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In this work, we explore the effect of deformation of the nuclei on collective flow in relativistic heavy-ion collisions. The parameter associated with the geometrical deformation in the Glauber model is tuned to reproduce the empirical multiplicity probability distributions correctly. Subsequently, the particle spectra and collective flows for Au+Au and U+U collisions are evaluated using a hybrid hydrodynamic code CHESS. We analyze the effects of the degrees of freedom associated with the IC on the final-state flow harmonics by exploring the parameter space of the former. The connection between the deformation parameters, specifically $\beta_2$ and $\beta_4$, and the flow anisotropies is scrutinized. In particular, deviations in elliptic flow at $p_{\mathrm{T}}\sim 2$ GeV are observed at smaller values of $\beta_2$ in Au+Au collisions. On the other hand, for U+U collisions, the averaged overall flow harmonics are found to be less sensitive to the geometrical parameters. Despite the difference in the model's specifications, our findings largely confirm those obtained in the literature employing different approaches, which indicate that flow harmonics can be used as a sensible probe for the initial geometry fluctuations and to discriminate between different theoretical models., Comment: 17 pages, 10 figures

In this work, we discuss the generalized Einstein-Maxwell-Dilaton gravity theory with a nonminimal coupling between the Maxwell field and scalar field. Considering different geometric properties of black hole horizon structure, the charged dilaton Lifshitz black hole solutions are presented in 4-dimensional spacetimes. Later, utilizing the Wald Formalism, we derive the thermodynamic first law of black hole and conserved quantities. According to the relationship between the heat capacity and the local stability of black hole, we study the stability of charged Lifshitz black holes and identify the thermodynamic stable region of black holes that meet the criteria., Comment: 12 pages, 2 figures

The strategy of permitting general traffic to use the bus lane for improved utilization while ensuring bus priority has gained increasingly attention, particularly with the support of vehicle-to-everything technology. In this study, we propose a novel lane usage strategy called Dynamic Spatial-Temporal Priority (DSTP) to ensure bus priority and optimize bus lane usage in a mixed traffic environment. DSTP leverages dynamic methods to identify available spatial-temporal resources in the lane, utilizing signal timing, road information, and vehicle data. A Right-of-Way assignment optimization model is then developed based on these resources to determine which vehicles can enter the bus lane. The model is dynamically enacted using a rolling horizon scheme to accommodate time-varying traffic conditions. Numerical studies have validated the advantages of DSTP, showing maintained bus priority, improved traffic efficiency, reduced fuel consumption, and lower CO2 emissions, especially during periods of high traffic demand and concentrated bus arrivals., Comment: 16 pages, 22 figures

Considering the nonminimal coupling of the dilaton field to the massive graviton field in Maxwell-dilaton-massive gravity, we obtain a class of analytical solutions of charged black holes, which are neither asymptotically flat nor (A)dS. The calculated thermodynamic quantities, such as mass, temperature and entropy, verify the validity of the first law of black hole thermodynamics. Moreover, we further investigate the critical behaviors of these black holes in the grand canonical and canonical ensemble, and find a novel critical phenomenon never before observed, known as the ``reverse" reentrant phase transition with a tricritical point. It implies that the system undergoes a novel ``SBH-LBH-SBH" phase transition process, and is the reverse of the ``LBH-SBH-LBH" process observed in reentrant phase transitions., Comment: 20 Pages, 5 figures, 8 tables

Damour-Solodukhin wormholes are intriguing theoretical constructs, closely mimicking many properties of black holes. This study delves into two distinct characteristics of the waveforms emitted from such wormholes, namely, the late-time tails and echoes, which can substantially be used to distinguish its identity. Notably, both features appear in the latter stages of quasinormal oscillations and stem from the singularities of the Green's function. The late-time tail, on the one hand, arises due to the branch cuts in the relevant Green's function. Within the Damour-Solodukhin wormhole paradigm, singularities are present in both ingoing and outgoing waveforms, which entails a generalization of the existing recipe for black hole metrics. On the other hand, the echoes are attributed to a new set of quasinormal poles, supplementing those of the respective black holes, reminiscent of the scenario where the spacetime metric possesses a discontinuity. It is inferred that both features are observationally relevant in distinguishing a wormhole from its black hole counterpart. Moreover, we suggest a potential interplay concerning the late-time evolution between the two mechanisms in question., Comment: 20 pages, 5 figures

