Bulletin of the American Physical Society
APS April Meeting 2021
Volume 66, Number 5
Saturday–Tuesday, April 17–20, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session T17: Topics in Classical General RelativityLive

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Sponsoring Units: DGRAV Chair: David Nichols, Univ. of Virginia 
Monday, April 19, 2021 3:45PM  3:57PM Live 
T17.00001: Higherorder effects in the dynamics of hierarchical triple systems. Quadrupolesquared terms Clifford Will We analyze the secular evolution of hierarchical triple systems to secondorder in the quadrupolar perturbation induced on the inner binary by the distant third body. In the Lagrange planetary equations for the evolution of the instantaneous orbital elements, secondorder effects arise from obtaining the firstorder solution for each element, consisting of a slowly varying piece and an oscillatory perturbative piece, and reinserting it to obtain a secondorder solution. After an average over the two orbital timescales to obtain longterm evolutions, these secondorder quadrupole ($Q^2$) terms would be expected to produce effects of order $R^6$, where $R$ is the ratio of the semimajor axes. However we find that the orbital average actually enhances the secondorder terms by a factor of the ratio of the two periods, $ \sim R^{3/2}$. For systems with a lowmass third body, the $Q^2$ effects are small, but for systems with a comparablemass or very massive third body, , such as a SunJupiter system orbiting a solarmass star, or a $100 \, M_\odot$ binary system orbiting a $10^6 \, M_\odot$ massive black hole, the $Q^2$ effects can completely suppress flips of the inner orbit from prograde to retrograde and back that occur in the firstorder solutions. [Preview Abstract] 
Monday, April 19, 2021 3:57PM  4:09PM Live 
T17.00002: Matching asymptotic charges between past and future null infinity in general relativity. Ibrahim Shehzad, Kartik Prabhu An important question in understanding the conservation laws that constrain classical gravitational scattering in asymptotically flat spacetimes in general relativity is the question of how the BondiMetznerSachs (BMS) asymptotic symmetries at past null infinity are related to those at future null infinity. In this presentation, I will review what is known about this “matching” of symmetries and talk about work in progress aimed at proving the matching of the full BMS group and the associated charges between past and future null infinity. [Preview Abstract] 
Monday, April 19, 2021 4:09PM  4:21PM Live 
T17.00003: Angular Momentum in Asymptotically Flat Spacetimes Arwa Elhashash, David Nichols The symmetries of asymptotically flat spacetimes in general relativity are described by the BondiMetznerSachs group (or its proposed extensions). Associated with these symmetries are conserved charges, which include the energymomentum, supermomentum, and relativistic angular momentum (or superangular momentum). Several formalisms have been used to compute the spacetime angular momentum. These angular momenta do not always agree, but the different definitions were recently summarized in a twoparameter family of angular momenta. Requiring the angular momentum to vanish in flat spacetime restricts the two parameters to be equal, but there is not as compelling a reason to fix the one remaining free parameter to a particular value. We examine the effect of this free parameter on the values of the angular momentum and superangular momentum of nonprecessing binaryblackhole mergers. We find the definitions of angular momentum differ only when these systems are radiating gravitational waves. The definitions of superangular momentum differ even after the gravitational waves pass, because of the gravitationalwave memory effect. Using numericalrelativity surrogate waveforms, we estimate these differences to be small, but of the order of the accuracy of the simulations. [Preview Abstract] 
Monday, April 19, 2021 4:21PM  4:33PM Live 
T17.00004: Spike behavior in the approach to spacetime singularities David Garfinkle, Frans Pretorius We perform numerical simulations of the approach to spacetime singularities. The simulations are done with sufficient resolution to resolve the small scale structures (known as spikes) that form in this process. We find an analytical formula for the shape of the spikes and show that the spikes in the simulations are well described by this formula. [Preview Abstract] 
Monday, April 19, 2021 4:33PM  4:45PM Live 
