Can the slow-rotation approximation be used in electromagnetic observations of black holes?

Abstract

Abstract.Future electromagnetic observations of black holes may allow us to test General Relativity in the strong-field regime. Such tests, however, require knowledge of rotating black hole solutions in modified gravity theories, a class of which does not admit the Kerr metric as a solution. Several rotating black hole solutions in modified theories have only been found in the slow-rotation approximation (i.e. assuming the spin angular momentum is much smaller than the mass squared). We here investigate whether the systematic error due to the approximate nature of these black hole metrics is small enough relative to the observational error to allow their use in electromagnetic observations to constrain deviations from General Relativity. We address this by considering whether electromagnetic observables constructed from a slow-rotation approximation to the Kerr metric can fit observables constructed from the full Kerr metric with systematic errors smaller than current observational errors. We focus on black hole shadow and continuum spectrum observations, as these are the least influenced by accretion disk physics, with current observational errors of about 10%. We find that the fractional systematic error introduced by using a second-order, slowly rotating Kerr metric is at most 2% for shadows created by black holes with dimensionless spins χ ≤ 0.6. We also find that the systematic error introduced by using the slowly rotating Kerr metric as an exact metric when constructing continuum spectrum observables is negligible for black holes with dimensionless spins of χ 0.9. Our results suggest that the modified gravity solutions found in the slow-rotation approximation may be used to constrain realistic deviations from General Relativity with continuum spectrum and black hole shadow observations.

Testing conformal gravity with the supermassive black hole in 1H0707-495

“…Many electromagnetic tests of the Kerr metric in the literature rely on the bottom-up approach. The main reason is that rotating black hole solutions in alternative theories of gravity are often unknown, while tests of the Kerr metric are not possible, or more challenging, with non-rotating or slow-rotating solutions [19]. This is related to the difficulties in solving the corresponding field equations for rotating solutions and it is evident even in the case of Einstein's gravity.…”

Black hole continuum spectra as a test of general relativity: quadratic gravity

“…Following the same prescription as [43], let us assume that the Kerr metric is the correct description of a BH spacetime and that the associated spectrum is our observation. We shall refer to the Kerr spectrum observation as the injected synthetic signal or injection for short.…”

“…Systematic error originates from the approximate nature of the models we use to analyze the data, in particular the approximate nature of BH solutions in modified gravity and of the astrophysical models for accretion disks. The impact of using approximate, slowly-rotating BH solutions for continuum spectrum observations was studied recently [43], with results suggesting that the systematic error introduced is negligible, provided the BH is not close to maximally rotating. The impact of using approximate accretion disk models is currently unknown, because of their complexity and the large number of proposed models.…”

Neutron star pulse profile observations as extreme gravity probes

“…Having reduced our parameter space and chosen our priors, we calculate the best-fit parameters by minimizing the relative chi-squared between the injection and the model pulse profiles, scanning the parameter space using 16 phase stamps over the course of one stellar revolution. The standard deviation of the distribution σ ε 15 is modeled as in [59,60] and chosen to capture the optimistic 5% accuracy at which NICER can infer m and R. From the chi-squared, we calculate the likelihood function and from it we obtain the marginalized posterior distributions p(ε 15 |d), p(log 10 |α 0 ||d) and p(β 0 |d). Figure 2 summarizes our results for f * = 600 Hz and EoS * = SLy4.…”

“…where σ ε 15 , σ log 10 |α 0 | and σ β 0 are the standard deviations on each injected parameter θ * var = {ε * 15 , log 10 |α * 0 |, β * 0 }. Since our injection is assumed to be consistent with general relativity, we set σ log 10 |α 0 | = σ β 0 = 0, while the standard deviation σ ε 15 is calculated by [59,60] σ ε 15 (φ i ) = 1 2 F inj (φ i , θ fix , {ε * 15 + δε + 15 , log 10 |α * 0 |, β * 0 }) − F inj (φ i , θ fix , {ε * 15 − δε − 15 , log 10 |α * 0 |, β * 0 }) , where (as explained in the main text) log 10 |α * 0 | = −5 and β * 0 = 0, while δε ± 15 remain to be specified. To obtain them, we start by assuming that m * = 1.93 M ⊙ as discussed in the main text.…”