The general relativistic constraint equations
A Carlotto - Living Reviews in Relativity, 2021 - Springer
We present the state-of-the-art concerning the relativistic constraints, which describe the
geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review …
geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review …
Approximations of elliptic optimal control problems with controls acting on a lower dimensional manifold
W Gong, G Wang, N Yan - SIAM JOURNAL on Control and Optimization, 2014 - SIAM
In this paper, we study finite element approximations to some elliptic optimal control
problems with controls acting on a lower dimensional manifold which can be a point, a …
problems with controls acting on a lower dimensional manifold which can be a point, a …
Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries
M Holst, C Meier - Classical and Quantum Gravity, 2014 - iopscience.iop.org
In this article we further develop the solution theory for the Einstein constraint equations on
an n-dimensional, asymptotically Euclidean manifold $\mathcal {M} $ with interior boundary …
an n-dimensional, asymptotically Euclidean manifold $\mathcal {M} $ with interior boundary …
The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools
On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave
Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light …
Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light …
Numerical bifurcation analysis of the conformal method
The conformal formulation of the Einstein constraint equations has been studied intensively
since the modern version of the conformal method was first pub-lished in the early 1970s …
since the modern version of the conformal method was first pub-lished in the early 1970s …
Non-CMC solutions of the Einstein constraint equations on compact manifolds with apparent horizon boundaries
M Holst, C Meier, G Tsogtgerel - Communications in Mathematical Physics, 2018 - Springer
In this article we continue our effort to do a systematic development of the solution theory for
conformal formulations of the Einstein constraint equations on compact manifolds with …
conformal formulations of the Einstein constraint equations on compact manifolds with …
Sobolev regularity of compactified 3-manifolds and the ADM Center of Mass
R Avalos - arXiv preprint arXiv:2403.04034, 2024 - arxiv.org
In this paper, we address the existence of preferred asymptotic coordinates on
asymptotically Euclidean (AE) manifolds $(M^ 3, g) $ such that $ g $ admits an …
asymptotically Euclidean (AE) manifolds $(M^ 3, g) $ such that $ g $ admits an …
The Einstein constraint equations on compact manifolds with boundary
J Dilts - Classical and Quantum Gravity, 2014 - iopscience.iop.org
We continue the study of the Einstein constraint equations on compact manifolds with
boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and …
boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and …
Initial data for rotating cosmologies
P Bizoń, S Pletka, W Simon - Classical and Quantum Gravity, 2015 - iopscience.iop.org
We revisit the construction of maximal initial data on compact manifolds in vacuum with
positive cosmological constant via the conformal method. We discuss, extend and apply …
positive cosmological constant via the conformal method. We discuss, extend and apply …
Energy in Fourth-Order Gravity
R Avalos, JH Lira, N Marque - Annales Henri Poincaré, 2024 - Springer
In this paper we make a detailed analysis of conservation principles in the context of a family
of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we …
of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we …