Related papers: Classifying post-Minkowskian geometries for gravit…
The dynamical system studied in previous papers of this series, namely a bound time-like geodesic motion in the exact static and axially symmetric space-time of an (originally) Schwarzschild black hole surrounded by a thin disc or ring, is…
We construct four-dimensional gravity theories that resolve the Schwarzschild singularity and enable dynamical studies of nonsingular gravitational collapse. The construction employs a class of nonpolynomial curvature invariants that…
The theory of anyon systems, as modular functors topologically and unitary modular tensor categories algebraically, is mature. To go beyond anyons, our first step is the interplay of anyons with conventional group symmetry due to the…
We discuss the branching structure of the quantum-gravitational wave function that describes the evaporation of a black hole. A global wave function which initially describes a classical Schwarzschild geometry is continually decohered into…
We extend the description of gravitational waves emitted by binary black holes during the final stages of inspiral and merger by introducing in the third post-Newtonian (3PN) effective-one-body (EOB) templates seven new ``flexibility''…
We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the "all-mass" case: integrals with generic external and internal masses. Specifically, we focus on $n$-particle integrals in…
Modified Einstein's equations implementing both an energy-dependent Newtonian and cosmological constant can be obtained via a modified action characterised by a non-minimal gravity-matter coupling. We show how different dynamics for the…
Effective-one-body (EOB) waveforms employed by the LIGO-Virgo-KAGRA Collaboration have primarily been developed by resumming the post-Newtonian expansion of the relativistic two-body problem. Given the recent significant advancements in…
We reduce the study of perturbations of rotating black holes in higher-derivative extensions of general relativity to a system of decoupled radial equations that stem from a set of universal Teukolsky equations. We detail a complete…
Feynman integrals appropriately generalized are $\mathsf A$-hypergeometric functions. Among the properties of $\mathsf A$-hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
We report on the results of a study of the motion of a four particle non-relativistic one-dimensional self-gravitating system. We show that the system can be visualized in terms of a single particle moving within a potential whose…
We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.
We study the generalized hypergeometric systems, in the sense of Gel'fand, Kapranov, and Zelevinsky, associated with one-loop Feynman integrals, and determine when their rank is independent of space-time dimension and propagator powers.…
We derive the classical gravitational radiation from an aligned spin binary black hole on \textit{closed} orbits, using a dictionary built from the 5-point QFT scattering amplitude of two massive particles exchanging and emitting a…
Over the next decade, third-generation interferometers and the space-based LISA mission will observe binaries in galactic centers involving supermassive black holes with millions of solar masses. More precise measurements of more extreme…
We consider the full set of master integrals with internal top-and $W$-propagators contributing to the three-loop Higgs self-energy diagrams of order ${\mathcal O}(\alpha^2 \alpha_s)$. We split the master integrals into a system relevant to…
As part of the study of the two-body problem in Einstein's gravity, the fourth post-Newtonian order (4PN) of the two-body effective action is being computed presently by both effective field theory (EFT) methods and others. Diagrams with 3…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
We consider the recently proposed non-relativistic Ho\v{r}ava-Lifshitz four-dimensional theory of gravity. We study a particular limit of the theory which admits flat Minkowski vacuum and we discuss thoroughly the quadratic fluctuations…