Estimating the Cosmological Constant from Shadows of Kerr–de Sitter Black Holes

The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant Λ as the vacuum energy leads to a deformation in the vicinity of a black hole—new Kerr–de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr–de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates (r0,θ0) in the domain (r0,rc) and estimate the cosmological constant Λ from its shadow observables. The shadow observables of the new Kerr–de Sitter black holes significantly deviate from the corresponding observables of the Kerr–de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for (Λ, a) where the observables of the two black holes are indistinguishable.

Linear Stability of Black Holes and Naked Singularities

A review of the current status of the linear stability of black holes and naked singularities is given. The standard modal approach, that takes advantage of the background symmetries and analyze separately the harmonic components of linear perturbations, is briefly introduced and used to prove that the naked singularities in the Kerr–Newman family, as well as the inner black hole regions beyond Cauchy horizons, are unstable and therefore unphysical. The proofs require a treatment of the boundary condition at the timelike boundary, which is given in detail. The nonmodal linear stability concept is then introduced, and used to prove that the domain of outer communications of a Schwarzschild black hole with a non-negative cosmological constant satisfies this stronger stability condition, which rules out transient growths of perturbations, and also to show that the perturbed black hole settles into a slowly rotating Kerr black hole. The encoding of the perturbation fields in gauge invariant curvature scalars and the effects of the perturbation on the geometry of the spacetime is discussed. These notes follow from a course delivered at the V José Plínio Baptista School of Cosmology, held at Guarapari (Espírito Santo) Brazil, from 30 September to 5 October 2021.

The irreducible mass of Christodoulou–Ruffini–Hawking mass formula

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking. (1) The Horizon Mass Theorem states that the mass at the event horizon of any black hole — neutral, charged, or rotating — is always twice its irreducible mass observed at infinity. (2) The External Energy Theorem asserts that the rotational energy of a Kerr black hole exists completely outside the horizon. This is due to the fact that the irreducible mass does not contain rotational energy. (3) The Moment of Inertia Theorem shows that every black hole has a moment of inertia. When the rotation stops, the irreducible mass of a Kerr black hole becomes the moment of inertia of a Schwarzschild black hole. This is recognized as the rotational equivalent of the rest mass of a moving body in relativity. Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it a limiting value in rotation, it determines black hole dynamics and structure. What is believed to be a black hole is a mechanical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

SUSY in the sky with gravitons

Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden $$ \mathcal{N} $$ N = 2 supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary D spacetime dimensions. Using the $$ \mathcal{N} $$ N = 2 supersymmetric worldline action, augmented by finite-size corrections for the non-Kerr black hole case, we build a quadratic-in-spin extension to the worldline quantum field theory (WQFT) formalism introduced in our previous work, and calculate the two bodies’ deflection and spin kick to sub-leading order in the post-Minkowskian expansion in Newton’s constant G. For spins aligned to the normal vector of the scattering plane we also obtain the scattering angle. All D-dimensional observables are derived from an eikonal phase given as the free energy of the WQFT that is invariant under the $$ \mathcal{N} $$ N = 2 supersymmetry transformations.

The Response of Black Hole Spark Gaps to External Changes: A Production Mechanism of Rapid TeV Flares?

We study the response of a starved Kerr black hole magnetosphere to abrupt changes in the intensity of disk emission and in the global magnetospheric current, by means of one-dimensional general relativistic particle-in-cell simulations. Such changes likely arise from the intermittency of the accretion process. We find that in cases where the pair-production opacity contributed by the soft disk photons is modest, as in, e.g., M87, such changes can give rise to delayed, strong teraelectronvolt (TeV) flares, dominated by curvature emission of particles accelerated in the gap. The flare rise time, and the delay between the external variation and the onset of the flare emitted from the outer gap boundary, are of the order of the light-crossing time of the gap. The rapid, large-amplitude TeV flares observed in M87, and perhaps, other active galactic nuclei may be produced by such a mechanism.

Testing the Kerr black hole hypothesis with the continuum-fitting and the iron line methods: the case of GRS 1915+105

The continuum-fitting and the iron line methods are currently the two leading techniques for probing the strong gravity region around accreting black holes. In the present work, we test the Kerr black hole hypothesis with the stellar-mass black hole in GRS 1915+105 by analyzing five disk-dominated RXTE spectra and one reflection-dominated Suzaku spectrum. The combination of the constraints from the continuum-fitting and the iron line methods has the potential to provide more stringent tests of the Kerr metric. Our constraint on the Johannsen deformation parameter α13 is -0.15 < α13 < 0.14 at 3σ, where the Kerr metric is recovered when α13 = 0.

Testing the Kerr Black Hole Hypothesis with GRS 1716-249 by Combining the Continuum Fitting and the Iron-line Methods

The continuum-fitting and the iron-line methods are currently the two leading techniques for measuring the spins of accreting black holes. In the past few years, these two methods have been developed for testing fundamental physics. In the present work, we employ state-of-the-art models to test black holes through the continuum-fitting and the iron-line methods and we analyze three NuSTAR observations of the black hole binary GRS 1716-249 during its outburst in 2016–2017. In these three observations, the source was in a hard-intermediate state and the spectra show both a strong thermal component and prominent relativistic reflection features. Our analysis confirms the Kerr nature of the black hole in GRS 1716-249 and provides quite stringent constraints on possible deviations from the predictions of general relativity.