arXiv subjects

Lior M. Burko

Publications and source records attributed to Lior M. Burko.

At least 19 recordsLinked to original sources

arXiv2026

Quantitative Black Hole Imaging Laboratory with the Black Hole Vision App: I. Schwarzschild Spacetime

This paper utilizes the {\it Black Hole Vision} smartphone application to catalyze a pedagogical shift in General Relativity education through the quantitative analysis of simulated black hole imaging. Presented here for the Schwarzschild spacetime, the investigation is designed with a hierarchical modularity suitable for undergraduate students, with an expanded version intended for graduate courses in General Relativity or Relativistic Astrophysics. By transforming the mobile device into an educational relativistic imaging tool, we triangulate the simulated Schwarzschild mass through independent probes and characterize anisotropic coordinate transformations via a Jacobian map. Global numerical consistency is investigated through integrated coordinate length, while the exponential instability of nearly bound orbits is quantified through a measurement of the simulated Lyapunov exponent. Finally, symmetry is constrained through a sub-pixel constraint on eccentricity in the simulated spacetime. By integrating this statistical framework, the paper enables students to explore the distinction between physical signatures and instrumental noise using established metrological protocols.

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arXiv2023

Aretakis Hair for Extreme Kerr Black Holes with Axisymmetric Scalar Perturbations

We study the evolution of axially-symmetric scalar field perturbations on an extreme Kerr spacetime for initial data with multipole moments $\ell^{\prime}$ higher than the least radiative mode, and we measure modes $\ell$ -- and for the first time also horizon charges -- that are excited by mode coupling interactions. We then find the Ori-Sela prefactors, a certain quantity that can be evaluated at finite distances and the Aretakis constant along the event horizon of the extreme Kerr black hole for a sequence of initial data preparations that differ only by their distance from the event horizon. We find that for initial data in the near field there is a linear relationship of the Aretakis constant and the Ori-Sela prefactor. For initial data farther than these the linear relationship is not universal, and we propose that stronger numerical simulations would be needed to regain linearity. The linear relationship suggests that the Aretakis charge along the event horizon can be measured at a finite distance, thereby extending this type of violation of the no-hair theorems from the least radiative axisymmetric mode also to situations that involve mode coupling.

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arXiv2022

New Horizons for Fundamental Physics with LISA

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.

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arXiv2020

Climbing up the memory staircase: Equatorial zoom-whirl orbits

The nonlinear, or null gravitational memory effect for zoom-whirl orbits around fast spinning Kerr black holes for extreme mass ratio systems has a staircase structure. The latter is characterized by a periodic fast increase in the memory during the whirl phases of the orbit, and near constant levels when the orbit is near apoapsis. We study the contribution of different spherical harmonic modes to this effect, and discuss the relative importance thereof. Because the hereditary memory effect increases in magnitude linearly in the number of periapsis passages on a dynamical time scale, while the oscillatory parent gravitational waves are sourced by an orbit that evolves on a much longer radiation reaction time scale, the magnitude of the former relative to the latter increases with time. We also consider orphan memory and the memory effect for extreme mass ratio inspirals. We then discuss the prospect of detection with the Laser Interferometer Space Antenna (LISA).

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arXiv2020

Scalar and gravitational hair for extreme Kerr black holes

For scalar perturbations of an extreme Reissner-Nordstr{\" o}m black hole we show numerically that the Ori pre-factor equals the Aretakis conserved charge. We demonstrate a linear relation of a generalized Ori pre-factor -- a certain expression obtained from the late-time expansion or the perturbation field at finite distances -- and the Aretakis conserved charge for a family of scalar or gravitational perturbations of an extreme Kerr black hole, whose members vary only in the radial location of the center of the initial packet. We infer that it can be established that there is an Aretakis conserved charge for scalar or gravitational perturbations of extreme Kerr black holes. This conclusion, in addition to the calculation of the Aretakis charge, can be made from measurements at a finite distance: Extreme Kerr black holes have gravitational hair that can be measured at finite distances. This gravitational hair can in principle be detected by gravitational-wave detectors.

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arXiv2019

(Transient) Scalar Hair for (Nearly) Extreme Black Holes

It has been shown recently that extreme Reissner-Nordström black holes perturbed by a minimally coupled, free, massless scalar field have permanent scalar hair. The hair - a conserved charge calculated at the black hole's event horizon - can be measured by a certain expression at future null infinity: the latter approaches the hair inversely in time. We generalize this newly discovered hair also for extreme Kerr black holes. We study the behavior of nearly extreme black hole hair and its measurement at future null infinity as a transient phenomenon. For nearly extreme black holes the measurement at future null infinity of the length of the newly grown hair decreases quadratically in time at intermediate times until its length becomes short and the rate at which the length shortens further slows down. Eventually, the nearly extreme BH becomes bald again like non-extreme BHs.

