Related papers: Choosing the phase for the spin-weighted spheroida…
Standard power series are used to construct and analyze angular and radial spheroidal functions, which are necessary for solving boundary value problems for Helmholtz equation in a spheroid. With an advanced approach the low-lying energy…
Gravitational waves from test masses bound to geodesic orbits of rotating black holes are simulated, using Teukolsky's black hole perturbation formalism, for about ten thousand generic orbital configurations. Each binary radiates power…
It has long been known that, in higher-dimensional general relativity, there are black hole solutions with an arbitrarily large angular momentum for a fixed mass. We examine the geometry of the event horizon of such ultra-spinning black…
We revisit the solutions of the Wheeler-DeWitt (WDW) equation inside the horizons of spherical black holes and planar topological black holes in arbitrary dimensions. For these systems, the solutions of the equations are found to have the…
We investigate spin-refined partition functions in AdS/CFT using Euclidean gravitational path integrals. We construct phase diagrams for $Z_X = \text{Tr} \big( e^{-\beta H} X \big)$ in various dimensions and for different choices of…
The Teukolsky equation describing scattering from Kerr black holes captures a few important effects in the process of binary mergers, such as tidal deformations and the decay of ringdown modes, thereby raising interest in the structure of…
In this work, we investigate the hairy black hole solutions and their dual phase diagram in the improved holographic Einstein-Maxwell-Dilaton (EMD) model.From the gravitational perspective, the rich phase structures observed in the dual…
An algorithm for computing eigenvalues and eigenfunctions of the angular spheroidal wave equation, based on a known but scarcely used method, is developed. By requiring the regularity of the wave function, represented by its series…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
Firstly we derive peculiar spherical Weyl solutions, using a general spherically symmetric metric due to a massive charged object with definite mass and radius. Afterwards, we present new analytical solutions for relevant cosmological…
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
In this paper, we will consider a subclass of models of Horndeski theories of gravity and we will check for several Static Spherically Symmetric solutions. We will find a model which admits an exact black hole solution and we will study its…
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator,…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…
The scattering cross section for a long-wavelength planar gravitational wave impinging upon a rotating black hole is calculated, for the special case in which the direction of incidence is aligned with the rotation axis. We show that black…
Within a semiclassical framework, we investigate spherically symmetric solutions of the Einstein equations that (i) develop a trapped region within a finite time as measured by distant observers, and (ii) remain sufficiently regular at the…
The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest…
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…
In the language of Feynman path integrals the quantization of gauge theories is most easily carried out with the help of the Schr\"odinger Functional (SF). Within this formalism the essentially unique gauge fixing condition is $A_{\circ} =…