160 citations · 1.3k across the 49 of their papers we have counts for
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Spherically symmetric Riemannian manifolds of constant scalar curvature and their conformally flat representations
Patryk Mach, Niall Ó Murchadha
All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are c…
Constant Mean Curvature Slices of the Reissner-Nordström Spacetime
Patrick Tuite, Niall Ó Murchadha
In order to specify a foliation of spacetime by spacelike hypersurfaces we need to place some restriction on the initial data and from this derive a way to calculate the lapse func…
Potentials for transverse trace-free tensors
Rory Conboye, Niall Ó Murchadha
In the initial conditions of the formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT te…
Scaling up the extrinsic curvature in asymptotically flat gravitational initial data: Generating trapped surfaces
Shan Bai, Niall Ó Murchadha
The existence of the initial value constraints means that specifying initial data for the Einstein equations is non-trivial. The standard method of constructing initial data in the…
Scaling up the extrinsic curvature in gravitational initial data
Shan Bai, Niall Ó Murchadha
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect th…
Intrinsic time gravity and the Lichnerowicz-York equation
Niall Ó Murchadha, Chopin Soo, Hoi-Lai Yu
We investigate the effect on the Hamiltonian structure of general relativity of choosing an intrinsic time to fix the time slicing. 3-covariance with momentum constraint is maintai…
Conformal Superspace: the configuration space of general relativity
Julian Barbour, Niall Ó Murchadha
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We hav…
The Brown-York mass and the Thorne hoop conjecture
Niall O Murchadha, Roh-Suan Tung, Naqing Xie +1
The Thorne hoop conjecture is an attempt to make precise the notion that gravitational collapse occurs if enough energy is compressed into a small enough volume, with the `size' be…
Bowen-York trumpet data and black-hole simulations
Mark Hannam, Sascha Husa, Niall Ó Murchadha
The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum vi…
Quasilocal Energy in General Relativity
Niall Ó Murchadha, Roh-Suan Tung, Naqing Xie
We show that the quasilocal mass defined by Wang and Yau is not well-defined at spatial infinity. It approaches neither the ADM mass nor the ADM energy. We suggest an alternative s…
Stationary hyperboloidal slicings with evolved gauge conditions
Frank Ohme, Mark Hannam, Sascha Husa +1
We analyze stationary slicings of the Schwarzschild spacetime defined by members of the Bona-Masso family of slicing conditions. Our main focus is on the influence of a non-vanishi…
With commuting Killing vectors, the lapse and shift of one Killing vector are constants along the other
Niall O Murchadha
Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shif…
Equilibrium initial data for moving puncture simulations: The stationary 1+log slicing
T. W. Baumgarte, Z. B. Etienne, Y. T. Liu +4
We propose and explore a "stationary 1+log" slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data wi…
Some remarks on the size of bodies and black holes
Gregory J. Galloway, Niall O'Murchadha
We consider the application of stable marginally outer trapped surfaces to problems concerning the size of material bodies and the area of black holes. The results presented extend…
The Liu-Yau mass as a good quasi-local energy in general relativity
Niall O Murchadha
A quasi-local mass has been a long sought after quantity in general relativity. A recent candidate has been the Liu-Yau mass. One can show that the Liu-Yau mass of any two-surface…
Where do moving punctures go?
Mark Hannam, Sascha Husa, Niall Ó Murchadha +3
Currently the most popular method to evolve black-hole binaries is the ``moving puncture'' method. It has recently been shown that when puncture initial data for a Schwarzschild bl…
The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
Thomas W. Baumgarte, Niall Ó Murchadha, Harald P. Pfeiffer
We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of sol…
Geometry and Regularity of Moving Punctures
Mark Hannam, Sascha Husa, Denis Pollney +2
Significant advances in numerical simulations of black-hole binaries have recently been achieved using the puncture method. We examine how and why this method works by evolving a s…
Readings of the Lichnerowicz-York equation
Niall O Murchadha
James York, in a major extension of André Lichnerowicz's work, showed how to construct solutions to the constraint equations of general relativity. The York method consists of choo…
The Jang equation, apparent horizons, and the Penrose inequality
Edward Malec, Niall Ó Murchadha
The Jang equation in the spherically symmetric case reduces to a first order equation. This permits an easy analysis of the role apparent horizons play in the (non)existence of sol…
The physical gravitational degrees of freedom
Edward Anderson, Julian Barbour, Brendan Z. Foster +2
When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dime…
Non CMC Conformal Data Sets Which Do Not Produce Solutions of the Einstein Constraint Equations
James Isenberg, Niall Ó Murchadha
The conformal formulation provides a method for constructing and parametrizing solutions of the Einstein constraint equations by mapping freely chosen sets of conformal data to sol…
Embedding spherical spacelike slices in a Schwarzschild solution
Niall Ó Murchadha, Krzysztof Roszkowski
Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothl…
Constant mean curvature slices in the extended Schwarzschild solution and collapse of the lapse: Part I
Edward Malec, Niall Ó Murchadha
We give a detailed description of the constant mean curvature foliations in the Schwarzschild solution; show that the lapse collapses exponentially, and compute the exponent.