arXiv subjects

Miguel Zilhão

Publications and source records attributed to Miguel Zilhão.

48 records · Page 3Linked to original sources

arXiv2016

Spacetime dynamics of spinning particles - exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers," a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.

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arXiv2015

Nonlinear interactions between black holes and Proca fields

Physics beyond the Standard Model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle "forces" all forms of matter to fall in the same way, and it is therefore natural to look for imprints of these fields in regions with strong gravitational fields, such as compact stars or black holes. Here we study General Relativity minimally coupled to a massive vector field, and how black holes in this theory lose "hair". Our results indicate that black holes can sustain Proca field condensates for extremely long time-scales.

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arXiv2015

Resolving the relative influence of strong field spacetime dynamics and MHD on circumbinary disk physics

In this paper we evolve magnetized and unmagnetized circumbinary accretion disks around supermassive black hole binaries in the relativistic regime. We use a post-Newtonian expansion to construct an analytical spacetime and determine how the order of the post-Newtonian (PN) expansion affects the dynamics of the gas. We find very small differences in the late-time bulk dynamics of non-magnetized hydrodynamic evolutions between the two spacetimes down to separations of approximately $40GM/c^2$ where $M$ is the total mass of the binary. For smaller separations, the differences due to PN-order become comparable to differences caused by using initial data further from equilibrium. For magnetized gas, MHD stresses, which drives the accretion dynamics, tends to mask all higher order PN effects even at separations of $20GM/c^2$, leading to essentially the same observed electromagnetic luminosity. This implies that our calculations of the EM signal may be robust down to small binary separations. Our investigation is the first to demonstrate how the level of PN accuracy affects a circumbinary disk's evolution and informs us of the range in separation within which to trust the PN approximation for this kind of study. We also address the influence the initial conditions and binary separation have on simulation predictions.

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arXiv2014

Testing the nonlinear stability of Kerr-Newman black holes

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and charge $Q$. Evolutions are performed to scan this parameter space within the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an extremality parameter $a/a_{\rm max}$ ($a_{\rm max} \equiv \sqrt{M^2-Q^2}$) ranging from $0$ to $0.995$. These KNBHs are evolved, together with a small bar-mode perturbation, up to a time of order $120M$. Our results suggest that for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\rm max}$, a universality also apparent in previous perturbative studies in the regime of small rotation. Using as a stability criterion the absence of significant relative variations in the horizon areal radius and BH spin, we find no evidence for any developing instability.

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arXiv2014

Dynamic Fisheye Grids for Binary Black Holes Simulations

We present a new warped gridding scheme adapted to simulating gas dynamics in binary black hole spacetimes. The grid concentrates grid points in the vicinity of each black hole to resolve the smaller scale structures there, and rarefies grid points away from each black hole to keep the overall problem size at a practical level. In this respect, our system can be thought of as a "double" version of the fisheye coordinate system, used before in numerical relativity codes for evolving binary black holes. The gridding scheme is constructed as a mapping between a uniform coordinate system--in which the equations of motion are solved--to the distorted system representing the spatial locations of our grid points. Since we are motivated to eventually use this system for circumbinary disc calculations, we demonstrate how the distorted system can be constructed to asymptote to the typical spherical polar coordinate system, amenable to efficiently simulating orbiting gas flows about central objects with little numerical diffusion. We discuss its implementation in the Harm3d code, tailored to evolve the magnetohydrodynamics equations in curved spacetimes. We evaluate the performance of the system's implementation in Harm3d with a series of tests, such as the advected magnetic field loop test, magnetized Bondi accretion, and evolutions of hydrodynamic discs about a single black hole and about a binary black hole. Like we have done with Harm3d, this gridding scheme can be implemented in other unigrid codes as a (possibly) simpler alternative to adaptive mesh refinement.

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arXiv2014

Collisions of oppositely charged black holes

The first fully non-linear numerical simulations of colliding charged black holes in D=4 Einstein-Maxwell theory were recently reported arXiv:1205.1063. These collisions were performed for black holes with equal charge-to-mass ratio, for which initial data can be found in closed analytic form. Here we generalize the study of collisions of charged black holes to the case of unequal charge-to-mass ratios. We focus on oppositely charged black holes, as to maximize acceleration-dependent effects. As |Q|/M increases from 0 to 0.99, we observe that the gravitational radiation emitted increases by a factor of ~ 2.7; the electromagnetic radiation emission becomes dominant for |Q|/M >~ 0.37 and at |Q|/M=0.99 is larger, by a factor of ~ 5.8, than its gravitational counterpart. We observe that these numerical results exhibit a precise and simple scaling with the charge. Furthermore, we show that the results from the numerical simulations are qualitatively captured by a simple analytic model that computes the electromagnetic dipolar radiation and the gravitational quadrupolar radiation of two non-relativistic interacting particles in Minkowski spacetime.

