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The motion of point particles in curved spacetime
, 2004
"... This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the partic ..."
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Cited by 64 (3 self)
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This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a selfforce that prevents the particle from moving on a geodesic of the background spacetime. The selfforce contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the selfforce matches the energy radiated away by the particle. The field’s action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field’s singular part and show that it exerts no force on the particle — its only effect is to contribute to the particle’s inertia. What remains after subtraction is a smooth field that is fully responsible for the selfforce. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative) field that interacts with the particle; it is this interaction that gives rise to the selfforce. The mathematical tools required to derive the equations of motion of a point scalar charge, a point
Decay of solutions of the Teukolsky equation for higher spin
 in the Schwarzschild geometry,” grqc/0607046
, 2009
"... We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin s = 1 or s = 2, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in L ∞ loc. 1 ..."
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Cited by 10 (2 self)
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We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin s = 1 or s = 2, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in L ∞ loc. 1
Linear stability of the Schwarzschild black hole under electromagnetic and gravitational perturbations
, 2006
"... We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin s = 1 or s = 2, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in L ∞ loc. 1 ..."
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Cited by 4 (1 self)
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We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin s = 1 or s = 2, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in L ∞ loc. 1
unknown title
, 2005
"... A fourth order convergent numerical algortihm to integrate nonrotating binary black hole perturbations in the extreme mass ratio limit ..."
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A fourth order convergent numerical algortihm to integrate nonrotating binary black hole perturbations in the extreme mass ratio limit
On the Existence of Radiation Gauges in Petrov type II spacetimes
, 2006
"... Abstract. The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be overspecified. Their specification consists of five conditions: four (which we treat here as) “gauge ” conditions plus an additional condition on the trace of the metric pertu ..."
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Abstract. The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be overspecified. Their specification consists of five conditions: four (which we treat here as) “gauge ” conditions plus an additional condition on the trace of the metric perturbation. In this work, we utilize a newly developed form of the perturbed Einstein equations to establish a condition — on a particular tetrad component of the stressenergy tensor — under which one can impose the full IRG/ORG. In a Petrov type II background, imposing the IRG/ORG additionally requires (consistently) setting a particular component of the metric perturbation to zero “by hand”. By contrast, in a generic type D background, gauge freedom can generally be used to achieve this. As a specific example, we work through the process of imposing the IRG in a Schwarzschild background, using a more traditional approach. Implications for metric reconstruction using the Teukolsky curvature perturbations in type D spacetimes are briefly discussed. Radiation Gauges in type II spacetimes 2 1.
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"... A timedomain fourthorderconvergent numerical algorithm to integrate black hole perturbations in the extrememassratio limit ..."
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A timedomain fourthorderconvergent numerical algorithm to integrate black hole perturbations in the extrememassratio limit
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, 2006
"... A timedomain fourthorderconvergent numerical algorithm to integrate black hole perturbations in the extrememassratio limit ..."
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A timedomain fourthorderconvergent numerical algorithm to integrate black hole perturbations in the extrememassratio limit
Boundary Conditions for KerrAdS Perturbations
"... The Teukolsky master equation and its associated spinweighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant bounda ..."
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The Teukolsky master equation and its associated spinweighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a nonzero expectation value for the CFT stressenergy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the KodamaIshisbashi (ReggeWheeler−Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the KodamaIshisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the KerrAdS black hole. As a warmup for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdSSchwarzschild, complementing previous analysis in the literature. ar X iv