In this paper, we focus on massive Einstein-dilaton gravity including the coupling of dilaton scalar field to massive graviton terms, and then derive static and spherically symmetric solutions of dilatonic black holes in four dimensional spacetime. We find that the dilatonic black hole could possess two horizons (event and cosmological), extreme (Nariai) and naked singularity for the suitably fixed parameters. In addition, we investigate thermodynamic properties of these dilatonic black holes, and check the corresponding first law of black hole thermodynamics. Extending to the massive Einstein-dilaton gravity in high dimensions, we further obtain the dilatonic black hole solutions in $(d+1)$ dimensional spacetime., Comment: 23 pages, 12 figures

Although partition temperature derived using the Darwin-Fowler method is exact for simple scenarios, the derivation for complex systems might reside on specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed form expression can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed., Comment: 12 pages, 2 figures, and 1 table

Multiplicity fluctuations play a crucial role in relativistic heavy-ion collisions. In this work, we explore how the multiplicity fluctuations can be effectively suppressed in the measurement of particle correlations. In particular, through proper normalization, particle correlations can be evaluated in a manner irrelevant to multiplicity. When the multiplicity fluctuations are adequately extracted, Monte Carlo simulations show that the remaining correlations possess distinct features buried in the otherwise overwhelming fluctuations. Moreover, we argue that such a normalization scheme naturally agrees with the multi-particle correlator, which can be evaluated using the Q-vectors. The implications of the present study in the data analysis are also addressed., Comment: 15 pages, 3 figures

In this paper, we investigate the detectability of secondary spin in the extreme mass ratio inspirals system within a modified gravity model coupled with a scalar field. The central black hole, which reduces to a Kerr one, is circularly spiralled by a scalar-charged spinning secondary body on the equatorial plane. The analysis reveals that the presence of the scalar field amplifies the secondary spin effect, allowing for a lower limit of the detectability and an improved resolution of the secondary spin when the scalar charge is sufficiently large. Our findings suggest that the secondary spin detection is more feasible when the primary mass is not large, and TianQin is the optimal choice for detection., Comment: 30 pages, 8 figures

In this paper, we discuss a fully nonlinear mechanism for the formation of scalarized rotating black holes in Einstein-scalar-Gauss-Bonnet gravity, where Kerr black holes are linearly stable, but unstable against nonlinear scalar perturbations. With the help of the pseudospectral method, we obtain a spectrum of nonlinearly scalarized rotating black hole solutions with multiple scalarized branches. Moreover, we investigate the thermodynamic properties of nonlinearly scalarized rotating black holes and find the phase transition between Kerr and these scalarized black holes., Comment: 23 pages, 8 figures and 2 tables

In relativistic heavy-ion collisions, event-by-event fluctuations are known to have non-trivial implications. Even though the probability distribution is geometrically isotropic for the initial conditions, the anisotropic $\varepsilon_n$ still differs from zero owing to the statistical fluctuations in the energy profile. On the other hand, the flow harmonics extracted from the hadron spectrum using the multi-particle correlators are inevitably subjected to non-vanishing variance due to the finite number of hadrons emitted in individual events. As one aims to extract information on the fluctuations in the initial conditions via flow harmonics and their fluctuations, finite multiplicity may play a role in interfering with such an effort. In this study, we explore the properties and impacts of such fluctuations in the initial and final states, which both notably appear to be statistical ones originating from the finite number of quanta of the underlying system. We elaborate on the properties of the initial-state eccentricities for the smooth and event-by-event fluctuating initial conditions and their distinct impacts on the resulting flow harmonics. Numerical simulations are performed. The possible implications of the present study are also addressed., Comment: 11 pages, 2 figures