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arXiv2013

An Introduction to the Einstein Toolkit

We give an introduction to the Einstein Toolkit, a mature, open-source computational infrastructure for numerical relativity based on the Cactus Framework, for the target group of new users. This toolkit is composed of several different modules, is developed by researchers from different institutions throughout the world and is in active continuous development. Documentation for the toolkit and its several modules is often scattered across different locations, a difficulty new users may at times have to struggle with. Scientific papers exist describing the toolkit and its methods in detail, but they might be overwhelming at first. With these lecture notes we hope to provide an initial overview for new users. We cover how to obtain, compile and run the toolkit, and give an overview of some of the tools and modules provided with it.

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arXiv2013

New frontiers in Numerical Relativity

The first attempts at solving a binary black hole spacetime date back to the 1960s, with the pioneering works of Hahn and Lindquist. In spite of all the computational advances and enormous efforts by several groups, the first stable, long-term evolution of the orbit and merger of two black holes was only accomplished over 40 years later, in 2005. Since then, the field of Numerical Relativity has matured, and been extensively used to explore and uncover a plethora of physical phenomena in various scenarios. In this thesis, we take this field to new frontiers by exploring its extensions to higher dimensions, non-asymptotically flat spacetimes and Einstein-Maxwell theory. We start by reviewing the usual formalism and tools, including the "3+1" decomposition, initial data construction, the BSSN evolution scheme and standard wave extraction procedures. We then present a dimensional reduction procedure that allows one to use existing numerical codes (with minor adaptations) to evolve higher-dimensional systems with enough symmetry, and show corresponding results obtained for five-dimensional head-on collisions of black holes. Finally, we show evolutions of black holes in non-asymptotically flat spacetimes, and in Einstein-Maxwell theory.

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arXiv2012

Collisions of charged black holes

We perform fully non-linear numerical simulations of charged-black-hole collisions, described by the Einstein-Maxwell equations, and contrast the results against analytic expectations. We focus on head-on collisions of non-spinning black holes, starting from rest and with the same charge to mass ratio, Q/M. The addition of charge to black holes introduces a new interesting channel of radiation and dynamics, most of which seem to be captured by Newtonian dynamics and flat-space intuition. The waveforms can be qualitatively described in terms of three stages; (i) an infall phase prior to the formation of a common apparent horizon; (ii) a nonlinear merger phase which corresponds to a peak in gravitational and electromagnetic energy; (iii) the ringdown marked by an oscillatory pattern with exponentially decaying amplitude and characteristic frequencies that are in good agreement with perturbative predictions. We observe that the amount of gravitational-wave energy generated throughout the collision decreases by about three orders of magnitude as the charge-to-mass ratio Q/M is increased from 0 to 0.98. We interpret this decrease as a consequence of the smaller accelerations present for larger values of the charge. In contrast, the ratio of energy carried by electromagnetic to gravitational radiation increases, reaching about 22% for the maximum Q/M ratio explored, which is in good agreement with analytic predictions.

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arXiv2012

Mathisson's helical motions demystified

The motion of spinning test particles in general relativity is described by Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin supplementary condition, the latter being today still an open question. The Mathisson-Pirani (MP) condition is known to lead to rather mysterious helical motions which have been deemed unphysical, and for this reason discarded. We show that these assessments are unfounded and originate from a subtle (but crucial) misconception. We discuss the kinematical explanation of the helical motions, and dynamically interpret them through the concept of hidden momentum, which has an electromagnetic analogue. We also show that, contrary to previous claims, the frequency of the helical motions coincides exactly with the zitterbewegung frequency of the Dirac equation for the electron.

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arXiv2011

Higher-dimensional puncture initial data

We calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of D dimensional vacuum gravity. The data are generated by a modification of the pseudo-spectral code presented in arXiv:gr-qc/0404056 and made available as the TwoPunctures thorn inside the Cactus computational toolkit. As examples, we exhibit convergence plots, the violation of the Hamiltonian constraint as well as the initial data for D=4,5,6,7. These initial data are the starting point to perform high energy collisions of black holes in D dimensions.

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arXiv2011

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron.

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