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The stability and other physical properties of a class of regular black holes, quasiblack holes, and other electrically charged compact objects are investigated in the present work. The compact objects are obtained by solving the…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…
In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…
I consider the initial-boundary-value-problem of nonlinear general relativistic vacuum spacetimes, which today cannot yet be evolved numerically in a satisfactory manner. Specifically, I look at gauge conditions, classifying them into gauge…
The superradiant instability of rotating black holes with negative cosmological constant is studied by numerically solving the full 3+1-dimensional Einstein equations. We find evidence for an epoch dominated by a solution with a single…
We study the existence of analogue nonstationary spherically symmetric black holes. The prime example is the acoustic model (cf. [V], [U]). We consider also a more general class of metrics that could be useful in other physical models of…
In this work we present 3D numerical relativity simulations of thick accretion disks around tilted Kerr BH. We investigate the evolution of three different initial disk models with a range of initial black hole spin magnitudes and tilt…
We have derived the criteria for thermal stability of charged rotating black holes, for horizon areas that are large relative to the Planck area (in these dimensions). In this paper, we generalized it for black holes with arbitrary hairs.…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
In this paper we explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to…
We establish a slow manifold for a fast-slow stochastic evolutionary system with anomalous diffusion, where both fast and slow components are influ- enced by white noise. Furthermore, we prove the exponential tracking property for the…
In this paper we study the stability and quasi-normal modes of scalar perturbations of black holes. The static charged black hole considered here is a solution to Born-Infeld electrodynamics coupled to gravity. We conclude that the black…
We initiate the study of dynamical instabilities of higher-dimensional black holes using the blackfold approach, focusing on asymptotically flat boosted black strings and singly-spinning black rings in $D\ge5$. We derive novel analytic…
We investigate black hole solutions with time-dependent (scalar) hair in scalar-tensor theories. Known exact solutions exist for such theories at the background level, where the metric takes on a standard GR form (e.g. Schwarzschild-de…
The effect of an accretion disk on the Blandford-Znajek process and the evolution of a black hole are discussed using a simplified system for the black hole - accretion disk in which the accretion rate is supposed to be dominated by the…
We present results from numerical solution of Einstein's equation in five dimensions describing evolution of rapidly rotating black holes. We show, for the first time, that the rapidly rotating black holes in higher dimensions are unstable…
The consistency of AI-native applications depends on the behavioral consistency of the model endpoints that power them. Traditional reliability metrics such as uptime, latency and throughput do not capture behavioral change, and an endpoint…