Topological stars are solutions of Einstein-Maxwell theory in D=5. For specific choices of the parameters, the solution is capped and thus smooth and horizonless and can be reduced to D=4 along a circle. We study the energy and angular momentum radiated by a scalar particle moving on a circular orbit in the D=4 noncompact directions, extending a previous study [Phys. Rev. D 110, 084077 (2024)PRVDAQ2470-001010.1103/PhysRevD.110.084077]. We also discuss self-force effects on the motion of a spinless probe.

We compute the conservative scattering angle of two classical charged particles at the sixth order in electromagnetic coupling, and at the fourth order in velocity, thereby going beyond the current state of the art [fifth order in coupling, derived by Bern et al., Phys. Rev. Lett. 132, 251601 (2024)]. Our result is obtained by using the electromagnetic version of the effective one-body formalism to transfer information from the exact circular binary-charge solution of Schild [Phys. Rev. 131, 2762 (1963)] to the postLorentzian expansion of the scattering angle.

Starting from the recently derived conservative tail-of-tail action [High precision black hole scattering: Tutti Frutti vs worldline effective field theory, arXiv:2504.20204.] we compute several dynamical observables of binary systems (Delaunay Hamiltonian, scattering angle), at the 6.5 post-Newtonian accuracy and up to the eighth post-Minkowskian order. We find perfect agreement with previous self-force results, and (when inserting a recent high-post-Newtonian order derivation of radiated angular momentum [Scattering of a point mass by a Schwarzschild black hole: Radiated energy and angular momentum, arXiv:2507.03442.]) with state-of-the-art post-Minkowskian scattering results [Emergence of Calabi–Yau manifolds in high-precision black-hole scattering, Nature (London) 641, 603 (2025).].

After studying properties of the Nariai solution, including its geodesics, in spherical and de Sitter coordinates, two kinds of accelerated motion are investigated in detail: either observers at rest with respect to the coordinates, or observers in radial motion. Next, massless scalar perturbations of Nariai spacetime in absence of sources are worked out, and an explicit example out of the black hole context of analytic self-force calculation is obtained. Last, self-force effects are studied as well, together with some variant of the type of Poynting-Robertson external force, and also building a test electromagnetic field and a test gravitational field in Nariai spacetime geometry.

We consider black hole scattering up to the fifth post-Minkowskian (G5) order and compare the predictions of the tutti frutti formalism to the results obtained within two different versions of worldline effective field theory. At the G4 order we highlight the complete agreement between tutti frutti results and the results of [C. Dlapa et al., [Phys. Rev. Lett. 130, 101401 (2023)]], and show how the tutti frutti approach allows one to extract the O(G3) angular momentum loss from the O(G4) impulse. We compare the sixth post-Newtonian (6PN) accurate tutti frutti predictions to the recent results of [M. Driesse et al., [Nature 641, 603 (2025)]], which are at the G5 order, and at the leading order in the two mass ratios, finding complete agreement. We highlight that this agreement involves the presence at the 5.5PN level of a nonlocal tail-of-tail contribution to the scattering (first computed in [D. Bini et al., [Phys. Rev. D 102, 084047 (2020)]]), and involves, at the 6PN level, the presence of a O(G4) contribution to the angular momentum loss [C. Heissenberg, [Phys. Rev. D 111, 126012 (2025)]]. At the second order in the mass ratios of the O(G5) order we predict two independent gauge-invariant observables to high-PN accuracy.

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 are the simplest example of coordinate transformation used 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′,θ′,φ′) coordinates for Schwarzschild spacetime, with special interest in their way of approaching our points at infinity. Next, Nariai, de Sitter and Gödel 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 Gödel spacetimes.

We compute the next-to-leading-order radiation-reaction modification to the harmonic coordinate quasi- Keplerian parametrization of the binary dynamics, the two bodies undergoing a scattering process. The solution for the radiation-reaction corrections to the orbital parameters is examined both in the time domain (exact results) and in the frequency domain (results presented in the limit of large angular momentum, i.e., as a post-Minkowskian series expansion). The knowledge of the radiation-reaction corrected orbit is a key ingredient for the calculation of the fractional 3.5 post-Newtonian corrections to the radiative losses as well as to the radiative multipole moments needed to build up the waveform at the same accuracy.

