Shahar Hadar

High and low dimensions in the black hole negative mode

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory–Laflamme black string instability. We analyze the eigenvalue as a function of spacetime dimension λ = λ(d) by constructing two perturbative expansions: one for large d and the other for small d − 3, and determining as many coefficients as we are able to compute analytically. By joining the two expansions, we obtain an interpolating rational function accurate to better than 2% through the whole range of dimensions including d = 4.

Gravity waves from extreme-mass-ratio plunges into Kerr black holes

Massive objects orbiting a near-extreme Kerr black hole quickly plunge into the horizon after passing the innermost stable circular orbit. The plunge trajectory is shown to be related by a conformal map to a circular orbit. Conformal symmetry of the near-horizon region is then used to compute the gravitational radiation produced during the plunge phase.

Fast plunges into Kerr black holes

A bstractMost extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.

Theory of post-Newtonian radiation and reaction

We address issues with extant formulations of dissipative effects in the effective field theory (EFT) which describes the post-Newtonian (PN) inspiral of two gravitating bodies by (re)formulating several parts of the theory. Novel ingredients include gauge invariant spherical fields in the radiation zone; a system zone which preserves time reversal such that its violation arises not from local odd propagation but rather from interaction with the radiation sector in a way which resembles the balayage method; 2-way multipoles to perform zone matching within the EFT action; and a double-field radiation-reaction action which is the non-quantum version of the Closed Time Path formalism and generalizes to any theory with directed propagators including theories which are defined by equations of motion rather than an action. This formulation unifies the treatment of outgoing radiation and its reaction force. We demonstrate the theory in the scalar, electromagnetic and gravitational cases by economizing the following: the expression for the radiation source multipoles; the derivation of the leading outgoing radiation and associated reaction force such that it is maximally reduced to mere multiplication; and the derivation of the gravitational next to leading PN order. In fact we present a novel expression for the +1PN correction to all mass multipoles. We introduce useful definitions for multi-index summation, for the normalization of Bessel functions and for the normalization of the gravito-magnetic vector potential.

Radiation reaction at the level of the action

The aim of this paper is to highlight a recently proposed method for the treatment of classical radiative effects, in particular radiation reaction, via effective field theory methods. We emphasize important features of the method and in particular the doubling of fields. We apply the method to two simple systems: a mass–rope system and an electromagnetic charge-field system. For the mass–rope system in 1 + 1 dimensions we derive a double-field effective action for the mass which describes a damped harmonic oscillator. For the EM charge-field system, i.e. the system of an accelerating electric charge in 3 + 1 dimensions, we show a reduction to a 1 + 1 dimensions radial system of an electric dipole source coupled to an electric dipole field (analogous to the mass coupled to the rope). For this system we derive a double-field effective action and reproduce in an analogous way the leading part of the Abraham–Lorentz–Dirac force.

Gravitational radiation-reaction in arbitrary dimension

We use effective field theory tools to study non-conservative effects in systems of gravitating objects in general spacetime dimension. Using the classical version of the Closed Time Path formalism, we treat both the radiative gravitational field and its dynamical sources within a single action principle. New results include the radiation-reaction effective action in arbitrary dimensions to leading and +1PN orders, as well as the generalized Quadrupole formula to order +1PN.

Comparing numerical and analytical calculations of post-innermost stable circular orbit ringdown amplitudes

We numerically compute the ringdown amplitudes following the plunge of a particle from the innermost stable circular orbit of a Schwarzschild black hole in the extreme-mass ratio limit. We show that the ringdown amplitudes computed in this way are in good agreement with a recent analytical calculation [S. Hadar and B. Kol, this issue, Phys. Rev. D 84 DM10604 (2011)].].

Post-innermost stable circular orbit ringdown amplitudes in extreme mass ratio inspiral

An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and plunge. The plunge trajectory from the innermost stable circular orbit (ISCO) is special (somewhat independent of initial conditions). We write an expression for its solution in closed-form and for the emitted waveform. In particular we extract an expression for the associated black-hole ringdown amplitudes, and evaluate them numerically.