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arXiv2019

Repeated Ringing of the Black Hole's Bell: Quasi-Normal Bursts from Highly Eccentric, Extreme Mass-Ratio Binaries

Recent studies of scalar and gravitational waveforms from high-eccentricity, extreme mass-ratio black hole binaries show the presence of quasi-normal bursts (QNB) -- lingering high frequency decaying oscillations (also known as ``wiggles'') -- soon after each periapsis passage. One puzzle associated with these QNB is that in the case of a nearly-extreme rotating central black hole the frequency of the QNB has been found to be in a range which is lower than the corresponding range of relevant quasi-normal modes. We reproduce these results using a different approach and perform a detailed analysis to find evidence for the resolution of the puzzle and for the origin of the QNB. We find that the QNB frequency as measured at future null infinity evolves in (retarded) time and approaches the dominant quasi-normal frequency exponentially in time. We also show that the QNB amplitude decays inversely in (retarded) time. We discuss the time dependence of both the QNB waveform frequency and its amplitude and argue that this behavior arises as a result of the excitation of many quasi-normal overtones and the summation thereof.

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arXiv2019

Two-dimensional collisions and conservation of momentum

Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the problem is to find the final velocities. In 1D there are therefore two unknown variables. One can write the equation for conservation of momentum, and either the equation for conservation of energy for the perfectly elastic case, or the expression for the coefficient of restitution (COR) otherwise. Thus, one has two equations for two unknowns, and one may solve the problem fully. An issue arises, however, in two-dimensional (2D) collisions: There are four unknown variables (two components of the final velocity of each object), but now there appear to be only three equations: two components of the equation of conservation of momentum, and the energy condition. The problem may appear therefore to be underdetermined. If this problem were in principle an underdetermined one, one would fail in predicting the outcome of the collision experiment. We describe how one may assign students an appropriate lab exercise and problems for an interesting class of 2D collisions for which one can determine uniquely the outcome of the collision.

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arXiv2019

The Marolf-Ori singularity inside fast spinning black holes

The effective shock wave singularity at the outgoing leg of the inner horizon of a linearly perturbed fast spinning black hole is studied numerically for either scalar field, or vacuum, gravitational perturbations. We demonstrate the occurrence of the Marolf-Ori singularity, including changes of order unity in the scalar field $ϕ$ for the scalar field model, and in the Weyl scalars $ψ_0$ and $ψ_4$ (rescaled appropriately by the horizon function $Δ$) and the Kretschmann curvature scalar $K$ for the vacuum, gravitational perturbations model for both null and timelike geodesic observers. We quantify the shock sharpening effect and show that in all cases its rate agrees with expectations.

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arXiv2018

Physical objects approaching the Cauchy horizon of a rapidly rotating Kerr black hole

We solve the 2+1-dimensional Teukolsky equation numerically for the Weyl scalars $ψ_0$ and $ψ_4$ along a time-like geodesic approaching the Cauchy horizon of a rapidly rotating perturbed Kerr black hole. We find that both the amplitude and frequency of the Weyl scalars agree with the results of linear perturbation analysis. We then model a physical object by a simple damped harmonic oscillator, which is driven by an external force that mimics the tidal force experienced by the infalling object. We use this model to find the total deformation of the object at the Cauchy horizon, and the resonant effect when the driving force's frequency matches the internal frequency of the oscillator that models the object.

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arXiv2018

Gravitational Wave Detection in the Introductory Lab

Great physics breakthroughs are rarely included in the introductory physics or astronomy course. General relativity and binary black hole coalescence are no different, and can be included in the introductory course only in a very limited sense. However, we can design activities that directly involve the detection of GW150914, the designation of the Gravitation Wave signal detected on September 14, 2015, thereby engage the students in this exciting discovery directly. The activities naturally do not include the construction of a detector or the detection of gravitational waves. Instead, we design it to include analysis of the data from GW150914, which includes some interesting analysis activities for students of the introductory course. The same activities can be assigned either as a laboratory exercise or as a computational project for the same population of students. The analysis tools used here are simple and available to the intended student population. It does not include the sophisticated analysis tools, which was used by LIGO to carefully analyze the detected signal. However, these simple tools are sufficient to allow the student to get important results.

physics.ed-ph↗

arXiv2017

Cauchy-horizon singularity inside perturbed Kerr black holes

The Cauchy horizon inside a perturbed Kerr black hole develops an instability that transforms it into a curvature singularity. We solve for the linearized Weyl scalars $ψ_0$ and $ψ_4$ and for the curvature scalar $R_{αβγδ}R^{αβγδ}$ along outgoing null rays approaching the Cauchy horizon in the interior of perturbed Kerr black holes using the Teukolsky equation, and compare our results with those found in perturbation analysis. Our results corroborate the previous perturbation analysis result that at its early parts the Cauchy horizon evolves into a deformationally-weak, null, scalar-curvature singularity. We find excellent agreement for $ψ_0(u={\rm const},v)$, where $u,v$ are advanced and retarded times, respectively. We do find, however, that the exponential growth rate of $R_{αβγδ}R^{αβγδ}(u={\rm const},v)$ approaching the singularity is dramatically slower than that found in perturbation analysis, and that the angular frequency is in excellent agreement.

