scholarly journals A worldsheet for Kerr

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Alfredo Guevara ◽  
Ben Maybee ◽  
Alexander Ochirov ◽  
Donal O’Connell ◽  
Justin Vines
Keyword(s):  
Black Hole ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Equations Of Motion ◽  
Kerr Black Hole ◽  
Single Copy ◽  
Kerr Solution

Abstract We show that the Newman-Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet effective action. This holds both in gravity, and for the single-copy $$ \sqrt{\mathrm{Kerr}} $$ Kerr solution in electrodynamics. At the level of equations of motion, we show that the Newman-Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions are conveniently described using chiral classical equations of motion with the help of the spinor-helicity method familiar from scattering amplitudes.

scholarly journals Gravitational perturbations from NHEK to Kerr

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Alejandra Castro ◽  
Victor Godet ◽  
Joan Simón ◽  
Wei Song ◽  
Boyang Yu
Keyword(s):  
Black Hole ◽  
Line Element ◽  
Kerr Black Hole ◽  
Kerr Solution ◽  
Regularity Conditions ◽  
New Developments ◽  
Gravitational Perturbations ◽  
Dynamical Properties ◽  
Complete Characterisation

Abstract We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS2 holography.

scholarly journals Breaking away from the near horizon of extreme Kerr

2020 ◽  
Vol 8 (6) ◽  
Author(s):  
Alejandra Castro ◽  
Victor Godet
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Conformal Symmetry ◽  
Kerr Black Hole ◽  
Einstein Equations ◽  
The Other ◽  
Conformal Dimension ◽  
Gravitational Perturbations ◽  
Horizon Geometry ◽  
Metric Fluctuations

We study gravitational perturbations around the near horizon geometry of the (near) extreme Kerr black hole. By considering a consistent truncation for the metric fluctuations, we obtain a solution to the linearized Einstein equations. The dynamics is governed by two master fields which, in the context of the nAdS_22/nCFT_11 correspondence, are both irrelevant operators of conformal dimension \Delta=2Δ=2. These fields control the departure from extremality by breaking the conformal symmetry of the near horizon region. One of the master fields is tied to large diffeomorphisms of the near horizon, with its equations of motion compatible with a Schwarzian effective action. The other field is essential for a consistent description of the geometry away from the horizon.

scholarly journals Second post-Minkowskian metric for a moving Kerr black hole

2014 ◽  
Vol 23 (09) ◽  
pp. 1450079 ◽  
Author(s):  
G. He ◽  
C. Jiang ◽  
W. Lin
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Test Particle ◽  
Constant Velocity ◽  
Arbitrary Constant ◽  
Equations Of Motion ◽  
Kerr Black Hole ◽  
Time Dependent

In this paper, the harmonic metric for a moving Kerr black hole is presented in the second post-Minkowskian approximation. It is further demonstrated that the obtained metric is consistent with the Liénard–Wiechert gravitational potential for a moving and spinning source with an arbitrary constant velocity. Based on the metric, we also give the post-Newtonian equations of motion for photon and massive test particle in the time-dependent gravitational field.

Rotating bodies; the Kerr metric

2021 ◽  
pp. 260-273
Author(s):  
Andrew M. Steane
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Kerr Black Hole ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Limit Surface ◽  
Generic Properties ◽  
Rotating Body ◽  
Particle Orbits ◽  
Rotating Bodies

Spacetime around a general rigidly rotating body is discussed, and the Kerr solution explored in detail. First we obtain generic properties of stationary, axisymmetric metrics. The stationary limit surface and ergoregion is defined. Then the Kerr metric is presented (without derivation) and discussed. Horizons and limit surfaces are obtained, and the overall structure of the Kerr black hole deduced. The mass and angular momentum is extracted. Equations for particle orbits are obtained, and their properties discussed.

The physics of black holes I

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Einstein Equations ◽  
Kerr Solution ◽  
Physical Processes ◽  
Physics Of Black Holes ◽  
Penrose Process ◽  
The Stability

This chapter describes two physical processes related to the Schwarzschild and Kerr solutions which can be induced by the gravitational field of a black hole. The first is the Penrose process, which suggests that rotating black holes are large energy reservoirs. Next is superradiance, which is the first step in the study of black-hole stability. The study of the stability of black holes involves the linearization of the Einstein equations about the Schwarzschild or Kerr solution. As this chapter shows, the equations of motion for perturbations of the metric are wave equations. The problem then is to determine whether or not these solutions are bounded.

TWO-LOOP BETA FUNCTION IN THE OPEN STRING SIGMA MODEL AND EQUIVALENCE WITH STRING EFFECTIVE EQUATIONS OF MOTION

1988 ◽  
Vol 03 (14) ◽  
pp. 1349-1359 ◽  
Author(s):  
O.D. ANDREEV ◽  
A.A. TSEYTLIN
Keyword(s):  
Vector Field ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Beta Function ◽  
Open String ◽  
Equation Of Motion ◽  
Β Function ◽  
The Given

We consider the sigma-model on the disc corresponding to the open bose string in external abelian vector field and compute the order ∂3F3-terms in its two-loop β-function. The vanishing of the two-loop β-function (modulo diffeomorphism and gauge terms) is shown to be equivalent (to the given order) to the equation of motion for the string theory effective action reconstructed from the string scattering amplitudes.

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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