arXiv subjects

Yu-Xiao Liu

Publications and source records attributed to Yu-Xiao Liu.

At least 73 records · Page 4Linked to original sources

arXiv2025

Generalized Free Energy Landscapes from Iyer-Wald Formalism

The generalized free energy landscape plays a pivotal role in understanding black hole thermodynamics and phase transitions. In general relativity, one can directly derive the generalized free energy from the contributions of black holes exhibiting conical singularities. In this work, we extend this idea to general covariant theories. By employing Noether's second theorem, we present an alternative formulation of the Lagrangian, which can elucidate the role of conical singularities. We demonstrate that, in general, the contribution from conical singularities depends on the specific implementation of the regularization scheme and is not uniquely determined; this feature is explicitly exhibited and confirmed in three-dimensional new massive gravity. Nevertheless, these ambiguities can be absorbed into the second-order (and higher) corrections induced by conical singularities when the gravitational theory is described by the Lagrangian $L(g_{ab},R_{abcd})$. Moreover, for certain theories such as general relativity and Bumblebee gravity, this contribution simplifies to a well-defined result. However, the interpretation of the generalized free energy in Bumblebee gravity is somewhat different, with its extrema corresponding to the geometry of conical singularities. Our results uncover the particular properties of the generalized free energy beyond general relativity.

hep-th↗

arXiv2025

Holographic thermodynamics of a five-dimensional neutral Gauss-Bonnet AdS black hole

Motivated by the recent progress on the holographic dual of the extended thermodynamics for black holes in anti-de-Sitter (AdS) space, we investiggate the hologrphic thermodynamics for the five-dimensional neutral Gauss-Bonnet AdS black hole in the context of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. Through the extended bulk thermodynamics for the five-dimensional Gauss-Bonnet AdS black hole, we derive the first law of the CFT thermodynamics which is obtained by directly translating the arbitrary conformal factors in the dual CFT. In addition to the newly defined chemical potential $μ$ conjugating to the central charge $C$, we obtain other pairs of thermodynamics for the CFT, such as the temperature $\tilde{T}$ and the entropy $S$, the Gauss-Bonnet coupling constant $\tildeα$ and its conjugate variable $ \tilde{\mathcal{A}}$, the pressure $\mathcal{P}$ and its conjugate volume $\mathcal{V}$. In the fixed $C$, $\mathcal{V}$ and $\tildeα$ canonical ensemble, we obtain the canonical description of the CFT thermodynamics and observe the standard swallowtail behavior in the Helmholtz free energy vs the temperature plot. The self-intersection point of the Helmholtz free energy indicates the phase transition between the high and low entropy states of the CFT. By using Maxwell's equal area law, we get the critical point and coexistence curve for the high and low entropy phases of the CFT. Besides, we get the critical exponents for the CFT, and find that the critical point and critical exponents associated with the $\tilde{T}-S$ criticality of the CFT are the same as those of the five-dimensional Gauss-Bonnet AdS black hole.

hep-th↗

arXiv2025

Constraining polymerized black holes with quasi-circular extreme mass-ratio inspirals

In this paper, we focus on the gravitational waves emitted by a stellar-mass object in a quasi-circular inspiral orbit around a central supermassive polymerized black hole in loop quantum gravity. Treating the stellar-mass object as a massive test particle, we derive its equations of motion and the corresponding radial effective potential. We find that the peak of the radial effective potential decreases with the quantum parameter $\hat{k}$. We also examine the impact of quantum corrections on the properties of stable circular orbits around the polymerized black hole. We model the smaller object's trajectory as an adiabatic evolution along stable circular orbits using a semi-relativistic approach. In this method, the motion of the object is described by relativistic geodesics, and changes in the object's energy and orbital angular momentum due to gravitational radiation are calculated using the mass quadrupole formula. The corresponding gravitational waveforms are generated using the numerical kludge method, revealing that quantum corrections cause phase advances in the gravitational waveforms. We further analyze the potential constraints on the quantum parameter $\hat{k}$ from future space-based gravitational wave observations, concluding that these observations will likely impose stronger constraints on $\hat{k}$ than those obtained from black hole shadow measurements.

