Abstract
In General Relativity, the spacetimes of black holes have three fundamental properties: (i) they are the same, to lowest order in spin, as the metrics of stellar objects; (ii) they are independent of mass, when expressed in geometric units; and (iii) they are described by the Kerr metric. In this paper, we quantify the upper bounds on potential black-hole metric deviations imposed by observations of black-hole shadows and of binary black-hole inspirals in order to explore the current experimental limits on possible violations of the last two predictions. We find that both types of experiments provide correlated constraints on deviation parameters that are primarily in the tt-components of the spacetimes, when expressed in areal coordinates. We conclude that, currently, there is no evidence for a deviations from the Kerr metric across the 8 orders of magnitudes in masses and 16 orders in curvatures spanned by the two types of black holes. Moreover, because of the particular masses of black holes in the current sample of gravitational-wave sources, the correlations imposed by the two experiments are aligned and of similar magnitudes when expressed in terms of the far field, post-Newtonian predictions of the metrics. If a future coalescing black-hole binary with two low-mass (e.g., ~3 Msun) components is discovered, the degeneracy between the deviation parameters can be broken by combining the inspiral constraints with those from the black-hole shadow measurements.
Highlights
Over the past century, numerous predictions of the theory of general relativity (GR) have been tested against multiple experiments and astrophysical observations [1]
This first paper will focus on the results of two types of observations: those of the black-hole shadow images obtained with the Event Horizon Telescope (EHT), and those of the gravitational waves from coalescing black holes detected with LIGO/Virgo
In order to break the complete degeneracy between varying the physical parameters of the black-hole binaries and the deviation terms of the metrics, we explore a different cross section of the parameter space of possibilities compared to previous work (e.g., Ref. [6])
Summary
Numerous predictions of the theory of general relativity (GR) have been tested against multiple experiments and astrophysical observations [1]. As discussed above, these constraints are expressed in different ways that are specific to each test, because they are merged with parameters that quantify the dynamics of the theory (as is the case with the gravitational-wave tests) or employ complexity that is necessary to avoid pathologies (as is the case with the shadow tests) The aim of this series of papers is to combine all existing tests of metrics of astrophysical objects in order to test three important GR predictions for the metrics of black holes, that: (i) the metric of a black hole, expanded to first order in spin, is identical (when expressed in geometric units) to that of a slowly spinning star—i.e., it is the Schwarzschild spacetime with the first-order frame-dragging terms; (ii) all black holes, independent of mass or curvature, are described by the same metric; and (iii) the black-hole spacetime is described by the Kerr metric.
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