arXiv subjects

Kostas Tzanavaris

Publications and source records attributed to Kostas Tzanavaris.

7 recordsLinked to original sources

arXiv2026

Superdiffusion at the Galactic Centre

Tracking S-star cluster orbits around Sgr A* calibrates orbital transport models for space-borne gravitational wave detectors. Standard kinetic theories model this cluster via local Fokker-Planck equations, which predict that general relativistic precession halts angular momentum diffusion at the Schwarzschild barrier. Because inverse-square gravitational encounters generate a Holtsmark torque distribution with infinite variance, resonant relaxation operates as a space-fractional process governed by non-local Lévy flights. We simulate this superdiffusive continuous-time random walk using a Markov chain initialized with empirical S-star orbits, including the recently observd S301. Integro-differential fractional operators allow trajectories to cross regions of quenched local diffusion without density buildup at the barrier. Non-equilibrium regimes yield immediate linear flux growth, while secular tidal heating at periastron inflates stellar radii to shift disruption boundaries. Regularized backward integration of the fractional transport equation traces current phase space configurations back to initial deposition states, matching the energy requirements of the \emph{Fermi} bubbles. Relativistic precession does not suppress mass-ratio inspiral rates, which provides a model for event topologies in target galactic nuclei.

astro-ph.GA↗

arXiv2026

The free boundary problem in general relativity

We study the action principle for space-times whose boundary is singular. We suggest that it is natural to treat the singularity as a {\it free} boundary, where the variation is unconstrained. Demanding that the action is stationary under such free variations then implies certain (on-shell) boundary conditions at the singularity. We derive these boundary conditions for the case of Einstein gravity coupled to matter and show that, when applied to an initial spacelike singularity, they exclude Kasner-like or BKL space-times, but admit conformally regular space-times (including FLRW models) sourced by fluids satisfying $0 \leq P < ρ$. For standard hot big bang FLRW cosmologies, the admissible linear (scalar, vector, tensor) perturbations satisfy reflecting boundary conditions at the bang, in agreement with large-scale cosmological observations.

gr-qc↗

arXiv2026

Perfect fluids revisited: an action principle approach

We revisit the variational principle for relativistic perfect fluids in a manifestly covariant formulation based on differential forms, with particular attention to the boundary data required for a well-posed action principle. For timelike flows, the formalism is largely a geometric reformulation of the Schutz action principle for perfect fluids. We then analyse the extension of the same variational principle to null flows. In that case, the system is not a generic perfect fluid: the equations of motion force the enthalpy density to vanish, $ρ+P=0$. The resulting stress-energy tensor decomposes into a vacuum energy-like term with variable pressure and a null dust contribution. This shows that the obstruction to the naive fluid extension is dynamical rather than kinematical. Since the matter action is formulated independently of any gravitational field equations, the construction can be generalised to first-order or non-metric theories of gravity.

gr-qc↗

arXiv2025

Popcorn EMRIs: Transient Gravitational Wave Signals and Their Analysis in Schwartz Space

We investigate extreme-mass ratio inspirals (EMRIs) with orbital periods exceeding the observational timescale of mHz gravitational wave observatories. In their early, highly eccentric phases, these systems generate transient gravitational wave bursts during pericentre passages, separated by long quiescent intervals; we designate these signals ``popcorn EMRIs.'' We utilize a steady-state analytical model based on the continuity equation in phase space to estimate the population in a Milky Way-like galaxy. The normalization of this model is linked to the solution of the Fokker-Planck equation describing stellar relaxation. Adopting a conservative one-year observation baseline ($P>1$ year), we estimate the steady-state population of popcorn EMRIs. We forecast an observable burst rate of 5 to 44 events per year. The low duty cycle ($\sim 10^{-4}$) confirms their manifestation as isolated transients. Individual bursts from the Galactic Centre exhibit high detectability. Analyzing these intrinsically transient signals demands a rigorous mathematical framework, as standard windowing techniques distort burst morphology. We establish an analytical foundation using standard smoothing techniques commonly used in real analysis. This yields the mathematically correct definition for the Fourier transform of transient signals, justifying the use of the direct Fourier transform without ad hoc windowing and ensuring the integrity of spectral analysis.

