Vacuum Spacetime With Multipole Moments: The Minimal Size Conjecture, Black Hole Shadow, and Gravitational Wave Observables

Fuente: arXiv
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Main Authors: Tahura, Shammi, Khalvati, Hassan, Yang, Huan
Format: Preprint
Published: 2023
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author Tahura, Shammi
Khalvati, Hassan
Yang, Huan
author_facet Tahura, Shammi
Khalvati, Hassan
Yang, Huan
contents In this work, we explicitly construct the vacuum solution of Einstein's equations with prescribed multipole moments. By observing the behavior of the multipole spacetime metric at small distances, we conjecture that for a sufficiently large multipole moment, there is a minimal size below which no object in nature can support such a moment. The examples we have investigated suggest that such minimal size scales as $(M_n)^{1/(n+1)}$ (instead of $(M_n/M)^{1/n}$), where $M$ is the mass and $M_n$ is the $n$th order multipole moment. With the metric of the "multipole spacetime", we analyze the shape of black hole shadow for various multipole moments and discuss the prospects of constraining the moments from shadow observations. In addition, we discuss the shift of gravitational wave phase with respect to those of the Kerr spacetime, for a test particle moving around an object with this set of multipole moments. These phase shifts are required for the program of mapping out the spacetime multipole moments based on gravitational wave observations of extreme mass-ratio inspirals.
format Preprint
id arxiv_https___arxiv_org_abs_2309_11491
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Vacuum Spacetime With Multipole Moments: The Minimal Size Conjecture, Black Hole Shadow, and Gravitational Wave Observables
Tahura, Shammi
Khalvati, Hassan
Yang, Huan
General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
In this work, we explicitly construct the vacuum solution of Einstein's equations with prescribed multipole moments. By observing the behavior of the multipole spacetime metric at small distances, we conjecture that for a sufficiently large multipole moment, there is a minimal size below which no object in nature can support such a moment. The examples we have investigated suggest that such minimal size scales as $(M_n)^{1/(n+1)}$ (instead of $(M_n/M)^{1/n}$), where $M$ is the mass and $M_n$ is the $n$th order multipole moment. With the metric of the "multipole spacetime", we analyze the shape of black hole shadow for various multipole moments and discuss the prospects of constraining the moments from shadow observations. In addition, we discuss the shift of gravitational wave phase with respect to those of the Kerr spacetime, for a test particle moving around an object with this set of multipole moments. These phase shifts are required for the program of mapping out the spacetime multipole moments based on gravitational wave observations of extreme mass-ratio inspirals.
title Vacuum Spacetime With Multipole Moments: The Minimal Size Conjecture, Black Hole Shadow, and Gravitational Wave Observables
topic General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
url https://arxiv.org/abs/2309.11491