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Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on…

General Relativity and Quantum Cosmology · Physics 2010-05-12 Jonathan Thornburg

Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial…

General Relativity and Quantum Cosmology · Physics 2011-04-05 José Luis Jaramillo , Marcus Ansorg , Nicolas Vasset

We have developed a powerful and efficient method for locating the event horizon of a black hole spacetime, making possible the study of the dynamics of event horizons in numerical relativity. We describe the method and apply it to a…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Peter Anninos , David Bernstein , Steven Brandt , Joan Masso , Edward Seidel , Larry Smarr , Wai-Mo Suen , Paul Walker

Event Horizon, a null hypersurface defining the boundary of the black hole region of a spacetime, is not particularly useful for evolving black holes since it is non-local in time. Instead, one uses the more tangible concept of Apparent…

General Relativity and Quantum Cosmology · Physics 2022-02-23 Emel Altas , Bayram Tekin

We present a series of test beds for numerical codes designed to find apparent horizons. We consider three apparent horizon finders that use different numerical methods: one of them in axisymmetry, and two fully three-dimensional. We…

General Relativity and Quantum Cosmology · Physics 2008-11-26 M. Alcubierre , S. Brandt , B. Bruegmann , C. Gundlach , J. Masso , E. Seidel , P. Walker

The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of…

General Relativity and Quantum Cosmology · Physics 2025-11-07 Daniel R. Terno

Apparent horizon (AH) finders are essential for characterizing black holes and excising their interiors in numerical relativity (NR) simulations. However, open-source AH finders to date are tightly coupled to individual NR codes. We…

General Relativity and Quantum Cosmology · Physics 2026-04-15 Zachariah B. Etienne , Thiago Assumpção , Leonardo Rosa Werneck , Samuel D. Tootle

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes:…

General Relativity and Quantum Cosmology · Physics 2009-02-15 Michael I. Cohen , Harald P. Pfeiffer , Mark A. Scheel

Recent advances in the observation of black-hole candidates have renewed interest in probing their near-horizon structure and in searching for departures from the standard singular solutions of general relativity. In this context,…

General Relativity and Quantum Cosmology · Physics 2026-04-13 Valentin Pomakov , Stefano Liberati

In a companion paper [1], we have presented a cross-correlation approach to near-horizon physics in which bulk dynamics is probed through the correlation of quantities defined at inner and outer spacetime hypersurfaces acting as test…

General Relativity and Quantum Cosmology · Physics 2012-05-08 José Luis Jaramillo , Rodrigo P. Macedo , Philipp Moesta , Luciano Rezzolla

In the field of gravitational wave science, next-generation detectors will be substantially more accurate than the current suite of detectors. Numerical relativity simulations of binary black hole (BBH) gravitational waveforms must become…

General Relativity and Quantum Cosmology · Physics 2025-08-14 Kyle C. Nelli , William Throwe , Nils Deppe , Mark A. Scheel , Lawrence E. Kidder , Nils L. Vu , Saul A. Teukolsky

Event horizons are (generically) not physically observable. In contrast, apparent horizons (and the closely related trapping horizons) are generically physically observable --- in the sense that they can be detected by observers working in…

General Relativity and Quantum Cosmology · Physics 2014-12-10 Matt Visser

This paper proposes a new method for horizon detection called the multi-scale cross modal linear feature. This method integrates three different concepts related to the presence of horizon in maritime images to increase the accuracy of…

Computer Vision and Pattern Recognition · Computer Science 2017-01-31 D. K. Prasad , D. Rajan , C. K. Prasath , L. Rachmawati , E. Rajabaly , C. Quek

Black holes in general relativity are characterized by their trapping horizon, a one-way membrane that can be crossed only inwards. The existence of trapping horizons in astrophysical black holes can be tested observationally using a…

General Relativity and Quantum Cosmology · Physics 2018-06-27 Raúl Carballo-Rubio , Pawan Kumar , Wenbin Lu

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we…

High Energy Physics - Theory · Physics 2015-03-13 Roberto Emparan , Troels Harmark , Vasilis Niarchos , Niels A. Obers

Apparent horizons are structures of spacelike hypersurfaces that can be determined locally in time. Closed surfaces of constant expansion (CE surfaces) are a generalisation of apparent horizons. I present an efficient method for locating CE…

General Relativity and Quantum Cosmology · Physics 2014-11-17 Erik Schnetter

In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such…

General Relativity and Quantum Cosmology · Physics 2017-11-01 Jahed Abedi , Hannah Dykaar , Niayesh Afshordi

We consider a spherically symmetric line element which admits either a black hole geometry or a wormhole geometry and show that in both cases the apparent horizon or the wormhole throat is partially characterized by the zero-set of a single…

General Relativity and Quantum Cosmology · Physics 2021-06-23 D. D. McNutt , W. Julius , M. Gorban , B. Mattingly , P. Brown , G. Cleaver

This paper investigates the global dynamics of the apparent horizon. We present an approach to establish its existence and its long-term behaviors. Our apparent horizon is constructed by solving the marginally outer trapped surface (MOTS)…

General Relativity and Quantum Cosmology · Physics 2025-05-20 Xinliang An , Taoran He

The event horizon of a black hole is arguably the most dramatic manifestation of the fact that in General Relativity, causal structure is dynamical and spacetimes can be separated into distinct regions by causal boundaries. Causal set…

General Relativity and Quantum Cosmology · Physics 2026-05-11 Astrid Eichhorn , Pedro Gamito , Nawder Stokes