gr-qc↗

arXiv2025

Polarization modes of gravitational waves in scalar-tensor-Rastall theory

Rastall theory, originally introduced in 1972, suggests a violation of the usual conservation law. We consider two generalizations of Rastall theory: Brans-Dicke-Rastall theory and the newly established scalar-tensor-Rastall theory, the latter being a further generalization of the former. The field equations in these two generalized theories are studied across different parameter spaces, and the polarization modes of gravitational waves, as a key focus, are subsequently investigated. The results show that the polarization modes of gravitational waves in Brans-Dicke-Rastall theory are the same as those in Brans-Dicke theory; specifically, both theories exhibit the plus, cross, and breathing modes. However, in scalar-tensor-Rastall theory, the polarization modes of gravitational waves depend on the parameter space of the theory. Particularly, over a broad range of the parameter space, regardless of some special values of the parameters, it allows only two tensor modes, just as in general relativity, without introducing any additional degrees of freedom. This indicates that Rastall theory offers a novel approach to constructing modified gravity theories that propagate only two tensor degrees of freedom. In the remaining regions of the parameter space, there is also one scalar mode in addition to the two tensor modes. The scalar mode can be either a mixture of the breathing and longitudinal modes or just a pure breathing mode, depending on the parameter space. These results will play a crucial role in constraining the theoretical parameters through future gravitational wave detection projects, such as LISA, Taiji, and TianQin.

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arXiv2025

Gravitational waveforms from periodic orbits around a quantum-corrected black hole

Extreme mass-ratio inspirals are crucial sources for future space-based gravitational wave detections. Gravitational waveforms emitted by extreme mass-ratio inspirals are closely related to the orbital dynamics of small celestial objects, which vary with the underlying spacetime geometry. Despite the tremendous success of general relativity, there are unsolved issues such as singularities in both black holes and cosmology. Loop quantum gravity, a theory addressing these singularity problems, offers a framework for regular black holes. In this paper, we focus on periodic orbits of a small celestial object around a supermassive quantum-corrected black hole in loop quantum gravity and compute the corresponding gravitational waveforms. We view the small celestial object as a massive test particle and obtain its four-velocity and effective potential. We explore the effects of quantum corrections on marginally bound orbits, innermost stable circular orbits, and other periodic orbits. Using the numerical kludge scheme, we further explore the gravitational waveforms of the small celestial object along different periodic orbits. The waveforms exhibit distinct zoom and whirl phases in a complete orbital period, closely tied to the quantum parameter $\hat α$. We also perform a spectral analysis of the gravitational waves from these periodic orbits and assess their detectability. With the steady progress of space-based gravitational wave detection programs, our findings will contribute to utilizing extreme mass-ratio inspirals to test and understand the properties of quantum-corrected black holes.

gr-qc↗

arXiv2025

Evolution of Fermion Resonance in Thick Brane

In this work, we investigate numerical evolution of massive Kaluza-Klein (KK) modes of a Dirac field on a thick brane. We deduce the Dirac equation in five-dimensional spacetime, and obtain the time-dependent evolution equation and Schrödinger-like equation of the extra-dimensional component. We use the Dirac KK resonances as the initial data and study the corresponding dynamics. By monitoring the decay law of the left- and right-chiral KK resonances, we compute the corresponding lifetimes and find that there could exist long-lived KK modes on the brane. Especially, for the lightest KK resonance with a large coupling parameter and a large three momentum, it will have an extremely long lifetime.

