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These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds.…

General Relativity and Quantum Cosmology · Physics 2016-10-13 Lars Andersson , Thomas Bäckdahl , Pieter Blue

We discuss parameterizations of black-hole spacetimes in and beyond General Relativity in view of their symmetry constraints: within the class of axisymmetric, stationary spacetimes, we propose a parameterization that includes non-circular…

General Relativity and Quantum Cosmology · Physics 2022-06-14 Héloïse Delaporte , Astrid Eichhorn , Aaron Held

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;…

General Relativity and Quantum Cosmology · Physics 2021-05-26 Dimitrios Psaltis , Colm Talbot , Ethan Payne , Ilya Mandel

Although General Relativity (GR) has been tested extensively in the weak gravity regime, similar tests in the strong gravity regime are still missing. In this paper we explore the possibility to use X-ray spectropolarimetric observations of…

General Relativity and Quantum Cosmology · Physics 2015-06-05 Henric Krawczynski

The Johannsen-Psaltis (JP) black hole is a phenomenologically viable metric obtained by judiciously deforming the Kerr black hole such that the metric is asymptotically flat and causal and is consistent with the weak field, post-Newtonian…

General Relativity and Quantum Cosmology · Physics 2024-05-29 Cagdas Ulus Agca , Bayram Tekin

According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric spacetimes which deviate from the Kerr metric have been proposed in…

General Relativity and Quantum Cosmology · Physics 2015-12-16 Tim Johannsen

In modified gravity models that allow for additional non-compact spacetime dimensions, energy from gravitational waves can leak into these extra spacetime dimensions, leading to a reduction in the amplitude of the observed gravitational…

High Energy Astrophysical Phenomena · Physics 2021-12-15 Ignacio Magana Hernandez

According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric deviations from the Kerr metric have been suggested to study…

General Relativity and Quantum Cosmology · Physics 2011-06-24 Tim Johannsen , Dimitrios Psaltis

The lack of rotating black hole models, which are typically found in nature, in loop quantum gravity (LQG) substantially hinders the progress of testing LQG from observations. Starting with a non-rotating LQG black hole as a seed metric, we…

General Relativity and Quantum Cosmology · Physics 2021-05-07 Suddhasattwa Brahma , Che-Yu Chen , Dong-han Yeom

Einstein's theory of General Relativity predicts that the spacetime metric around astrophysical black holes is described by the Kerr solution. In this work, we employ state-of-the-art in relativistic reflection modeling to analyze a…

High Energy Astrophysical Phenomena · Physics 2021-05-31 Ashutosh Tripathi , Yuexin Zhang , Askar B. Abdikamalov , Dimitry Ayzenberg , Cosimo Bambi , Jiachen Jiang , Honghui Liu , Menglei Zhou

In the vicinity of black holes, the influence of strong gravity, plasma physics, and emission processes govern the behavior of the system. Since observations such as those carried out by the EHT are not yet able to unambiguously constrain…

High Energy Astrophysical Phenomena · Physics 2023-03-22 Jan Röder , Alejandro Cruz-Osorio , Christian M. Fromm , Yosuke Mizuno , Ziri Younsi , Luciano Rezzolla

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames…

General Relativity and Quantum Cosmology · Physics 2014-12-25 Tamara Gheorghiu , Olivia Vacaru , Sergiu I. Vacaru

The strong gravitational field near massive blackhole is an interesting regime to test General Relativity(GR) and modified gravity theories. The knowledge of spacetime metric around a blackhole is a primary step for such tests. Solving…

General Relativity and Quantum Cosmology · Physics 2020-08-26 Utkarsh Kumar , Sukanta Panda , Avani Patel

Despite its success in the weak gravity regime, General Relativity (GR) has yet to be verified in the regime of strong gravity. In this paper, we present the results of detailed ray tracing simulations aiming at clarifying if the combined…

High Energy Astrophysical Phenomena · Physics 2016-03-23 Janie K. Hoormann , Banafsheh Beheshtipour , Henric Krawczynski

The analysis of the properties of the X-ray radiation emitted from geometrically thin accretion disks around black holes can be a powerful tool to test General Relativity in the strong field regime. This chapter reviews the state-of-the-art…

General Relativity and Quantum Cosmology · Physics 2024-07-12 Cosimo Bambi

We are fitting dynamics of electrically neutral hot-spot orbiting around Sgr A* source in Galactic center, represented by various modifications of the standard Kerr black hole (BH), to the three flares observed by the GRAVITY instrument on…

General Relativity and Quantum Cosmology · Physics 2024-03-19 Misbah Shahzadi , Martin Kološ , Zdeněk Stuchlík , Yousaf Habib

In general relativity, astrophysical black holes are uniquely described by the Kerr metric. Observational tests of the Kerr nature of these compact objects and, hence, of general relativity, require a metric that encompasses a broader class…

General Relativity and Quantum Cosmology · Physics 2015-06-11 Tim Johannsen

Black holes are among the most intriguing objects in nature. They are believed to be fully described by General Relativity (GR), and the astrophysical black holes are expected to belong to the Kerr family, obeying the no-hair theorems.…

General Relativity and Quantum Cosmology · Physics 2020-05-12 Renan B. Magalhães , Luiz C. S. Leite , Luís C. B. Crispino

We study propagation of high-frequency electromagnetic and gravitational waves in the gravitational field of a rotating black hole. Due to the interaction of the spin of the field with the spacetime curvature, the standard geometric optics…

General Relativity and Quantum Cosmology · Physics 2025-06-04 Valeri P. Frolov , Alex Koek

General relativity predicts the spacetime metric around an astrophysical black hole to be described by the Kerr solution, which is a massive rotating black hole without any residual charge. In a previous paper, we analyzed the NuSTAR…

High Energy Astrophysical Phenomena · Physics 2026-01-06 Ashutosh Tripathi , Swarnim Shashank , Gitika Mall , Askar Abdikamalov