We explore the possibility of evaluating flow harmonics by employing the maximum likelihood estimator (MLE). For a given finite multiplicity, the MLE simultaneously furnishes estimations for all the parameters of the underlying distribution function while efficiently suppressing the variance of measures. Also, the method provides a means to assess a specific class of mixed harmonics, which is not straightforwardly feasible by the approaches primarily based on particle correlations. The results are analyzed using the Wald, likelihood ratio, and score tests of hypotheses. Besides, the resultant flow harmonics obtained using MLE are compared with those derived using particle correlations and event plane methods. The dependencies of extracted flow harmonics on the multiplicity of individual events and the total number of events are analyzed. It is shown that the proposed approach works efficiently to deal with the deficiency in detector acceptability. Moreover, we elaborate on a fictitious scenario where the event plane is not a well-defined quantity in the distribution function. For the latter case, the MLE is shown to largely perform better than the two-particle correlation estimator. In this regard, one concludes that the MLE furnishes a meaningful alternative to the existing approaches for flow analysis., Comment: 15 pages, 5 figures, and 8 tables

Inspired by the combinatorial algebraic approach proposed by Dhurandhar {\it et al.}, we propose two novel classes of second-generation time-delay interferometry (TDI) solutions and their further generalization. The primary strategy of the algorithm is to enumerate specific types of residual laser frequency noise associated with second-order commutators in products of time-displacement operators. The derivations are based on analyzing the delay time residual when expanded in time derivatives of the armlengths order by order. It is observed that the solutions obtained by such a scheme are primarily captured by the geometric TDI approach and therefore possess an intuitive interpretation. Nonetheless, the fully-symmetric Sagnac and Sagnac-inspired combinations inherit the properties from the original algebraic approach, and subsequently lie outside of the scope of geometric TDI. We explicitly show that novel solutions, distinct from existing ones in terms of both algebraic structure and sensitivity curve, are encountered. Moreover, at its lowest order, the solution is furnished by commutators of relatively compact form. Besides the original Michelson-type solution, we elaborate on other types of solutions such as the Monitor, Beacon, Relay, Sagnac, fully-symmetric Sagnac, and Sagnac-inspired ones. The average response functions, residual noise power spectral density, and sensitivity curves are evaluated for the obtained solutions. Also, the relations between the present scheme and other existing algorithms are discussed., Comment: 22 pages, 4 figures

We investigate the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with a positive coupling parameter $\alpha$. This corresponds to exploring the onset of spontaneous scalarization for KN black holes. For this purpose, we use the hyperboloidal foliation method (HFM) to solve the linearized scalar equation numerically. We obtain a 3D graph [$\log_{10}\alpha(a,Q)$] which indicates the onset surface for spontaneous scalarization of KN black holes in the EMS theory. We find that there is no lower bound on the rotational parameter $a$, but its upper bound is given by $M^2-Q^2 \ge a^2$. Also, we confirm that the high rotation enhances spontaneous scalarization of KN black holes in the EMS theory., Comment: 21 pages, 6 figures, Version accepted for publication in PRD. arXiv admin note: text overlap with arXiv:2206.11587

In this paper, we consider the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with nonminimal negative scalar coupling to Maxwell term, and then obtain a bound $(\frac{a}{r_+}\geq0.4142)$ for spin parameter $a$ of KN black hole in the limit of coupling constant $\alpha\rightarrow-\infty$ by using analytical method. In addition, we perform a $(2+1)$-dimensional time evolution of linearized scalar field perturbation on the KN black hole background by implementing the hyperboloidal foliation method numerically in the EMS theory. It recovers the \textit{spontaneous scalarization} phenomenon for KN black hole in some certain regions of the parameter spaces. We further plot corresponding threshold curves $\alpha(a)$ which describe a boundary between bald KN black holes and scalarized spinning black holes in the EMS theory., Comment: 23 pages, 6 figures

It was first pointed out by Koyama and Tomimatsu that, under reasonable assumptions, the asymptotic late-time tails of massive scalar perturbations in the far zone of spherically symmetric black hole spacetimes decays universally as $t^{-5/6}$. The late-time tail is furnished by the contribution from the branch cut of the frequency-domain Green's function, which is constructed in terms of two appropriate solutions of the corresponding homogeneous equation. The present study is focused on some particular forms of the in-going wave that were not explicitly considered in the original derivations but nonetheless have been taken into account in the literature by other authors. In this regard, we reassess the authors' arguments and provide a detailed complimentary analysis that covers a few specific aspects. For some particular cases, the tail is found to possess the form $t^{-1}$. We also discuss the possible implications of the present findings., Comment: 18 pages, 2 figures

