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Register a new userCausal concept for black hole shadows
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Masaru Siino
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Causal concept for the general black hole shadow is investigated, instead of the photon sphere. We define several `wandering null geodesics as complete null geodesics accompanied by repetitive conjugate points, which would correspond to null geodesics on the photon sphere in Schwarzschild spacetime. We also define a `wandering set, that is, a set of totally wandering null geodesics as a counterpart of the photon sphere, and moreover, a truncated wandering null geodesic to symbolically discuss its formation. Then we examine the existence of a wandering null geodesic in general black hole spacetimes mainly in terms of Weyl focusing. We will see the essence of the black hole shadow is not the stationary cycling of the photon orbits which is the concept only available in a stationary spacetime, but their accumulation. A wandering null geodesic implies that this accumulation will be occur somewhere in an asymptotically flat spacetime.
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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.
We present a scheme for generating first-order metric perturbation initial data for an arbitrary background and source. We then apply this scheme to derive metric perturbations in order-reduced dynamical Chern-Simons gravity (dCS). In particular, we solve for metric perturbations on a black hole background that are sourced by a first-order dCS scalar field. This gives us the leading-order metric perturbation to the spacetime in dCS gravity. We then use these solutions to compute black hole shadows in the linearly perturbed spacetime by evolving null geodesics. We present a novel scheme to decompose the shape of the shadow into multipoles parametrized by the spin of the background black hole and the perturbation parameter $varepsilon^2$. We find that we can differentiate the presence of a pure Kerr spacetime from a spacetime with a dCS perturbation using the shadow, allowing in part for a null-hypothesis test of general relativity. We then consider these results in the context of the Event Horizon Telescope.
In this article, we provide a review of the current state of the research of the black hole shadow, focusing on analytical (as opposed to numerical and observational) studies. We start with particular attention to the definition of the shadow and its relation to the often used concepts of escape cone, critical impact parameter and particle cross-section. For methodological purposes, we present the derivation of the angular size of the shadow for an arbitrary spherically symmetric and static space-time, which allows one to calculate the shadow for an observer at arbitrary distance from the center. Then we discuss the calculation of the shadow of a Kerr black hole, for an observer anywhere outside of the black hole. For observers at large distances we present and compare two methods used in the literature. Special attention is given to calculating the shadow in space-times which are not asymptotically flat. Shadows of wormholes and other black-hole impostors are reviewed. Then we discuss the calculation of the black hole shadow in an expanding universe as seen by a comoving observer. The influence of a plasma on the shadow of a black hole is also considered.
We investigate the relationship between shadow radius and microstructure for a general static spherically symmetric black hole and confirm their close connection. In this regard, we take the Reissner-Nordstrom (AdS) black hole as an example to do the concrete analysis. On the other hand, we study for the Kerr (AdS) black hole the relationship between its shadow and thermodynamics in the aspects of phase transition and microstructure. Our results for the Kerr (AdS) black hole show that the shadow radius $r_{rm sh}$, the deformation parameters $delta _{s}$ and $k_{s}$, and the circularity deviation $Delta C$ can reflect the black hole thermodynamics. In addition, we give the constraints to the relaxation time of the M$87^{*}$ black hole by combining its shadow data and the Bekenstein-Hod universal bounds when the M$87^{*}$ is regarded as the Reissner-Nordstrom or Kerr black hole. Especially, we obtain the formula of the minimum relaxation time $tau _{rm min}$ which equals $8GM/c^3$ for a fixed black hole mass $M$, and predict that the minimum relaxation times of M$87^{*}$ black hole and Sgr $A^{*}$ black hole are approximately 3 days and 2.64 minutes, respectively. Finally, we draw the first graph of the minimum relaxation time $tau _{rm min}$ with respect to the maximum shadow radius $ r_{rm sh}^{rm max}$ at different mass levels.
A perturbed black hole rings down by emitting gravitational waves in tones with specific frequencies and durations. Such tones encode prized information about the geometry of the source spacetime and the fundamental nature of gravity, making the measurement of black hole ringdowns a key goal of gravitational wave astronomy. However, this task is plagued by technical challenges that invalidate the naive application of standard data analysis methods and complicate sensitivity projections. In this paper, we provide a comprehensive account of the formalism required to properly carry out ringdown analyses, examining in detail the foundations of recent observational results, and providing a framework for future measurements. We build on those insights to clarify the concepts of ringdown detectability and resolvability -- touching on the drawbacks of both Bayes factors and naive Fisher matrix approaches -- and find that overly pessimistic heuristics have led previous works to underestimate the role of ringdown overtones for black hole spectroscopy. We put our framework to work on the analysis of a variety of simulated signals in colored noise, including analytic injections and a numerical relativity simulation consistent with GW150914. We demonstrate that we can use tones of the quadrupolar angular harmonic to test the no-hair theorem at current sensitivity, with precision comparable to published constraints from real data. Finally, we assess the role of modeling systematics, and project measurements for future, louder signals. We release ringdown, a Python library for analyzing black hole ringdowns using the the methods discussed in this paper, under a permissive open-source license at https://github.com/maxisi/ringdown
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