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arXiv2017

Linearized Stability of Extreme Black Holes

Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar $ψ_4$ blows up along their event horizons at very late advanced times. We show numerically, by solving the Teukolsky equation in 2+1D, that all algebraically-independent curvature scalar polynomials approach limits that exist when advanced time along the event horizon approaches infinity. Therefore, the horizons of extreme black holes are stable against linearized gravitational perturbations. We argue that the divergence of $ψ_4$ is a consequence of the choice of a fixed tetrad, and that in a suitable dynamical tetrad all Weyl scalars, including $ψ_4$, approach their background extreme Kerr values. We make similar conclusions also for the case of scalar field perturbations of extreme Kerr.

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arXiv2016

Gravitational waves from a plunge into a nearly extremal Kerr black hole

We study numerically in the time domain the linearized gravitational waves emitted from a plunge into a nearly extremal Kerr black hole by solving the inhomogeneous Teukolsky equation. We consider spinning black holes for which the specific spin angular momentum $a/M=1-ε$, and we consider values of $ε\geq 10^{-6}$. We find an effective transient behavior for the quasi-normal ringdown: the early phase of the quasi-normal ringdown is governed by a decay according to inverse time, with frequency equaling twice the black hole's horizon frequency. The smaller $ε$ the later the transition from this transient inverse time decay to exponential decay. Such sources, if exist, may be interesting potential sources for terrestrial or space borne gravitational wave observatories.

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arXiv2016

Using the case-study method in teaching college physics

The case-study teaching method has a long history (starting at least with Socrates), and wide current use in business schools, medical schools, law schools, and a variety of other disciplines. However, relatively little use is made of it in the physical sciences, specifically in physics or astronomy. The case-study method should be considered by physics faculty as part of the effort to transition the teaching of college physics from the traditional frontal-lecture format to other formats that enhance active student participation. In this paper we endeavor to interest physics instructors in the case-study method, and hope that it would also serve as a call for more instructors to produce cases that they use in their own classes and that can also be adopted by other instructors.

physics.ed-ph↗

arXiv2015

Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III: Spin-orbit coupling revisited

The first- and second-order dissipative self force and the first order conservative self force are applied together with spin-orbit coupling to the quasi-circular motion of a test mass in the spacetime of a Schwarzschild black hole, for extreme or intermediate mass ratios. The partial dephasing of the gravitational waveform (at the order that is independent of the system's mass ratio) due to the self force is compared with that of spin-orbit coupling. We find that accurate waveforms for parameter estimation need to include both effects. Specifically, we find a particular value for the spin parameter such that the spin-orbit effect cancels out the self-force effect on the waveform. Exclusion of dephasing effects that are independent of the mass ratio therefore might lead to a non-perturbative error in the estimation of the system's parameters.

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arXiv2014

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed "splitting". We discuss far-field "splitting" in the full field and near-horizon "splitting" in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the "splitting" behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field "splitting" is explained by competition between projected modes. The near-horizon "splitting" is due to excitation of lower multipole modes that back excite the multipole mode for which "splitting" is observed. In both cases "splitting" is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.

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arXiv2013

Mode coupling mechanism for late-time Kerr tails

We consider the decay rate for scalar fields in Kerr spacetime. We consider pure initial (azimuthal) multipoles $\ell'$ with respect to the class which includes Boyer-Lindquist coordinates, and focus attention on the decay rate of the multipole $\ell$. We use an iterative method proposed by Gleiser, Price, and Pullin, and identify the mode coupling mechanism through the iterations in powers of the square of the Kerr black hole's specific angular momentum that gives rise to a decay rate formula recently proposed by Zenginoğlu, Khanna, and Burko. Modes $\ell$ may be excited through different channels, each leading to its own decay rate. The asymptotic decay rate of the mode $\ell$ is the slowest of the decay rate of the various channels. In some cases, more than one channel leads to the same decay rate, and then the amplitude of the mode is the sum of the amplitudes of the partial fields generated by the individual channels. We also show that one may identify the asymptotically-dominant channel of mode excitations, and obtain approximate results for the mode of interest by studying the dominant channel. The results of the dominant channel approximation approach the full-mode results at late times, and their difference approaches zero quadratically in inverse time.

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