin-dependent orbital elements. We perform consistency checks with existing PN-based and PM-based results. In the former case, we compare our expressions for both radiated energy and angular momentum with those obtained in [JHEP \textbf{04}, 154 (2022)] by applying the boundary-to-bound correspondence to known results for ellipticlike orbits, finding agreement. The linear momentum loss is instead newly computed here. In the latter case, we also find agreement with the low-velocity limit of recent calculations of the total radiated energy, angular momentum and linear momentum in the framework of an extension of the worldline quantum field theory approach to the classical scattering of spinning bodies at the leading post-Minkowskian order [Phys. Rev. Lett. \textbf{128}, no.1, 011101 (2022), Phys. Rev. D \textbf{106}, no.4, 044013 (2022)]. We get exact expressions of the radiative losses in terms of the orbital elements, even if they are at the leading post-Newtonian order, so that their expansion for large values of the eccentricity parameter (or equivalently of the impact parameter) provides higher-order terms in the corresponding post-Minkowskian expansion, which can be useful for future crosschecks of other approaches., Comment: 10 pages, no figures, revtex macros; v2 minimal text modifications

Based on a previous ansatz by Zel'dovich for the gravitational energy of virtual particle-antiparticle pairs, supplemented with the Holographic Principle, we estimate the vacuum energy in a fairly reasonable agreement with the experimental values of the Cosmological Constant. We further highlight a connection between Wheeler's quantum foam and graviton condensation, as contemplated in the quantum $N$-portrait paradigm, and show that such connection also leads to a satisfactory prediction of the value of the cosmological constant. The above results suggest that the "unnaturally" small value of the cosmological constant may find a quite "natural" explanation once the nonlocal perspective of the large $N$-portrait gravitational condensation is endorsed., Comment: 6 pages, 0 figures

We compute the variation of the Fokker-Wheeler-Feynman total linear and angular momentum of a gravitationally interacting binary system under the second post-Minkowskian retarded dynamics. The resulting $O(G^2)$ equations-of-motion-based, total change in the system's angular momentum is found to agree with existing computations that assumed balance with angular momentum fluxes in the radiation zone., Comment: 18 pages, 2 eps figures

We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated as gravitational waves in a two-body system undergoing gravitational scattering. We include, for the first time, all the relevant {\it time-asymmetric} effects that arise when consistently going three post Newtonian orders beyond the leading post Newtonian order. We find that the inclusion of time-asymmetric radiative effects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the mass-polynomiality of the post-Minkowskian expansion ($G$ expansion) of the radiated 4-momentum. Imposing the mass-polynomiality of the corresponding individual impulses determines the conservativelike radiative contributions at the fourth post-Minkowskian order, and strongly constrains them at the fifth post-Minkowskian order., Comment: 38 pages; revtex macros used; V2: slightly expanded version

This Letter proposes a solution of the Vacuum Energy and the Cosmological Constant (CC) paradox based on the Zel'dovich's ansatz, which states that the observable contribution to the vacuum energy density is given by the gravitational energy of virtual particle-antiparticle pairs, continually generated and annihilated in the vacuum state. The novelty of this work is the use of an ultraviolet cut-off length based on the Holographic Principle, which is shown to yield current values of the CC in good agreement with experimental observations., Comment: 4 pages, 0 figures

We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first order Post-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interfere with the process of black hole formation, leading to a potentially strong coupling between these two highly nonlinear phenomena. It is further found that a power-law turbulent energy spectrum $E(k) \sim k^{-n}$ generates metric fluctuations scaling like $x^{n-2}$, where $x$ is a four-dimensional distance from an arbitrary origin in spacetime. This highlights the onset of metric singularities whenever $n <2$, meaning that $2d$ fluid turbulence ($n=3$) yields smooth %(differentiable) metric fluctuations, scaling like $x$, while $3d$ turbulence ($n=5/3$) yields a weakly singular metric $x^{-1/3}$and purely random fluctuations, $n=1$, generate a stronger $1/x$ singularity. Finally, the effect of metric fluctuations on the geodesic motion of test particles is also discussed as a potential technique to extract information on the spectral characteristics of fluctuating spacetime., Comment: 11 pages; 5 figures

Gravitational radiation can be decomposed as an infinite sum of radiative multipole moments, which parametrize the waveform at infinity. The multipolar-post-Minkowskian formalism provides a connection between these multipoles and the source multipole moments, known as explicit integrals over the matter source. The gravitational wave energy, angular momentum and linear momentum fluxes are then expressed as multipolar expansions containing certain combinations of the source moments. We compute several gauge-invariant quantities as "building blocks" entering the multipolar expansion of both radiated energy and angular momentum at the 2.5 post-Newtonian (PN) level of accuracy in the case of hyperboliclike motion, by completing previous studies through the calculation of tail effects up to the fractional 1PN order. We express such multipolar invariants in terms of certain eccentricity enhancement factor functions, which are the counterpart of the well known enhancement functions already introduced in the literature for ellipticlike motion. Finally, we use the complete 2.5PN-accurate averaged energy and angular momentum fluxes to study the associated adiabatic evolution of orbital elements under gravitational radiation reaction., Comment: 25 pages, revtex macros used

In the description of the relativistic two-body interaction, together with the effects of energy and angular momentum losses due to the emission of gravitational radiation, one has to take into account also the loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum flux for a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The corresponding orbital averages are evaluated at their leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity (or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricity expansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energy and angular momentum losses [Phys. Rev. D \textbf{104}, no.10, 104020 (2021)], providing brick-type results which will be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodies undergoing a scattering process., Comment: 15 pages, revtex macros used; v2: Eq. (2.6) (and related) completed; minor text modifications

We briefly review the known properties of Melvin's magnetic universe and study the propagation of test charged matter waves in this static spacetime. Moreover, the possible correspondence between the wave perturbations on the background Melvin universe and the motion of charged test particles is discussed. Next, we explore a simple scenario for turning Melvin's static universe into one that undergoes gravitational collapse. In the resulting dynamic gravitational field, the formation of cosmic double-jet configurations is emphasized., Comment: 28 pages, 4 figures; v2: expanded version, references added; v3: amended version to appear in Phys. Rev. D; v4: typos corrected, reference [10] added

Mass currents in astrophysics generate gravitomagnetic fields of enormous complexity. Gravitomagnetic helicity, in direct analogy with magnetic helicity, is a measure of entwining of the gravitomagnetic field lines. We discuss gravitomagnetic helicity within the gravitoelectromagnetic (GEM) framework of linearized general relativity. Furthermore, we employ the spacetime curvature approach to GEM in order to determine the gravitomagnetic helicity for static observers in Kerr spacetime., Comment: 30 pages; v2: improved version to appear in Phys. Rev. D; v3: typos corrected

The class of Petrov type I curvature tensors is further divided into those for which the span of the set of distinct principal null directions has dimension four (maximally spanning type I) or dimension three (nonmaximally spanning type I). Explicit examples are provided for both vacuum and nonvacuum spacetimes., Comment: v1: 16 pages; v2: 21 pages, references added, discussion expanded; v3: 21 pages, final version matching the published one