In this work, we investigate the quasinormal modes (QNMs) and the late time oscillatory tails of graviscalar perturbations in a thick brane. By considering the scalar perturbations of the thick brane metric, we obtain the main equations of graviscalar Kaluza-Klein modes. Using these equations, the frequencies of the graviscalar QNMs of the thick brane are obtained by the Wentzel-Kramers-Brillouin, asymptotic iteration, and numerical evolution methods. The results show that the scalar fluctuation of the thick brane has a series of discrete QNMs. In the four-dimensional spacetime, these modes manifest as decaying massive scalar particles. We also study in detail the late time tails of the scalar fluctuation. We find that the brane has slowly decaying oscillatory tails that may be new sources of the gravitational wave backgrounds. These novel phenomena may have potential phenomenological significance, and signals from these extra dimensions may potentially be found in current or future gravitational wave detectors.

China

Qin Tan

Sheng Long

Weike Deng

Jiliang Jing

Graviscalar quasinormal modes and asymptotic tails of a thick brane

We have studied the polarized image of an equatorial emitting ring around a rotating braneworld black hole. This black hole possesses a tidal charge parameter $\textit{b}$, which describes the effects of the free gravitational field in the bulk on the brane. Results show that the effects of the tidal charge parameter on the polarized image depend on the magnetic field structure, the observer inclination, the velocity of the fluid and the radii of the emitting ring. For a given value of the rotation parameter, the observed polarization intensity increases monotonously with $\textit{b}$ when the magnetic field lies in the equatorial plane, while it no longer changes monotonically with $\textit{b}$ when the magnetic field is perpendicular to the equatorial plane. The effect of parameter $\textit{b}$ on polarized images is similar in both stronger and weaker gravitational fields when the magnetic field is within the equatorial plane, and the differences in polarization vectors for different $\textit{b}$ become noticeable in stronger gravitational fields. We also probe the effects of $\textit{b}$ on the Stokes Q-U loops.

Xin Qin

Songbai Chen

Xiangyun Fu

Yang Huang

Polarized image of an equatorial emitting ring around a rotating braneworld black hole

We consider how charging performances of a quantum battery, modeled as a two-level system, are influenced by the presence of vacuum fluctuations of a quantum field satisfying the Dirichlet, transparent, and Neumann boundary conditions in the BTZ spacetime. The quantum battery is subjected to an external static driving which works as a charger. Meanwhile, the quantum field is assumed to be coupled to both longitudinal and transverse spin components of the quantum battery including decoherence and pure dephasing mechanisms. Charging and discharging dynamics of the quantum battery are derived by extending the previous open quantum system approach in the relativistic framework to this more general scenario including both the driving and multiple coupling. Analytic expressions for the time evolution of the energy stored are presented. We find that when the driving amplitude is stronger/weaker than the energy-level spacing of the quantum battery the pure dephasing dissipative coupling results in better/worse charging performances than the decoherence dissipative coupling case. We also find that higher local Hawking temperature helps to improve the charging performance under certain conditions compared with the closed quantum battery case, implying the feasibility of energy extraction from vacuum fluctuations in curved spacetime via dissipation in charging protocol. Different boundary conditions for quantum field may lead to different charging performance. Furthermore, we also address the charging stability by monitoring the energy behaviour after the charging protocol has been switched off. Our study presents a general framework to investigate relaxation effects in curved spacetime, and reveals how spacetime properties and field boundary condition affect the charging process, which in turn may shed light on the exploration of the spacetime properties and thermodynamics via the charging protocol.

Zehua Tian

Xiaobao Liu

Jieci Wang

Dissipative dynamics of an open quantum battery in the BTZ spacetime

In this work, we study the gravitational quasinormal modes and the gravitational echoes of a double braneworld. The double braneworld is a kind of split thick brane, which is crucial for addressing the hierarchy problem in the thick brane scenarios. Using the Bernstein spectral method, direct integration method, and asymptotic iteration method, we calculate the quasinormal mode frequencies of the double brane. We find that the quasinormal spectrum is very different from that of the single brane model, especially the high overtone mode. We also perform numerical evolution to study the time-domain properties of the characteristic modes of the double brane. The results show that when the degree of brane splitting is large, gravitational echoes of oscillation attenuation between sub-branes will appear in the thick brane. Furthermore, different long-lived Kaluza-Klein modes interfere with each other, resulting in a beating effect. Compared to a single brane model, the phenomenon of the split double brane is richer, and the lifetime of the massive Kaluza-Klein graviton of the double brane is longer. These phenomena may have potential phenomenological interest. We also explore the gravitational wave signature of the KK graviton of the thick brane and find that the violent splitting of the brane may cause the corresponding frequency to fall within the detection range of the high-frequency gravitational wave detector.

Quasinormal modes and echoes of a double braneworld

We investigate the motion of particles in the spacetime of a Kerr black hole immersed in swirling universes. Using the Poincaré section, fast Lyapunov exponent indicator, bifurcation diagram, and basins of attraction, we present the effects of the swirling parameter and the spin parameter on the dynamical behaviors of the motion of particles, and confirm the presence of chaos in the motion of particles in this background spacetime. We find that the swirling parameter can change the range of the spin parameter where the chaos occurs, and vice versa. Moreover, we observe clearly that, regardless of the spin parameter, there exist some self-similar fractal fine structures in the basins boundaries of attractors for the spacetime of a black hole immersed in swirling universes. The combination of the swirling parameter and the spin parameter provides richer physics in the motion of particles.

