arXiv subjects

Jozef Skakala

Publications and source records attributed to Jozef Skakala.

26 records · Page 2Linked to original sources

arXiv2010

Generic master equations for quasi-normal frequencies

Generic master equations governing the highly-damped quasi-normal frequencies [QNFs] of one-horizon, two-horizon, and even three-horizon spacetimes can be obtained through either semi-analytic or monodromy techniques. While many technical details differ, both between the semi-analytic and monodromy approaches, and quite often among various authors seeking to apply the monodromy technique, there is nevertheless widespread agreement regarding the the general form of the QNF master equations. Within this class of generic master equations we can establish some rather general results, relating the existence of "families" of QNFs of the form omega_{a,n} = (offset)_a + i n (gap) to the question of whether or not certain ratios of parameters are rational or irrational.

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arXiv2010

Quasi-normal frequencies: Semi-analytic results for highly damped modes

Black hole highly-damped quasi-normal frequencies (QNFs) are very often of the form (offset)} + i n (gap). We have investigated the genericity of this phenomenon for the Schwarzschild--deSitter (SdS) black hole by considering a model potential that is piecewise Eckart (piecewise Poeschl-Teller), and developing an analytic ``quantization condition'' for the highly-damped quasi-normal frequencies. We find that the (offset) + i n(gap) behaviour is common but not universal, with the controlling feature being whether or not the ratio of the surface gravities is a rational number. We furthermore observed that the relation between rational ratios of surface gravities and periodicity of QNFs is very generic, and also occurs within different analytic approaches applied to various types of black hole spacetimes. These observations are of direct relevance to any physical situation where highly-damped quasi-normal modes are important.

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arXiv2010

Semi-analytic results for quasi-normal frequencies

The last decade has seen considerable interest in the quasi-normal frequencies [QNFs] of black holes (and even wormholes), both asymptotically flat and with cosmological horizons. There is wide agreement that the QNFs are often of the form omega_n = (offset) + i n (gap), though some authors have encountered situations where this behaviour seems to fail. To get a better understanding of the general situation we consider a semi-analytic model based on a piecewise Eckart (Poeschl-Teller) potential, allowing for different heights and different rates of exponential falloff in the two asymptotic directions. This model is sufficiently general to capture and display key features of the black hole QNFs while simultaneously being analytically tractable, at least for asymptotically large imaginary parts of the QNFs. We shall derive an appropriate "quantization condition" for the asymptotic QNFs, and extract as much analytic information as possible. In particular, we shall explicitly verify that the (offset)+ i n (gap) behaviour is common but not universal, with this behaviour failing unless the ratio of rates of exponential falloff on the two sides of the potential is a rational number. (This is "common but not universal" in the sense that the rational numbers are dense in the reals.) We argue that this behaviour is likely to persist for black holes with cosmological horizons.

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arXiv2010

Highly-damped quasi-normal frequencies for piecewise Eckart potentials

Highly-damped quasi-normal frequencies are very often of the form omega_n = (offset) + i n (gap). We investigate the genericity of this phenomenon by considering a model potential that is piecewise Eckart (piecewise Poeschl-Teller), and developing an analytic "quantization condition" for the highly-damped quasi-normal frequencies. We find that this omega_n = (offset) + i n (gap) behaviour is generic but not universal, with the controlling feature being whether or not the ratio of the rates of exponential falloff in the two asymptotic directions is a rational number. These observations are of direct relevance to any physical situation where highly-damped quasi-normal modes (damped modes) are important --- in particular (but not limited to) to black hole physics, both theoretical and observational.

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arXiv2010

Bi-metric pseudo-Finslerian spacetimes

Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. Because physicists need to use pseudo-Finsler structures to describe propagation}of signals, there will be nonzero null vectors in both the tangent and cotangent spaces --- this causes significant problems in that many of the mathematical results normally obtained for "usual" (Euclidean signature) Finsler structures either do not apply, or require significant modifications to their formulation and/or proof. We shall first provide a few basic definitions, explicitly demonstrating the interpretation of bi-metric theories in terms of pseudo-Finsler norms. We shall then discuss the tricky issues that arise when trying to construct an appropriate pseudo-Finsler metric appropriate to bi-metric spacetimes. Whereas in Euclidian signature the construction of the Finsler metric typically fails at the zero vector, in Lorentzian signature the Finsler metric is typically ill-defined on the entire null cone.

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arXiv2010

Pseudo-Finslerian spacetimes and multi-refringence

It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo-Finslerian spacetimes (an extension of pseudo-Riemannian spacetime). What is less commonly appreciated is that there are two separate and quite disjoint pseudo-Finsler structures for the two photon polarizations, and further, that there are separate tangent-space pseudo-Finsler structures defined by the group velocity and co-tangent-space pseudo-co-Finsler structures defined by the phase velocity. The inter-connections between these four separate pseudo-Finsler structures are rather subtle. One particular source of technical difficulty is the fact that because physicists need to use pseudo-Finsler structures to describe propagation of signals, there will be nonzero null vectors in both the tangent and cotangent spaces -- this causes significant problems in that many of the mathematical results normally obtained for "usual'' (Euclidean signature) Finsler structures either do not apply, or require significant modifications to their formulation. We shall first provide a few basic definitions, and then present a tutorial outline of the relevant physics of birefringent optics, explicitly demonstrating the interpretation in terms of pseudo-Finsler spacetimes. We shall then discuss the tricky issues that arise when trying to inter-relate the various pseudo-Finsler structures we encounter, and finish by connecting these technical questions (which of course arise in what is a physically a very well-understood situation) back to ongoing research into possible extensions and modifications of general relativity.

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arXiv2009

Birkhoff-like theorem for rotating stars in (2+1) dimensions

Consider a rotating and possibly pulsating "star" in (2+1) dimensions. If the star is axially symmetric, then in the vacuum region surrounding the star, (a region that we assume at most contains a cosmological constant), the Einstein equations imply that under physically plausible conditions the geometry is in fact stationary. Furthermore, the geometry external to the star is then uniquely guaranteed to be the (2+1) dimensional analogue of the Kerr-de Sitter spacetime, the BTZ geometry. This Birkhoff-like theorem is very special to (2+1) dimensions, and fails in (3+1) dimensions. Effectively, this is a "no hair" theorem for (2+1) dimensional axially symmetric stars: the exterior geometry is completely specified by the mass, angular momentum, and cosmological constant.

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arXiv2008

Birefringence in pseudo-Finsler spacetimes

Based on the analogue spacetime programme, and many other ideas currently mooted in "quantum gravity", there is considerable ongoing speculation that the usual pseudo-Riemannian (Lorentzian) manifolds of general relativity might eventually be modified at short distances. Two specific modifications that are often advocated are the adoption of Finsler geometries (or more specifically, pseudo-Finsler spacetimes) and the possibility of birefringence (or more generally, multi-refringence). We have investigated the possibility of whether it is possible to usefully and cleanly deal with these two possibilities simultaneously. That is, given two (or more) "signal cones": Is it possible to naturally and intuitively construct a "unified" pseudo-Finsler spacetime such that the pseudo-Finsler metric is null on these "signal cones", but has no other zeros or singularities? Our results are much less encouraging than we had originally hoped, and suggest that while pseudo-Finsler spacetimes are certainly useful constructs, it is physically more appropriate to think of physics as taking place in a single topological manifold that carries several distinct pseudo-Finsler metrics, one for each polarization mode.

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