We show that the null geodesic radial action for unbound orbits in the Kerr spacetime, and consequently the scattering angle, can be resummed in terms of hypergeometric functions, extending previous results [Ivanov et al., Resummation of universal tails in gravitational waveforms, arXiv:2504.07862.]. We provide explicit expressions as series expansions in powers of the Kerr rotational parameter up to the fourth order included.We finally use the Mano-Suzuki-Takasugi formalism to prove the relation between the renormalized angular momentum and the radial action highlighted in previous works.

We show that for a topological star the renormalized angular momentum parameter, ν, appearing in the Mano-Suzuki-Takasugi-type or in the quantum-Seiberg-Witten-type approaches of the perturbation equations, (1) has a direct link with the geodesic radial action computed along the null orbits of the background and (2) admits an exact resummation in terms of hypergeometric functions, generalizing previous results valid in the Schwarzschild case; see [M. M. Ivanov, Y. Z. Li, J. Parra-Martinez, and Z. Zhou, Resummation of universal tails in gravitational waveforms, arXiv:2504.07862.].

We compute the scattering angle for a scalar neutral probe undergoing unbound motion around a topological star, including self-force effects. Moreover, we identify the “electromagnetic” source of the background as a Papapetrou field compatible with the isometries and characterize topological stars by studying their sectional curvature, geometric transport along special curves, and gravitational energy content in terms of the superenergy tensors.

We analyze scalar wave emission from unbound orbits in a topological star spacetime. Our study uses a self-force approach and leads to a post-Newtonian reconstruction of the field along the orbit, both in the time domain and in the frequency domain. We also compute leading-order radiation losses, namely energy and angular momentum.

We study deviations from geodesic motions in a topological star spacetime for either massive, charged and spinning particles, elucidating different behaviors with the Schwarzschild spacetime. We also consider the deviations for the motion of electrically charged stringy probes in D = 5, framing all cases within a unified picture.

Explicit solution of the gravitational two-body problem at the second post-Minkowskian order

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 of which are related to the solutions of a Heun confluent equation but appear in different contexts in the literature: the first in black hole perturbation theory and the second in quantum curves in super-Yang-Mills theories.

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(G4), or two-loop order), and at the fractional second post-Newtonian accuracy [O(v4/c4)]. The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, Um(ω),Vm(ω), 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 against existing classical soft theorems. We also complete our previous results on the O(G2) bremsstrahlung waveform by computing the O(G3) spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity.

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 nongravitational 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 [L. Barack, Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model, Phys. Rev. D 108, 024025 (2023)PRVDAQ2470-001010.1103/PhysRevD.108.024025], 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.

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 thirtieth 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 [D. Bini, Novel approach to binary dynamics: Application to the fifth post-Newtonian level, Phys. Rev. Lett. 123, 231104 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.231104] and on recent post-Minkowskian advances [Z. Bern, Scattering amplitudes, the tail effect, and conservative binary dynamics at O(G4), Phys. Rev. Lett. 128, 161103 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.161103; C. Dlapa, Conservative dynamics of binary systems at fourth post-Minkowskian order in the large-eccentricity expansion, Phys. Rev. Lett. 128, 161104 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.161104; C. Dlapa, Local in time conservative binary dynamics at fourth post-Minkowskian order, 132, 221401 (2024)PRLTAO0031-900710.1103/PhysRevLett.132.221401].

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∼G+G2+G3 (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 [A. Georgoudis et al., J. High Energy Phys. 03 (2024) 08910.1007/JHEP03(2024)089], the term quadratic in the amplitude in the observable-based formalism [D. A. Kosower et al., J. High Energy Phys. 02 (2019) 137JHEPFG1029-847910.1007/JHEP02(2019)137] 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∼G1 and at order h∼G3 when including disconnected diagrams in the observable-based formalism.

We investigate the geometrical properties, spectral classification, geodesics, and causal structure of Bonnor's spacetime [W. B. Bonnor, A rotating dust cloud in general relativity, J. Phys. A 10, 1673 (1977)JPHAC50305-447010.1088/0305-4470/10/10/004], 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 around 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 toward 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.

We discuss the solution proposed by Fermi to the so called “4/3 problem” in the classical theory of the electron, a problem which puzzled the physics community for many decades before and after his contribution. Unfortunately his early resolution of the problem in 1922–1923 published in three versions in Italian and German journals (after three preliminary articles on the topic) went largely unnoticed. Even more recent texts devoted to classical electron theory still do not present his argument or acknowledge the actual content of those articles. The calculations initiated by Fermi at the time are completed here by formulating and discussing the conservation of the total 4-momentum of the accelerated electron as seen from the instantaneous rest frame in which it is momentarily at rest.