Deshui Cao

Lina Zhang

Qiyuan Pan

Chaotic motion of particles in the spacetime of a Kerr black hole immersed in swirling universes

Recently, magnetic reconnection has attracted considerable attention as a novel energy extraction mechanism, relying on the rapid reconnection of magnetic field lines within the ergosphere. We have investigated the properties of the energy extraction via magnetic reconnection in a Konoplya–Zhidenko rotating non-Kerr black hole spacetime with an extra deformation parameter. Our results show that the positive deformation parameter expands the possible region of energy extraction and improves the maximum power, maximum efficiency, and the maximum ratio of energy extraction between magnetic reconnection and the Blandford–Znajek process. This means that in the Konoplya–Zhidenko rotating non-Kerr black hole spacetime one can extract more energy via magnetic reconnection than in the Kerr black hole case. These effects of the deformation parameter may provide valuable clues for future astronomical observations of black holes and verification of gravity theories.

Fen Long

Shangyun Wang

Magnetic reconnection and energy extraction from a Konoplya–Zhidenko rotating non-Kerr black hole

We investigate the scalar perturbation around a rotating Einstein-bumblebee BTZ black hole under Robin boundary conditions. It is shown that the relationship curves between real and imaginary parts of scalar quasinormal modes in the complex plane depend on the black hole spin parameter <italic>j</italic> and the Lorentz symmetry breaking parameter <italic>s</italic>. The shapes of these curves are similar for different <italic>s</italic>, but heavily depend on the spin parameter <italic>j</italic>. With the increase of <italic>j</italic>, the symmetry of these curves with respect to the imaginary axis in the complex plane is gradually broken for different <italic>s</italic>. We also discuss the energy and angular momentum fluxes across the black hole horizon under Robin boundary conditions, and probe the changes of the threshold parameter related to the superradiance in Robin boundary conditions with the symmetry breaking parameter and the spin parameter. The combination of the Lorentz symmetry violation and the Robin boundary condition provides richer physics in the scalar perturbation around a rotating Einstein-bumblebee BTZ black hole.

Chengjia Chen

Fengkai Ge

Scalar perturbation around rotating Einstein-bumblebee BTZ black holes under Robin boundary conditions: Quasinormal modes and superradiance

We investigate the radiative efficiency and jet power in the spacetime of a rotating black hole within the framework of loop quantum gravity (LQG), which includes an additional LQG parameter. The results show that as the LQG parameter increases, the radiative efficiency decreases for slowly rotating black holes while it increases for rapidly rotating black holes. Furthermore, the jet power is found to increase for different black hole spins. With the observed data from the well-known sources A0620-00, H1743-322, XTE J1550-564, GRS1124-683, GRO J1655-40, and GRS1915+105, we make some constraints on the black hole spin parameter and the LQG parameter. The presence of the LQG parameter broadens the allowed range of the black hole spin parameter for sources A0620-00, H1743-322, XTE J1550-564 and GRO J1655-40. However, for the source GRS 1915+105, there is no overlap between the allowed parameter regions, which implies that the rotating LQG black hole cannot simultaneously account for the observed jet power and the radiative efficiency as in other black hole spacetimes

Zhengwei Cheng

Signatures from the observed jet power and the radiative efficiency for rotating black holes in loop quantum gravity

We study geometrically thick non-self gravitating equilibrium tori orbiting a Schwarzschild black hole immersed in swirling universes. This solution is axially symmetric and non-asymptotically flat, and its north and south hemispheres spin in opposite directions. Due to repulsive effects arising from the swirl of the background spacetime, the equilibrium torus exists only in the small swirling case. With the increase of the swirling parameter, the disk structure becomes small and the excretion of matter near the black hole becomes strong. Moreover, the odd  $$Z_2$$  <math> <msub> <mi>Z</mi> <mn>2</mn> </msub> </math>   symmetry of spacetimes originating from the swirling parameter yields that the orientation of closed equipotential surfaces deviates away from the horizontal axis and the corresponding disk does not longer possess the symmetry with respect to the equatorial plane. These significant features could help to further understand the equilibrium tori and geometrically thick accretion disks around black holes in swirling universes.

Geometrically thick equilibrium tori around a Schwarzschild black hole in swirling universes

We propose a scheme for the quantum metrology of the Schwinger effect and the dynamics of Gaussian interference power (GIP). The ongoing reliability of the estimation strategy for the probe state prepared in particle–particle modes is demonstrated. Although the GIP sensitively depends on the strength of the external electric field and the transverse momentum, the advantage of quantum parameter estimation is still maintained even in the limit of an infinite electric field and zero transverse momentum. It is shown that the entanglement between the particle–particle modes provides a guarantee for obtaining higher precision for the black-box estimation. In contrast, for the probe state prepared in particle–antiparticle modes, the advantage of quantum parameter estimation can also be ensured even though there is no entanglement in the probe state. Put differently, some non-entanglement quantum correlations play the role of quantum resources in the estimation for particle–antiparticle modes.