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In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…

Differential Geometry · Mathematics 2024-05-27 Jake McNaughton

We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes…

General Relativity and Quantum Cosmology · Physics 2018-02-21 Oliver J. Tattersall , Pedro G. Ferreira , Macarena Lagos

Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D…

General Relativity and Quantum Cosmology · Physics 2016-11-15 Jeremy Miller , Barry Wardell , Adam Pound

Cosmological analysis based on currently available observations are unable to rule out a sizeable coupling among the dark energy and dark matter fluids. We explore a variety of coupled dark matter-dark energy models, which satisfy cosmic…

Cosmology and Nongalactic Astrophysics · Physics 2010-12-10 Laura Lopez Honorez , Beth A. Reid , Olga Mena , Licia Verde , Raul Jimenez

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…

Analysis of PDEs · Mathematics 2017-02-21 Nikos Katzourakis

The leading corrections to General Relativity can be parametrized by higher-derivative interactions in a low-energy effective field theory, in a way that is general and agnostic to the precise UV completion of gravity. Using numerical…

General Relativity and Quantum Cosmology · Physics 2026-04-17 Pedro G. S. Fernandes

The collision of black holes and the emission of gravitational radiation in higher-dimensional spacetimes are of interest in various research areas, including the gauge-gravity duality, the TeV gravity scenarios evoked for the explanation…

General Relativity and Quantum Cosmology · Physics 2017-12-13 William G. Cook , Ulrich Sperhake , Emanuele Berti , Vitor Cardoso

Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd…

High Energy Physics - Theory · Physics 2009-05-29 Hari K. Kunduri , James Lucietti , Harvey S. Reall

An attempt is made in order to clarify the so called regular black holes issue. It is revisited that if one works within General Relativity minimally coupled with non linear source, mainly of electromagnetic origin, and within a static…

General Relativity and Quantum Cosmology · Physics 2017-05-24 Stefano Chinaglia , Sergio Zerbini

We establish various general results concerning static and spherically symmetric black hole solutions of general higher-derivative extensions of Einstein gravity. We prove that the only theories susceptible of admitting solutions with…

High Energy Physics - Theory · Physics 2017-08-16 Pablo Bueno , Pablo A. Cano

Since the original derivation of Hawking radiation, there have been lots of alternative approaches to show the same fact that black holes emit particles as hot bodies with a temperature. These alternative methods generally rely on different…

General Relativity and Quantum Cosmology · Physics 2025-09-03 Chon Man Sou

In general relativity without a cosmological constant, a classical theorem due to Hawking states that stationary black holes must be topologically spherical. This result is one of the several ingredients that collectively imply the…

General Relativity and Quantum Cosmology · Physics 2020-11-18 Sourabh Nampalliwar , Arthur G. Suvorov , Kostas D. Kokkotas

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of…

High Energy Physics - Theory · Physics 2015-05-06 H. Lu , A. Perkins , C. N. Pope , K. S. Stelle

In the case of a large class of static spherically symmetric black hole solutions in higher order modified gravity models, an expression for the associated energy is proposed and identified as a quantity proportional to the constant of…

General Relativity and Quantum Cosmology · Physics 2011-08-08 Guido Cognola , Olesya Gorbunova , Lorenzo Sebastiani , Sergio Zerbini

Non-minimal couplings between matter and curvature tensors arise in many different contexts. Such couplings modify solutions of general relativity (GR) and therefore can be probed in various astrophysical systems. A particularly interesting…

General Relativity and Quantum Cosmology · Physics 2025-10-31 Stephon Alexander , Tatsuya Daniel , Tucker Manton

Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same…

General Relativity and Quantum Cosmology · Physics 2024-02-06 Alexey Golovnev , Maria-Jose Guzman

Physics beyond the Standard Model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle "forces" all forms of matter to fall in the same way, and it is therefore…

General Relativity and Quantum Cosmology · Physics 2015-11-16 Miguel Zilhão , Helvi Witek , Vitor Cardoso

The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring…

High Energy Physics - Theory · Physics 2015-01-26 S. Deser , K. Izumi , Y. C. Ong , A. Waldron

Unless the reality of spacetime singularities is assumed, astrophysical black holes cannot be identical to their mathematical counterparts obtained as solutions of the Einstein field equations. Mechanisms for singularity regularization…

General Relativity and Quantum Cosmology · Physics 2021-02-01 Raúl Carballo-Rubio , Francesco Di Filippo , Stefano Liberati , Matt Visser

Approximating light charged point-like particles in terms of (nonextremal) dilatonic black holes is shown to lead to certain pathologies in Planckian scattering in the eikonal approximation, which are traced to the presence of a (naked)…

High Energy Physics - Theory · Physics 2014-11-18 Saurya Das , Parthasarathi Majumdar