hep-th↗

arXiv2025

Black hole thermodynamics from an ensemble-averaged theory

The path integral approach to a quantum theory of gravity is widely regarded as an indispensable strategy. However, determining what additional elements, beyond black hole or AdS spacetime, should be incorporated into the path integral remains crucial yet perplexing. We argue that the spacetime with a conical singularity in its Euclidean counterpart should be the most important ingredient to append to the path integral. Therefore, physical quantities should be ensemble-averaged over all geometries since they are described by the same Lorentzian metric. When the ensemble average is introduced, the Hawking-Page transition for the Schwarzschild-AdS black hole and the small-large black hole transition for the Reissner-Nordström-AdS black hole naturally arise as semi-classical approximations, when the size of the black hole system is much larger than the Planck length. Away from the semi-classical limit, the system is a superposition of different geometries, and the averaged quantities would deviate from the black hole thermodynamics. Expanding around the classical saddles, the subleading order of the Newton constant contributions can be derived, which are half of the Hawking temperature both for the Schwarzschild and Reissner-Nordström black holes. The result may imply a universal structure. The subsubleading terms and more intriguing physics that diverge from black hole thermodynamics are revealed. The ensemble-averaged theory provides a new way of studying subleading effects and extending the traditional AdS/CFT correspondence.

gr-qc↗

arXiv2025

Strong gravitational lensing of a five-dimensional charged, equally rotating black hole with a cosmological constant

We study the lensing phenomena of the strong gravity regime of five-dimensional charged, equally rotating black holes with a cosmological constant, familiarly known as the Cveti\v c-Lü-Pope black holes. These black holes are characterized by three observable parameters, the mass $M$, the charge $Q$ and the angular momentum $J$, in addition to the cosmological constant. We investigate the strong gravitational lensing observables, mainly the photon sphere radius, the minimum impact parameter, the deflection angle, the angular size, and the magnification of the relativistic images. We model the $M87$ and $SgrA^*$ for these observables. We also focus on the relativistic time delay effect in the strong-field regime of gravity and the impact of the observable on it. The analytical expressions for the observables of the relativistic images with vanishing angular momentum ($j=0$) are discussed in some detail. We shed a light on the gravitational time delay effect by incorporating the lensing observables. The gravitational time delay has a direct consequence on the photon sphere radius and hence on the quasinormal modes.

gr-qc↗

arXiv2025

Gravitational Echoes from Braneworlds

Gravitational echoes can be used to probe the structure of spacetime. In this paper, we investigate the gravitational echoes in different braneworld models in five-dimensional spacetime. We derive the gravitational perturbation equations of these models, and obtain the time-dependent evolution equations of the extra-dimensional and radial components. Using a Gaussian wave packet as initial data, we study the time evolution of the gravitational perturbation. By monitoring the evolution of the Gaussian wave packet, the gravitational echoes are observed whether the wave packet is generated from inside or outside the braneworld. Furthermore, we can restrict the parameters of the braneworld by calculating the strength of the first gravitational echo and using the current gravitational wave data.

gr-qc↗

arXiv2025

Charged spherically symmetric and slowly rotating charged black hole solutions in bumblebee gravity

In this paper, we present charged spherically symmetric black hole solutions and slowly rotating charged solutions in bumblebee gravity with and without a cosmological constant. The static spherically symmetric solutions describe the Reissner-Nordström-like black hole and ReissnerNordström-(anti) de Sitter-like black hole, while the stationary and axially symmetric soltuions describe Kerr-Newman-like black hole and Kerr-Newman-(anti) de Sitter-like black hole. We utilize the Hamilton-Jacobi formalism to study the shadows of the black holes. Additionally, we investigate the effect of the electric charge and Lorentz-violating parameters on the radius of the shadow reference circle and the distortion parameter. We find that the radius of the reference circle decreases with the Lorentz-violating parameter and charge parameter, while the distortion parameter increases with the Lorentz-violating parameter and the charge parameter.