gr-qc↗

arXiv2025

Black Mirrors: CPT-Symmetric Alternatives to Black Holes

Einstein's equations imply that a gravitationally collapsed object forms an event horizon. But what lies on the other side of this horizon? In this paper, we question the reality of the conventional solution (the black hole), and point out another, topologically distinct solution: the black mirror. In the black hole solution, the horizon connects the exterior metric to an interior metric which contains a curvature singularity. In the black mirror, the horizon instead connects the exterior metric to its own CPT mirror image, yielding a solution with smooth, bounded curvature. We give the general stationary (charged, rotating) black mirror solution explicitly, and also describe the general black mirror formed by gravitational collapse. The black mirror is the relevant stationary point when the quantum path integral is equipped with suitably CPT-symmetric boundary conditions, that we propose. It appears to avoid many vexing puzzles which plague the conventional black hole.

hep-th↗

arXiv2024

Mono- and oligochromatic extreme-mass ratio inspirals

The gravitational capture of a stellar-mass object by a supermassive black hole represents a unique probe of warped spacetime. The small object, typically a stellar-mass black hole, describes a very large number of cycles before crossing the event horizon. Because of the mass difference, we call these captures extreme-mass ratio inspirals (EMRIs). Their merger event rate at the Galactic Centre is negligible, but the amount of time spent in the early inspiral is not. Early EMRIs (E-EMRIs) spend hundreds of thousands of years in band during this phase. At very early stages, the peak of the frequency will not change during an observational time. At later stages, it will change a bit and finally the EMRI explores a wide range of them when it is close to merger. We distinguish between "monocromatic" E-EMRIs, which do not change their (peak) frequency, oligochromatic E-EMRIs, which explore a short range and polychromatic ones, the EMRIs which have been discussed so far in the literature. We derive the number of E-EMRIs at the Galactic Centre, and their signal-to-noise ratios (SNR) and perform a study of parameter extraction. We show that parameters such as the spin and the mass can be extracted with an error which can be as small as $10^{-11}$ and $10^{-5}\,M_{\odot}$. There are between hundreds and thousands of E-EMRIs in their monochromatic stage at the GC, and tens in their oligochromatic phase. The SNR ranges from a minimum of $10$ (larger likelihood) to a maximum of $10^6$ (smaller likelihood). Moreover, we derive the contribution signal corresponding to the incoherent sum of continuous with two representatives masses; $10\,M_{\odot}$ and $40\,M_{\odot}$ and show that their curves will cover a significant part of LISA's sensitivity curve. Depending on their level of circularisation, they might be detected as individual sources or form a foreground population.

astro-ph.CO↗

arXiv2022

Curvature conditions for spatial isotropy

In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalised) Robertson-Walker space-time is important. In particular, it is a requirement for the development of initial data to reproduce or approximate the standard cosmological model. Usually these conditions involve the Einstein field equations, which change if one considers alternative theories of gravity or if the coupling matter fields change. Therefore, the derivation of conditions which do not depend on the field equations is an advantage. In this work we present a geometric derivation of such a condition. We require the existence of a unit vector field to distinguish at each point of space two (non-equal) sectional curvatures. This is equivalent for the Riemann tensor to adopt a specific form. Our geometrical approach yields a local isometry between the space and a Robertson-Walker space of the same dimension, curvature and metric tensor sign (the dimension of the largest subspace on which the metric tensor is negative definite). Remarkably, if the space is simply-connected, the isometry is global. Our result generalize to a class of spaces of non-constant curvature the theorem that spaces of the same constant curvature, dimension and metric tensor sign must be locally isometric. Because we do not make any assumptions regarding field equations, matter fields or metric tensor sign, one can readily use this result to study cosmological models within alternative theories of gravity or with different matter fields.

math.DG↗