Critical phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case

Critical phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case

In numerical simulations of black hole binaries, Pretorius and Khurana [ Classical Quantum Gravity 24 S83 (2007)] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n?-?ln?|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent ?. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n??0.41/?, where ? is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter

084022-[17pp]

Gundlach, Carsten

586f1eb5-3185-4b2b-8656-c29c436040fc

Akcay, Sarp

dcb16394-6b37-43a3-90ca-925458bfd668

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Sago, Norichika

c4baa9a1-e4fb-448e-8818-f7d189ed2773

2012

Gundlach, Carsten

586f1eb5-3185-4b2b-8656-c29c436040fc

Akcay, Sarp

dcb16394-6b37-43a3-90ca-925458bfd668

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Sago, Norichika

c4baa9a1-e4fb-448e-8818-f7d189ed2773

Gundlach, Carsten, Akcay, Sarp, Barack, Leor and Sago, Norichika
(2012)
Critical phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case.
*Physical Review D*, 86 (84022), .
(doi:10.1103/PhysRevD.86.084022).

## Abstract

In numerical simulations of black hole binaries, Pretorius and Khurana [ Classical Quantum Gravity 24 S83 (2007)] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n?-?ln?|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent ?. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n??0.41/?, where ? is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter

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## More information

Published date: 2012

Organisations:
Applied Mathematics

## Identifiers

Local EPrints ID: 347765

URI: https://eprints.soton.ac.uk/id/eprint/347765

ISSN: 1550-7998

PURE UUID: 7fa69846-7f34-48a5-844c-37033cbed0e0

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Date deposited: 30 Jan 2013 11:39

Last modified: 20 Jul 2018 00:34

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## Contributors

Author:
Sarp Akcay

Author:
Norichika Sago

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