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The observation of gravitational waves has inaugurated a new era for testing gravitational theories in strong-field, nonlinear regimes. Gravitational waves emit during the ringdown phase of binary black hole mergers and from extreme mass ratio inspirals are particularly sensitive to the properties of black holes, making them crucial for probing deviations from general relativity. These studies need a robust foundation in black hole perturbation theory beyond general relativity. While existing studies have employed black hole perturbation theories to explore modifications beyond general relativity, they often focus on specific alternative theories or phenomenological models of quantum gravity. In this paper, we establish a modified decoupled Teukolsky formalism that is broadly applicable to spherically symmetric spacetimes without requiring a predetermined gravitational Lagrangian. This formalism uses the Newman-Penrose framework, which utilizes curvature perturbations characterized by Weyl scalars, to accommodate a wider class of spacetimes beyond general relativity. Our approach correctly handles non-Ricci-flat backgrounds and circumvents subtle analytical issues associated with effective potentials that are present in other modified Teukolsky formalisms., Comment: 17 pages

Ultralight bosons are attractive dark-matter candidates and appear in various scenarios beyond standard model. They can induce superradiant instabilities around spinning black holes (BHs), extracting the energy and angular momentum from BHs, and then dissipated through monochromatic gravitational radiation, which become promising sources of gravitational wave detectors. In this letter, we focus on massive tensor fields coupled to BHs and compute the stochastic gravitational wave backgrounds emitted by these sources. We then undertake a search for this background within the data from LIGO/Virgo O1$\sim$ O3 runs. Our analysis reveals no discernible evidence of such signals, allowing us to impose stringent limits on the mass range of tensor bosons. Specifically, we exclude the existence of tensor bosons with masses ranging from $4.0\times10^{-14}$ to $2.0\times10^{-12}$ eV at $95\%$ confidence level., Comment: 7 pages, 2 figures

Both ultralight dark matter and exploring the quantum nature of black holes are all topics of great interest in gravitational wave astronomy at present. The superradiant instability allows an exotic compact object (ECO) to be surrounded by an ultralight boson cloud, which leads to the emission of gravitational waves and further triggers rich dynamical effects. In this paper, we study the gravitational effects of superradiant instabilities by calculating the energy fluxes of gravitational waves emitted from ultralight scalar dark matter fields by solving the Teukolsky equation in the background of a massive ECO phenomenologically described by a Kerr geometry with a reflective boundary condition at its physical boundary. We find that both the amplitude and phase of the reflectivity will either suppress or enhance the energy flux of GWs by several orders of magnitude if $M\mu \gtrsim 0.5$ where $M$ and $\mu$ are the mass of ECO and boson, respectively. However, the modifications to energy flux are negligible if $M \mu \lesssim 0.5$. Our results suggest that reflectivity will play a significant role in the near-horizon physics of ECO., Comment: 20 pages, 6 figures

Extending previous results of Godefroy and Shapiro we characterize the hypercyclic, mixing and chaotic conjugate multipliers on some reflexive spaces of analytic functions., Comment: arXiv admin note: substantial text overlap with arXiv:2207.05274

In this paper, we characterize mixing unilateral backward shifts on barrelled and ultrabarrelled topological sequence spaces respectively, which extend several well-known results in the existing literature. We present some nontrivial examples to show the validity of our results.

Extending previous results of Bourdon and Shapiro we characterize the hypercyclic and mixing composition operators $C_{\varphi}$ for the automorphisms of $\mathbb{D}$ on any of the spaces $H^{p}$ with $1\leqslant p<+\infty$.

Ultralight bosons, as important candidates of dark matter, can condense around spinning black holes (BHs) to form long-lived ``boson clouds'' due to superradiance instability. The boson-BH system can be observed through gravitational wave detection and may become a new window to find traces of ultralight bosons. In this letter we explore the effects on the superradiant instability of BHs from the near-horizon microstructure. By introducing the reflection parameter near a BH horizon, we derived analytical results on the corrections to both energy levels of bosonic cloud and its characteristic frequencies of superradiance instability. Our results imply that the evolution of a boson-BH system and gravitational waves it emits would be influenced by the near-horizon physics of a BH., Comment: 5 pages

In this letter we calculate the gravitational waves (GWs) emitted from a small binary (SB) by solving the Teukolsky equation in the background of a massive exotic compact object (ECO) which is phenomenologically described by a Schwarzschild geometry with a reflective boundary condition at its "would-be" horizon. The "continuous echo" waves propagating to infinity due to reflectivity of ECO at its "would-be" horizon provide an exquisite probe to the nature of the ECO's horizon., Comment: 6 pages, 3 figures; Detectability of the continuous echo added

We study the independence density for finite families of finite tuples of sets for continuous actions of discrete groups on compact metrizable spaces. We use it to show that actions with positive naive entropy are Li-Yorke chaotic and untame. In particular, distal actions have zero naive entropy. This answers a question of Lewis Bowen., Comment: 14 pages. Section 5 is added. To appear in Ergod. Th. Dynam. Sys

Answering a question of Glasner, we show that any finitely generated nonabelian free group has a minimal null action which is a RIM non-open extension of an effective strongly proximal action., Comment: 24 pages. Minor changes. To appear in Israel J. Math

We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is analyzed. We find that, the linear spectrum can be described by a supersymmetric quantum mechanics problem, and the criteria for stable static solutions can be given analytically. We also construct a superpotential formalism for finding analytical static kink solutions. Using this formalism we first reproduce some existed solutions and then offer a new solution. The properties of our solution is studied and compared without those preexisted. We also show the possibility in constructing twinlike model in the higher derivative theory, and give the consistency conditions for twinlike models corresponding to the canonical scalar field theory., Comment: 14 pages, 5 figures

Recently, Briegel et al. present a quantum repeaters protocol using nest entanglement purification for long distance quantum communication(Physical Review Letters \textbf{81},5932). In this paper we present a modified scheme for constructing an optimal quantum repeater using doubly entangled photon pairs that overcomes the limitations of quantum communication via noisy channels. Based on the imperfect quantum operations and classical communications, the polarization entangled quantum channels can be built with a better efficiency., Comment: 5 pages and 3 figures