We study extreme mass ratio inspirals occurring in modified gravity, for which the system is modeled by a small compact object with scalar charge spiraling into a supermassive Kerr black hole. Besides the tensorial gravitational waves arising from the metric perturbations, radiations are also induced by the scalar field. The relevant metric and scalar perturbations are triggered by the orbital motion of the small object, which give rise to a system of inhomogeneous differential equations under the adiabatic approximation. Such a system of equations is then solved numerically using Green's function furnished by the solutions of the corresponding homogeneous equations. To explore the present scenario from an observational perspective, we investigate how the pertinent observables are dependent on specific spacetime configurations. In this regard, the energy fluxes and the gravitational wave dephasing accumulated during the process are evaluated, as functions of the scalar charge, mass ratio, and spin of the central supermassive black hole. In particular, the presence of additional scalar emission leads to a more significant rate of overall energy loss, which, in turn, decreases the total number of orbital cycles before the small object plunges into the central black hole. Moreover, for a central black hole with a higher spin, the imprints of the scalar charge on the resultant gravitational radiations are found to be more significant, which indicates the possibility of detecting the scalar charge., Comment: 22 pages, 7 figures

In this work, we study the black hole light echoes in terms of the two-photon autocorrelation and explore their connection with the quasinormal modes. It is shown that the above time-domain phenomenon can be analyzed by utilizing the well-known frequency-domain relations between the quasinormal modes and characteristic parameters of null geodesics. We found that the time-domain correlator, obtained by the inverse Fourier transform, naturally acquires the echo feature, which can be attributed to a collective effect of the asymptotic poles through a weighted summation of the squared modulus of the relevant Green's functions. Specifically, the contour integral leads to a summation taking over both the overtone index and angular momentum. Moreover, the dominant contributions to the light echoes are from those in the eikonal limit, consistent with the existing findings using the geometric-optics arguments. For the Schwarzschild black holes, we demonstrate the results numerically by considering a transient spherical light source. Also, for the Kerr spacetimes, we point out a potential difference between the resulting light echoes using the geometric-optics approach and those obtained by the black hole perturbation theory. Possible astrophysical implications of the present study are addressed., Comment: 12 pages, 3 figures

Gravitational wave echoes from the black holes have been suggested as a crucial observable to probe the spacetime in the vicinity of the horizon. In particular, it was speculated that the echoes are closely connected with specific characteristics of the exotic compact objects, and moreover, possibly provide an access to the quantum nature of gravity. Recently, it was shown that the discontinuity in the black hole metric substantially modifies the asymptotical behavior of quasinormal frequencies. In the present study, we proceed further and argue that a discontinuity planted into the metric furnishes an alternative mechanism for the black hole echoes. Physically, the latter may correspond to an uneven matter distribution inside the surrounding halo. To demonstrate the results, we first numerically investigate the temporal evolution of the scalar perturbations around a black hole that possesses a nonsmooth effective potential. It is shown that the phenomenon persists even though the discontinuity can be located further away from the horizon with rather insignificant strength. Besides, we show that the echoes in the present model can be derived analytically based on the modified pole structure of the associated Green function. The asymptotical properties of the quasinormal mode spectrum and the echoes are found to be closely connected, as both features can be attributed to the same origin. In particular, the period of the echoes in the time domain $T$ is shown to be related to the asymptotic spacing between successive poles along the real axis in the frequency domain $\Delta(\Re\omega)$, by a simple relation $\lim\limits_{\Re\omega\to+\infty}\Delta(\Re\omega) = 2\pi/T$. Moreover, we discuss possible distinguishment between different echo mechanisms. The potential astrophysical implications of the present findings are also addressed., Comment: 14 pages and 9 figures

In this paper, the $P-V$ criticality and Joule-Thomson Expansion of Hayward-AdS black holes in 4D Einstein-Gauss-Bonnet gravity are studied in the extended phase space. We find the black hole always exhibits a phase transition similar to that of the Van der Waals system for any arbitrary positive parameters $\alpha$ and $g$. We also study the dependence of $\alpha$ and $g$ on the inversion curves and plot the inversion and isenthalpic curves in the $T-P$ plane, which can determine the cooling-heating regions., Comment: arXiv admin note: text overlap with arXiv:2009.03096

