A 4D asymptotically flat rotating black hole solution including supertraslation correction

Abstract

In this study, beginning with the 4D asymptotically flat Kerr black hole solution in the Boyer-Lindquist (BL) coordinate system, then by using the technique of frame-dragging and some coordinate transformation to incorporate the linear-order supertranslation correction, we finally obtain a 4D asymptotically flat black hole solution with an arbitrary $a$ in the linear-order supertranslated BL coordinate system. We can confirm that this satisfies the Einstein equation. At the end, we calculate the angular momentum of the spacetime we obtained in this study including the linear-order correction. Since the supertranslation is a type of the general coordinate transformation, which is usually defined by linear-order, the corrections we incorporate in this study is sufficient, considering the fact that $a$ is arbitrary. This work is interesting as a generalization of the supertranslated spacetime to the rotating system.

24 pages; v5: accepted version

References in corpus (19)

• Flat Holography: Aspects of the dual field theory
• The gravitational-wave memory effect
• Gluon Amplitudes as 2d Conformal Correlators
• The Kerr Metric
• Searching for gravitational wave memory bursts with the Parkes Pulsar Timing Array
• Thanks for the memory: measuring gravitational-wave memory in the first LIGO/Virgo gravitational-wave transient catalog
• Color Memory
• Adding Gravitational Memory to Waveform Catalogs using BMS Balance Laws
• The NANOGrav 11-Year Data Set: Limits on Gravitational Wave Memory
• Gravitational-wave memory effects in Brans-Dicke theory: Waveforms and effects in the post-Newtonian approximation
• Horizon supertranslation and degenerate black hole solutions
• Gravitational Memory and Compact Extra Dimensions
• Pulsar Timing Perturbations from Galactic Gravitational Wave Bursts with Memory
• The First-Order Velocity Memory Effect from Compact Binary Coalescing Sources
• Gravitational wave memory of the binary black hole events in GWTC-2
• Can we detect a supertranslated black hole?
• Black Hole Shadow with Soft Hair
• Nonlinear gravitational-wave memory from cusps and kinks on cosmic strings
• Hawking flux of 4D Schwarzschild black hole with supertransition correction to second-order