Διεπιφάνειες τοπολογικού μονωτή με κύματα πυκνότητας φορτίου, σπιν και υπεραγώγιμες καταστάσεις τάξης

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Μικροσυστήματα και Νανοδιατάξεις

Quasinormal modes and Strong Cosmic Censorship

The fate of Cauchy horizons, such as those found inside charged black holes, is intrinsically connected to the decay of small perturbations exterior to the event horizon. As such, the validity of the strong cosmic censorship (SCC) conjecture is tied to how effectively the exterior damps fluctuations. Here, we study massless scalar fields in the exterior of Reissner--Nordstrom--de Sitter black holes. Their decay rates are governed by quasinormal modes of the black hole. We identify three families of modes in these spacetimes: one directly linked to the photon sphere, well described by standard WKB-type tools; another family whose existence and timescale is closely related to the de Sitter horizon. Finally, a third family which dominates for near-extremally-charged black holes and which is also present in asymptotically flat spacetimes. The last two families of modes seem to have gone unnoticed in the literature. We give a detailed description of linear scalar perturbations of such black holes, and conjecture that SCC is violated in the near extremal regime.Comment: To appear in Physical Review Letters, as an Editors' Suggestio

Charged Fermions and Strong Cosmic Censorship

It was recently shown that the Strong Cosmic Censorship conjecture might be violated for near-extremally-charged black holes in de Sitter space. Here, we extend our study to charged fermionic fields in the exterior of Reissner-Nordstr\"{o}m-de Sitter black holes. We identify three families of modes; one related to the photon sphere, a second related to the de Sitter horizon and a third which dominates near extremality. We show that for near-extremally-charged black holes there is a critical fermionic charge below which Strong Cosmic Censorship may potentially be violated. Surprisingly enough, as one approaches extremality even more, violation of Strong Cosmic Censorship may occur even beyond the critical fermionic charge.Comment: 10 pages, 6 figures, matches version to appear in Physics Letters

Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum

Black-hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational-wave spectroscopy, thus it is critical to understand if the quasinormal mode spectrum itself is affected by astrophysical environments, quantum corrections, and other generic modifications. In this chapter, we will review the black-hole spectroscopy program and its challenges regarding quasinormal mode detection, the overtone status and the recent evidence that supports the existence of nonlinearities in the spectrum of black holes. We will then discuss a newly introduced non-modal tool in black-hole physics, namely the pseudospectrum; a mathematical notion that can shed light on the spectral stability of quasinormal modes, and discuss its novel applications in black holes and exotic horizonless compact objects. We will show that quasinormal modes generically suffer from spectral instabilities, explore how such phenomena can further affect black-hole spectroscopy, and discuss potential ringdown imprints and waveform stability issues in current and future gravitational-wave detectors.Comment: 35 pages, 24 figures, Topical review presented on the 11th Aegean Summer School, Syros, Greece, References adde

Slowly-rotating compact objects: the nonintegrability of Hartle-Thorne particle geodesics

X-ray astronomy provides information regarding the electromagnetic emission of active galactic nuclei and X-ray binaries. These events provide details regarding the astrophysical environment of black holes and stars, and help us understand gamma-ray bursts. They produce estimates for the maximum mass of neutron stars and eventually will contribute to the discovery of their equation of state. Thus, it is crucial to study these configurations to increase the yield of X-ray astronomy when combined with multimessenger gravitational-wave astrophysics and black hole shadows. Unfortunately, an exact solution of the field equations does not exist for neutron stars. Nevertheless, there exist a variety of approximate compact objects that may characterize massive or neutron stars. The most studied approximation is the Hartle-Thorne metric that represents slowly-rotating compact objects, like massive stars, white dwarfs and neutron stars. Recent investigations of photon orbits and shadows of such metric revealed that it exhibits chaos close to resonances. Here, we thoroughly investigate particle orbits around the Hartle-Thorne spacetime. We perform an exhaustive analysis of bound motion, by varying all parameters involved in the system. We demonstrate that chaotic regions, known as Birkhoff islands, form around resonances, where the ratio of the radial and polar frequency of geodesics, known as the rotation number, is shared throughout the island. This leads to the formation of plateaus in rotation curves during the most prominent $2/3$ resonance, which designate nonintegrability. We measure their width and show how each parameter affects it. The nonintegrability of Hartle-Thorne metric may affect quasiperiodic oscillations of low-mass X-ray binaries, when chaos is taken into account, and improve estimates of mass, angular momentum and multipole moments of astrophysical compact objects.Comment: 12 pages, 5 figure

Quasinormal mode (in)stability and strong cosmic censorship

Recent studies have shown that quasinormal modes suffer from spectral instabilities, a frailty of black holes that leads to disproportional migration of their spectra in the complex plane when black-hole effective potentials are modified by minuscule perturbations. Similar results have been found with the mathematical notion of the pseudospectrum which was recently introduced in gravitational physics. Environmental effects, such as the addition of a thin accretion disk or a matter shell, lead to a secondary bump that appears in the effective potential of black hole perturbations. Regardless of the environment's small contribution to the effective potential, its presence can completely destabilize the fundamental quasinormal mode and may potentially affect black hole spectroscopy. Here, we perform a comprehensive analysis of such phenomenon for Schwarzschild, Reissner-Nordstr\"om, Schwarzschild-de Sitter, and Reissner-Nordstr\"om-de Sitter black holes by considering the potential for a test scalar field with the addition of a tiny bump sufficiently away from the photon sphere. We find a qualitatively similar destabilization pattern for photon sphere, complex, scalar quasinormal modes in all cases, and a surprising spectral stability for dominant scalar, purely imaginary, de Sitter and near-extremal modes that belong to different families of the spectrum. For Reissner-Nordstr\"om-de Sitter black holes, we re-evaluate the validity of the strong cosmic censorship and find that the addition of a realistic bump in the effective potential cannot prevent its violation due to a combination of the spectral stability of dominant de Sitter and near-extremal modes for small cosmological constants and an ineffective migration of the photon sphere modes that dominate the late-time ringdown signal for sufficiently large cosmological constants.Comment: 16 pages, 12 figure

Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers

Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical objects lurking in galactic centers are black holes. Sgr A*, one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. The well-established presence of accretion disks and astrophysical environments around supermassive objects can deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that traverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.Comment: 16 pages, 7 figures, minor revision, accepted for publication in General Relativity and Gravitation, abstract minimally trimmed due to arxiv limitation