T17.00005: An AlmostFLRW Universe as the Averaged Geometry in Macroscopic Gravity Anish Agashe, Mustapha Ishak The dynamics of the universe are traditionally modelled by employing cosmological solutions to the Einstein field equations. In these solutions, the matter distribution is taken to be averaged over cosmological scales, and hence, the Einstein tensor needs to be averaged as well. To construct such an averaged theory of gravity, one needs a covariant averaging procedure for tensor fields. Macroscopic gravity (MG) is one such theory. It gives the macroscopic Einstein field equations where the effects due to averaging (the backreaction) are encapsulated in a correction term to the matter distribution. We find solutions to these field equations assuming that the averaged geometry of the universe is modelled by a linearly perturbed FLRW metric. We find several solutions with different assumptions on the functional form and space/time dependencies of the perturbations. These solutions lead to different effective corrections. We write the field equations of MG in linearised form to get the generalised Poisson equation and the dynamical evolution equation for the density contrast. Both these equations now have backreaction terms. It is found that, in general, the effect of averaging is intertwined with the perturbations in a nontrivial manner. That is, the solutions with inhomogeneous perturbations do not reduce to the exact FLRW solutions simply by taking the perturbations to be zero. This highlights the nonlinearity of the backreaction in MG. [Preview Abstract] 
Monday, April 19, 2021 4:45PM  4:57PM Live 
T17.00006: Generalized geodesic deviation equation Isaac Raj Waldstein, David Brown The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The ``standard" GDE assumes that nearby geodesics have a small rate of separation, which is formally treated as the same order in smallness as the separation itself. This assumption is discussed in various papers, but is not recognized in most textbooks. Relaxing the restrictive assumption that the rate of separation is small leads to the generalized geodesic deviation equation (GGDE). We explore the GGDE via the metric on a unit twosphere, by considering a fiducial geodesic and a secondary geodesic (both great circles) that cross at the poles. These geodesics are spanned by a ``connecting geodesic", whose tangent evaluated at the fiducial geodesic defines the separation vector. The second derivative of the separation vector describes the relative acceleration between the fiducial and secondary geodesics. Near the north pole, where the separation between these geodesics is small but the rate of change of separation can be large, we show that the GGDE holds but the GDE fails to apply. [Preview Abstract] 
Monday, April 19, 2021 4:57PM  5:09PM Live 
T17.00007: Open problems in the nature of singularities in relativistic spacetimes Deborah Konkowski I will discuss the status of our understanding of singularities in general relativistic spacetimes. I will cover briefly their definition, location, and existence, while focusing on their classical and quantum nature. I will emphasize what we know, and what we do not know about the effect of test particles and waves on a zoo of singularities, from quasiregular to nonscalar curvature to scalar curvature in both localized and cosmological scenarios. [Preview Abstract] 
Monday, April 19, 2021 5:09PM  5:21PM Live 
T17.00008: Critical Phenomena in the Gravitational Collapse of Electromagnetic Waves Maria Perez Mendoza, Thomas Baumgarte Critical phenomena in the collapse of vacuum gravitational waves remain mysterious even 25 years after they were first reported. This case differs qualitatively from other, better understood examples of critical collapse in that the critical solution cannot be spherically symmetric. We report on critical phenomena in the gravitational collapse of electromagnetic waves, which also do not allow spherically symmetric solutions, but are easier to handle numerically than the vacuum case. Generalizing earlier results on dipolar initial data we consider higher multipole moments, which appear to lead to a bifurcation akin to similar effects observed in other highly aspherical cases. [Preview Abstract] 
Monday, April 19, 2021 5:21PM  5:33PM Live 
T17.00009: Extreme Kerr black holes are nonunique Lior Burko, Gaurav Khanna, Subir Sabharwal The uniqueness of classical black holes  the celebrated "no hair theorems"  guarantee that no parameters other than the mass, charge, and spin angular momentum of stationary black holes can me measured. 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 demonstrate a linear relation of a generalized Ori prefactor – a certain expression obtained from the latetime expansion or the perturbation field at finite distances – and the Aretakis conserved charge . 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, and violates the uniqueness theorems. This gravitational hair can in principle be detected by gravitationalwave detectors. We identify the failure of the uniqueness theorems to apply with the time dependence of extreme black holes along their event horizons (Aretakis behavior of certain transverse derivatives), although external perturbations decay. [Preview Abstract] 
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