gr-qc↗

arXiv2025

Emerging black hole shadow from collapsing boson star

This work devotes to investigate the dynamical emergence of black hole shadow from gravitational lensing in dynamical spacetime by using the collapsing boson star. Two characterized scenarios are adopted with or without considering the time delay of light propagation. As the boson star evolves, new Einstein rings emerge from the lensing center, with their radius gradually increasing, and their number continues to grow infinitely before the light-ring forms. The shadow forms instantaneously at the moment the black hole appears when ignoring the time delay of light propagation. Considering the time delay for light propagation in dynamical spacetime, a more intricate process of the shadow formation is uncovered: it first appears as a minute dot in the lensing center, then gradually grows as the black hole grows, eventually expands the inner region of the light-ring. During the quasi-stable phases of boson star and black hole, the lensing and shadow structures from two scenarios are nearly identical and remain almost unchanged. Our results present the universal dynamic patterns of the lensing and shadow structures, and reveal the potential observed phenomena near the collapsing star and the event horizon of the newly formed black hole.

gr-qc↗

arXiv2025

Quasinormal modes and greybody factor of a Lorentz-violating black hole

Recently, a static spherically symmetric black hole solution was found in gravity nonminimally coupled a background Kalb-Ramond field. The Lorentz symmetry is spontaneously broken when the Kalb-Ramond field has a nonvanishing vacuum expectation value. In this work, we focus on the quasinormal modes and greybody factor of this black hole. The master equations for the perturbed scalar field, electromagnetic field, and gravitational field can be written into a uniform form. We use three methods to solve the quasinormal frequencies in the frequency domain. The results agree well with each other. The time evolution of a Gaussian wave packet is studied. The quasinormal frequencies fitted from the time evolution data agree well with that of frequency domain. The greybody factor is calculated by Wentzel-Kramers-Brillouin (WKB) method. The effect of the Lorentz-violating parameter on the quasinormal modes and greybody factor are also studied.

gr-qc↗

arXiv2025

Hereditary Effects and New Optical Properties of Nonlinear Gravitational Waves

We investigate new optical effects of nonlinear gravitational waves that arise from hereditary effects. Firstly, we show that the amplitude of continuous plane waves has a hereditary effect that grows with distance. This can make the amplitude of nonlinear gravitational waves decay more slowly with distance. This will also lead to observable nonlinear effects in future observations. Secondly, hereditary effects also imply that nonlinear perturbations are nonlocally dependent on linear ones, and this property leads to some special optical effects which allow nonlinear gravitational waves to contain more information. It is even possible to extract information on the distance and direction of the wave source as well as the polarization from the waveform of nonlinear gravitational waves.

gr-qc↗

arXiv2025

Parameterized quasinormal frequencies and Hawking radiation for axial gravitational perturbations of a holonomy-corrected black hole

As the fingerprints of black holes, quasinormal modes are closely associated with many properties of black holes. Especially, the ringdown phase of gravitational waveforms from the merger of compact binary components can be described by quasinormal modes. Serving as a model-independent approach, the framework of parameterized quasinormal frequencies offers a universal method for investigating quasinormal modes of diverse black holes. In this work, we first obtain the Schrödinger-like master equation of the axial gravitational perturbation of a holonomy-corrected black hole. We calculate the corresponding quasinormal frequencies using the Wentzel-Kramers-Brillouin approximation and asymptotic iteration methods. We investigate the numerical evolution of an initial wave packet on the background spacetime. Then, we deduce the parameterized expression of the quasinormal frequencies and find that $r_0 \leq 10^{-2}$ is a necessary condition for the parameterized approximation to be valid. We also study the impact of the quantum parameter $r_0$ on the greybody factor and Hawking radiation. With more ringdown signals of gravitational waves detected in the future, our research will contribute to the study of the quantum properties of black holes.

