Leyla Ogurol | Searcharxiv

arXiv2026

Perturbative Analytical Construction of Bowen-York Initial Data for Binary Black Holes up to Third Order in Spin and Linear Momentum

We analytically construct initial data for binary black hole systems by solving the Einstein constraint equations within the Bowen-York framework. Allowing for arbitrarily oriented linear momenta and spins, we obtain a perturbative solution of the vacuum Hamiltonian constraint up to third order in the source parameters. Our solution explicitly incorporates the system's binary nature via position-weighted multipole moments. The momentum constraints are solved exactly, while the conformal factor is determined analytically. Using the resulting initial data, we compute the ADM energy, linear and angular momenta, and the irreducible mass. We also determine the shape of the apparent horizon and show that it is geometrically consistent with the inner-end regularity. The resulting expressions are written in a manifestly tensorial form and provide an analytic benchmark for numerical-relativity calculations within the perturbative far-zone regime considered here.

gr-qc↗

arXiv2025

Physical Interpretations of Integration Constants and Large Gauge Effects in Flat and AdS Spacetimes

As in other partial differential equations, one ends up with some arbitrary constants or arbitrary functions when one integrates Einstein's equations, or more generally field equations of any other gravity. Interpretation of these arbitrary constants and functions as some physical quantities that can, in principle, be measured is a non-trivial matter. Concentrating on the case of constants, one usually identifies them as conserved mass, momentum, angular momentum, center of mass, or some other hairs of the solution. This can be done via the Arnowitt-Deser-Misner (ADM)-type construction based on pure geometry, and the solution is typically a black hole. Hence, one talks about the black hole mass and angular momentum, etc. Here we show that there are several misunderstandings: First of all, the physical interpretation of the constants of a given geometry depends not only on pure geometry, i.e. the metric, but also on the theory under consideration. This becomes quite important, especially when there is a cosmological constant. Secondly, one usually assigns the maximally symmetric spacetime, say the flat or the (anti)-de Sitter spacetime, to have zero mass and angular momentum and linear momentum. This declares the maximally symmetric spacetime to be the vacuum of the theory, but such an assignment depends on the coordinates in the ADM-type constructions and their extensions: in fact, one can introduce large gauge transformations (new coordinates) which map, say, the flat spacetime to flat spacetime but the resultant flat spacetime can have a nontrivial mass and angular momentum, if the new coordinates are such that the metric components do not decay properly. These issues, which are often overlooked, will be examined in detail, and a resolution, via the use of a divergence-free rank $(0,4)$-tensor, will be shown for the case of anti-de Sitter spacetimes.

gr-qc↗