Cuspy shadow was first reported for hairy rotating black holes, whose metrics deviate significantly from the Kerr one. The non-smooth edge of the shadow is attributed to a transition between different branches of unstable but bounded orbits, known as the fundamental photon orbits, which end up at the light rings. In searching for a minimal theoretical setup to reproduce such a salient feature, in this work, we devise a toy model with axisymmetry, a slowly rotating Kerr black hole enveloped by a thin slowly rotating dark matter shell. Despite its simplicity, we show rich structures regarding fundamental photon orbits explicitly in such a system. We observe two disconnected branches of unstable spherical photon orbits, and the jump between them gives rise to a pair of cusps in the resultant black hole shadow. Besides the cuspy shadow, we explore other intriguing phenomena when the Maxwell construction cannot be established. We find that it is possible to have an incomplete arc of Einstein rings and a "fractured" shadow. The potential astrophysical significance of the corresponding findings is addressed., Comment: 15 pages, 3 figures

It was pointed out that the black hole quasinormal modes resulting from a piecewise approximate potential are drastically distinct from those pertaining to the original black hole metric. In particular, instead of lining up parallel to the imaginary axis, the spectrum is found to stretch out along the real axis. In this work, we prove that if there is a single discontinuity in the effective potential, no matter how insignificant it is, the asymptotical behavior of the quasinormal modes will be appreciably modified. Besides showing numerical evidence, we give analytical derivations to support the above assertion even when the discontinuity is located significantly further away from the maximum of the potential and/or the size of the step is arbitrarily small. Moreover, we discuss the astrophysical significance of the potential implications in terms of the present findings., Comment: 25 pages, 4 figures, and 1 table, typo correction

In this paper, we study the quasinormal modes(QNMs) of massless scalar perturbations to probe the Van der Waals like small and large black holes(SBH/LBH) phase transition of (charged) AdS black holes in the 4-dimensional Einstein Gauss-Bonnet gravity. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNMs frequencies change drastically different in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe of the thermodynamic properties in black holes.

In the study of perturbations around black hole configurations, whether an external source can influence the perturbation behavior is an interesting topic to investigate. When the source acts as an initial pulse, it is intuitively acceptable that the existing quasinormal frequencies will remain unchanged. However, the confirmation of such an intuition is not trivial for the rotating black hole, since the eigenvalues in the radial and angular parts of the master equations are coupled. We show that for the rotating black holes, a moderate source term in the master equation in the Laplace s-domain does not modify the quasinormal modes. Furthermore, we generalize our discussions to the case where the external source serves as a driving force. Different from an initial pulse, an external source may further drive the system to experience new perturbation modes. To be specific, novel dissipative singularities might be brought into existence and enrich the pole structure. This is a physically relevant scenario, due to its possible implication in modified gravity. Our arguments are based on exploring the pole structure of the solution in the Laplace s-domain with the presence of the external source. The analytical analyses are verified numerically by solving the inhomogeneous differential equation and extracting the dominant complex frequencies by employing the Prony method., Comment: 17 pages, 3 figures, accepted for publication on EPJC

We study the variation of the massive black hole in both normal and extended thermodynamic phase spaces via two methods. The first method includes a charged particle absorbed by the black hole, while the second method includes a shell of dust falling into the black hole. Using the former method, the first and second laws of thermodynamics are always satisfied in the normal phase space, while in the extended phase space, the first law of thermodynamics is also satisfied, but the validity of the second law of thermodynamics depends on the model parameters. Applying the latter method, the first and second laws of thermodynamics are both valid. We argue that the possible reason for the violation of the second law of thermodynamics via the former method may be attributed to the assumption that the change of internal energy of the black hole is equal to the energy of the particle. Finally, we show that the event horizon always exists to guarantee the validity of the weak cosmic censorship in both phase spaces, which means that the violation of the second law of thermodynamics under the assumption does not affect the weak cosmic censorship conjecture. This further supports our argument that the assumption in the first method may be the reason for the violation of the law and it requires deeper treatment., Comment: 26 pages, 5 figures