Related papers: Machine learning automorphic forms for black holes
We construct 2 families of automorphic forms related to twisted fake monster algebras and calculate their Fourier expansions. This gives a new proof of their denominator identities and shows that they define automorphic forms of singular…
We develop an algorithm to compute Fourier expansions of vector valued modular for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three…
We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a…
In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\infty$ and $0$. As an application, we give explicit…
Identifying weak gravitational wave signals in noise and estimating the source properties require high-precision waveform templates. Numerical relativity (NR) simulations can provide the most accurate waveforms. However, it is challenging…
Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called $t$-$t'$-$t''$-$J$ model, where the…
We consider the classification of asymptotically flat, stationary, vacuum black hole spacetimes in four and five dimensions, that admit one and two commuting axial Killing fields respectively. It is well known that the Einstein equations…
Machine learning is a powerful technique, becoming increasingly popular in astrophysics. In this paper, we apply machine learning to more than a thousand globular cluster (GC) models simulated as part of the 'MOCCA-Survey Database I'…
We give a comprehensive treatment of the transformation laws of theta functions from an algebro-geometric perspective, that is, in terms of moduli of abelian schemes. This is accomplished by introducing geometric notions of theta-descent…
In this paper, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the…
We propose a machine learning-based approach for parameter estimation of Massive Black Hole Binaries (MBHBs), leveraging normalizing flows to approximate the likelihood function. By training these flows on simulated data, we can generate…
Extremal BPS-saturated black holes in $N=2$, $d=4$ supergravity can carry electric and magnetic charges $(q^\Lambda_{(m)},q_\Lambda^{(e)})$. It is shown that in smooth cases the moduli fields at the horizon take a fixed "rational" value…
Jacobi forms can be considered as vector valued modular forms, and Jacobi forms of critical weight correspond to vector valued modular forms of weight $\frac12$. Since the only modular forms of weight $\frac12$ on congruence subgroups of…
Recent works have suggested that nonlinear (quadratic) effects in black hole perturbation theory may be important for describing a black hole ringdown. We show that the technique of uniform approximations can be used to accurately compute…
Quantum gravity theories predict deformations of black hole solutions relative to their classical counterparts. A model-independent approach was advocated in \cite{Binetti:2022xdi} that uses metric deformations parametrised in terms of…
We describe Jacobi forms of vector-valued weights in terms of classical ones, extending previous results by Ibukiyama and Kyomura to the case of arbitrary cogenus. As in their result, our isomorphisms are given by holomorphic covariant…
We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to interpolate the remnant mass, spin, and…
We study generating functions of certain shapes of planar polygons arising from homological mirror symmetry of elliptic curves. We express these generating functions in terms of rational functions of the Jacobi theta function and Zwegers'…
We study the deformation of the input space by a trained autoencoder via the Jacobians of the trained weight matrices. In doing so, we prove bounds for the mean squared errors for points in the input space, under assumptions regarding the…
Observations of neutron star mergers in the late Universe have given significant restrictions to the class of viable scalar-tensor theories. In this paper we construct black holes within the "self-tuning" class of this restricted set,…