gr-qc↗

arXiv2025

Polarization modes of gravitational waves in general Einstein-vector theory

We study the polarization modes of gravitational waves in general Einstein-vector theory with an arbitrary constant background vector field under a Minkowski background. We compare these polarization modes with those of other vector-tensor theories and constrain the parameter spaces based on the gravitational-wave event GW170817 with its electromagnetic counterpart GRB170817A and observations of pulsar timing arrays. The presence of the background vector field leads to the anisotropy of space and a rich variety of gravitational wave contents. Our results reveal that the polarization modes of gravitational waves depend on the parameter spaces. There are at least two and at most five independent polarization modes in one parameter space. In different parameter spaces, some mixture modes are allowed, including tensor-vector, tensor-scalar, tensor-vector-scalar, vector-scalar, and scalar-scalar mixture modes, as well as five independent modes (excluding $P_l$): $P_+$, $P_{\times}$, $P_x$, $P_y$, and $P_b$. In all regions of the parameter spaces, there are always two tensor modes, which can be either independent of or mixed with other modes. The independent $P_b$ mode consistently exhibits the same speed as light. If the speed of tensorial gravitational waves strictly equals that of light, only the $P_+$, $P_{\times}$, and $P_b$ modes are permitted. Furthermore, through comparisons of some vector-tensor theories and based on the observations of gravitational waves, the $P_b$ mode is expected to be allowed.

gr-qc↗

arXiv2025

Quasinormal ringing of thick braneworlds with a finite extra dimension

In this work, we investigate the quasinormal modes of the Poincaré thick brane with a finite extra dimension. Unlike the case with an infinite extra dimension, the gravitational effective potential exhibits three distinct shapes within different ranges of the parameter $n$ in the warp factor: harmonic oscillator potential, Pöschl-Teller potential, and volcano-like potential. We then study various types of perturbations in this system. Utilizing a combination of analytical, semi-analytical, and numerical methods, we obtain the quasinormal modes of the perturbed fields. Our findings reveal a set of discrete quasinormal modes for the thick brane, similar to those of black holes. Interestingly, when $n=1$, the quasinormal modes exhibit purely imaginary behavior. This study may provide a new way to detect the existence of extra dimensions.

gr-qc↗

arXiv2024

Quasinormal Ringing of de Sitter Braneworlds

Compared with the Poincaré braneworld, the de Sitter (dS) braneworld aligns more closely with the present universe characterized by a small but finite cosmological constant. To explore the quasinormal ringing properties within the dS brane scenario, we investigate the gravitational perturbations in both thin and thick dS brane configurations. Analysis of the perturbation equations reveals that the effective potential along the extra dimension exhibits the shape of Pöschl-Teller potential, asymptotically approaching a constant value (mass gap) at infinity. And analytical calculations further indicate that the gravitational perturbations, apart from the zero mode, possess a series of discrete, purely imaginary quasinormal modes in the late stages. This result implies that these perturbations decay without oscillation over time. The analytical findings also demonstrate that the brane structure primarily determines the distribution of the quasinormal spectrum while preserving the purely imaginary nature of the quasinormal frequencies. Subsequently, we further simulate the gravitational wave signal by numerically evolving the perturbation equations, which yield late-stage results consistent with the analytical predictions. Interestingly, these quasinormal modes carry information about the cosmological constant on the brane, which provides a potential new pathway for the study of cosmology in the dS brane scenario.

gr-qc↗

arXiv2024

Dynamical formation of axionic hair around charged black hole

In this paper, we present a nonlinear numerical investigation on the dynamical scalarization process of a Reissner-Nordström black hole, incorporating an axionic scalar potential within the framework of the Einstein-Maxwell-dilaton theory. By scrutinizing the evolution of the irreducible mass of the black hole and the value of scalar field on the apparent horizon across various parameters of the axionic potential, we elucidate the correlations between the final states of scalarized charged black hole and the axionic potential. We observe that the inclusion of the axionic potential can either decrease or increase the irreducible mass of the final scalarized black hole, depending on the strength of the coupling between the dilation and the electric invariant $F_{μν}F^{μν}$. Regarding the value of the scalar field on the apparent horizon, we find that it decreases with the inclusion of the axionic potential. Our results contribute to an important understanding of the dynamical scalarization of black holes and the potential configurations of scalar hair with various self-interactions.

gr-qc↗