arXiv subjects

Trevor Gravely

Publications and source records attributed to Trevor Gravely.

5 recordsLinked to original sources

arXiv2026

Chaos and fractals of the black hole photon ring

The photon ring of a Kerr black hole decomposes into a self-similar hierarchy of subrings. Here, we show that this self-similar structure persists in phase space. Moreover, near the photon shell of bound photon orbits, dynamics are controlled by a Lyapunov exponent $γ$, whose role we highlight by computing the first-return map for light rays close to an unstably bound orbit. Despite an exponential $e^γ$ sensitivity to initial conditions, nearly bound rays do not exhibit chaotic behavior. However, as the background spacetime is deformed away from the Kerr geometry, chaos sets in, with its first onset most visible near strongly resonant bound orbits in the photon shell. We display two animations: one illustrating the emergence of chaos near the photon shell, which results in a fractal phase-space structure, and another exhibiting how this chaotic, fractal, self-similar structure is encoded in the first-return map.

gr-qc↗

arXiv2026

Black Hole Vision: An Interactive iOS Application for Visualizing Black Holes

The Black Hole Explorer (BHEX) is a proposed mission to launch a sub-millimeter radio telescope into Earth orbit that will take the sharpest images in the history of astronomy and reveal novel horizon-scale features of supermassive black holes. Black Hole Vision is an open-source application, freely available on the iOS App Store, that produces lensed images which highlight the key features expected to appear in the black hole images BHEX will capture. The app combines video feeds from the front- and rear-facing iPhone cameras and uses the black hole lensing equations to synthesize an onscreen image displaying the user's surroundings as if they were gravitationally lensed by a black hole within the cameras' field of view. Here, we describe how light rays are lensed by non-rotating (Schwarzschild) and rotating (Kerr) black holes, and we list the equations needed for computing black-hole-lensed images. We also describe their specific implementation within Black Hole Vision.

gr-qc↗

arXiv2025

Gravitational Waves on Kerr Black Holes I: Reconstruction of Linearized Metric Perturbations

The gravitational perturbations of a rotating Kerr black hole are notoriously complicated, even at the linear level. In 1973, Teukolsky showed that their physical degrees of freedom are encoded in two gauge-invariant Weyl curvature scalars that obey a separable wave equation. Determining these scalars is sufficient for many purposes, such as the computation of energy fluxes. However, some applications -- such as second-order perturbation theory -- require the reconstruction of metric perturbations. In principle, this problem was solved long ago, but in practice, the solution has never been worked out explicitly. Here, we do so by writing down the metric perturbation (in either ingoing or outgoing radiation gauge) that corresponds to a given mode of either Weyl scalar. Our formulas make no reference to the Hertz potential (an intermediate quantity that plays no fundamental role) and involve only the radial and angular Kerr modes, but not their derivatives, which can be altogether eliminated using the Teukolsky--Starobinsky identities. We expect these analytic results to prove useful in numerical studies and for extending black hole perturbation theory beyond the linear regime.

gr-qc↗

arXiv2025

Gravitational Waves on Kerr Black Holes II: Metric Reconstruction with Cosmological Constant

In this second paper of our series started with \cite{Berens2024}, we investigate linearized gravitational perturbations of a rotating Kerr black hole in a non-asymptotically flat spacetime with (anti-)de Sitter boundary conditions. Here, we explicitly write down the metric components (in both ingoing and outgoing radiation gauge) of the perturbations that correspond to a given mode of either Weyl scalar. We provide formulas involving Hertz potentials (intermediate quantities with a holographic interpretation) as well as some that involve only the separated radial and angular modes. We expect these analytic results to prove useful in numerical studies of black hole perturbation theory in the context of the holographic correspondence.

gr-qc↗

arXiv2024

The Black Hole Explorer: Using the Photon Ring to Visualize Spacetime Around the Black Hole

The Black Hole Explorer (BHEX), an orbiting, multi-band, millimeter radio-telescope, in hybrid combination with millimeter terrestrial radio-telescopes, is designed to discover and measure the thin photon ring around the supermassive black holes M87* and Sgr A*. As background to the BHEX instruments, this paper explores various aspects of the photon ring, focusing on the intricate flow of light around a spinning black hole, and tracking, through visual simulations, photons as they course along geodesics. Ultimately, the aim of these visualizations is to advance the foundational aims of the BHEX instrument, and through this experiment to articulate spacetime geometry via the photon ring.

gr-qc↗