The effects of fluctuating initial conditions are studied in the context of relativistic heavy ion collisions where a rapidly evolving system is formed. Two-particle correlation analysis is applied to events generated with the NEXSPHERIO hydrodynamic code, starting with fluctuating nonsmooth initial conditions (IC). The results show that the nonsmoothness in the IC survives the hydroevolution and can be seen as topological features of the angular correlation function of the particles emerging from the evolving system. A long range correlation is observed in the longitudinal direction and in the azimuthal direction a double peak structure is observed in the opposite direction to the trigger particle. This analysis provides clear evidence that these are signatures of the combined effect of tubular structures present in the IC and the proceeding collective dynamics of the hot and dense medium.

In this work, we study the quasinormal modes of Schwarzschild and Schwarzschild (Anti-) de Sitter black holes by a matrix method. The proposed method involves discretizing the master field equation and expressing it in the form of a homogeneous system of linear algebraic equations. The resulting homogeneous matrix equation furnishes a non-standard eigenvalue problem, which can then be solved numerically to obtain the quasinormal frequencies. A key feature of the present approach is that the discretization of the wave function and its derivatives is made to be independent of any specific metric through coordinate transformation. In many cases, it can be carried out beforehand, which in turn improves the efficiency and facilitates the numerical implementation. We also analyze the precision and efficiency of the present method as well as compare the results to those obtained by different approaches.

We show the effects of the granular structure of the initial conditions of a hydrodynamic description of high-energy nucleus-nucleus collisions on some observables, especially on the elliptic-flow parameter $v_2$. Such a structure enhances production of isotropically distributed high-$p_T$ particles, making $v_2$ smaller there. Also, it reduces $v_2$ in the forward and backward regions where the global matter density is smaller and, therefore, where such effects become more efficacious.

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 asymptotic 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.

Gravitational wave echoes from 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 $\mathrm{\Delta }(\Re \omega )$ by a simple relation ${\lim }_{\Re \omega \to +\infty }\mathrm{\Delta }(\Re \omega )=2\pi /T$. Moreover, we discuss possible distinguishment between different echo mechanisms. The potential astrophysical implications of the present findings are also addressed.