## BIOGRAPHY

## Research Interests

The following is a brief statement of my research strategy and the impact I have had on my discipline.

General Relativity, when regarded as a dynamical system, splits, just like the Maxwell equations, into constraints and propogation equations. If we wish to solve the Einstein equations, we first need to solve the constraints to pose initial data. These, unfortunately, reflect the fundemental nonlinearity of the gravitational field. We split the initial data into independent and dependent parts. This splitting should be such that, upon substitution into the constraints, the equations reduce to an elliptic system. There are several ways of doing this.

I regard myself as a mathematical relativist, and most of my career has been devoted to understanding and solving these elliptic systems. I try and keep in contact with the pure mathematics community. I see myself as a bridge between the mathematicians and the physicists. Elliptic systems theory, from a geometrical perspective, has been a rapidly developing area, and physicists have much to learn from it. At the same time, the mathematicians are, usually, interested in generality while I am interested in one specific elliptic system, the Einstein constraints. Thus I do not just take existing, textbook, theorems and apply them. These have to be molded to suit and often the outcomes are much better than a straightforward application would lead one to expect.

The other `half' of the Einstein equations, the propogation equations, are equally challenging. Again, as in Maxwell's theory, these can be written as a hyperbolic system if one makes an appropriate choice.

The people who really use this approach to gravity are the numerical relativists. This exercise, solvin

g the Einstein equations on a (super-)computer, has been a disaster. The keystone problem, binary black hole collisions, has been a story of 20 years of continuing failure. However, amazingly, everything worked in 2003. Now the question is just improving the codes.

In the last few years, I have set out to attach myself to this numerical community. It is not that I have any intention of writing code, it is that a whole range of interesting mathematical and analytical problems have been thrown up in the process of solving the binary black hole problem. The numerical community is so pleased at having codes that work that no one wants to ask `why'? I think that I am one of a few people who understands the `why', not just the `how'. This makes the possibility of improvement much cleaner.

This improvement will take several forms. We need better specification of the initial data, which is where my understanding of the constraints comes in. The final aim is to predict the gravitational wave output. Therefore we also need better ways of writing the hyperbolic part, and also better ways of posing boundary conditions.

Therefore I see myself as a double bridge, one link is between the pure mathematicians and the analytical relativity community, the other is between the mathematical and the numerical relativists. I think it works well.

The following highlights my top three research outputs and describes their significance.

M. Hannam, S. Husa, F. Ohme, B. Bruegmann and N. Ó Murchadha, `Wormholes and trumpets: the Schwarzschild spacetime for the moving puncture generation", Phys. Rev. D78, 064020 (2008).

This article is essentially the extended version of the Phys. Rev. Lett. 99, 241102(2007). It turns out that essentially all the successful binary black hole codes use the same formulation of the Einstein equations. This is called the `moving puncture' method. It is a surprise that this technique works, because the data specification has two points in it (the locations of the black holes) where things diverge, and thus should give terrible problems to the numerics. They do not. This article explains why. The grid points get dragged away from the `bad' points very rapidly and so the codes, in some sense, are self-healing. We demonstrate this effect by applying the `moving puncture' method to the Schwarzschild solution where we can use a mixture of analytic and numerical techniques to understand what is happening.

E. Anderson, J. Barbour, B. Foster, B. Kelleher and N. Ó Murchadha, `The physical gravitational degrees of freedom", Class. Quant. Grav. 22, 1795 - 1802 (2005).

Julian Barbour is an `independent scientist'who works in general relativity and has very interesting ideas on the structure of the Einstein equations. He is also an expert on the history of mechanics, `The discovery of dynamics', published by the OUP(2001), is a key work. I have had an extended collaboration with Julian and this is one of the articles we wrote together. The other 3 authors were graduate students at the time. Julian had the idea that `scale-free dynamics' is the key to understanding the Einstein equations. This is an implementation of this idea.

E. Malec and N. Ó Murchadha, `Constant mean curvature slices of the Schwarzschild solution", Phys. Rev. D68, 124019 (2003).

Mass hyperboloids in Minkowski space are objects that constant mean curvature surfaces. The have the property that they are spacelike, but go null at infinity. This article is an analysis of the equivalent such surfaces in the Schwarzschild solution. We were able to write down everything analytically. The property that CMC surfaces are spacelike means that initial data can be posed on them easily, the fact that they go null at infinity means that gravitational waves can be easily observed on them. I expect that such CMC slices will be used in future in the binary black hole problem.

## Publications

### Book Chapters

Year | Publication | |
---|---|---|

(1993) | 'Brill Waves [X4003]' Ó Murchadha, N.; (1993) 'Brill Waves [X4003]' In: Directions in General Relativity. [Details] | |

(1992) | 'Boundary Conditions for the Momentum Constraint [X4000]' Ó Murchadha, N.; (1992) 'Boundary Conditions for the Momentum Constraint [X4000]' In: R. d'Inverno (eds). Approaches to Numerical Relativity. UK: Cambridge University Press. [Details] | |

(1991) | 'The Yamabe Constant'' N. Ó Murchadha; (1991) 'The Yamabe Constant'' In: J.C. D'Olivo (eds). Proceedings of SILARG VII. Singapore: World Scientific Press. [Details] |

### Peer Reviewed Journals

Year | Publication | |
---|---|---|

(2008) | 'Wormholes and trumpets: the Schwarzschild spacetime for the moving puncture generation' M. Hannam, S. Husa, F. Ohme, B. Bruegmann and N. Ó Murchadha,; (2008) 'Wormholes and trumpets: the Schwarzschild spacetime for the moving puncture generation' [Details] | |

(2008) | 'Some remarks on the size of bodies and black holes' G. Galloway and N. Ó Murchadha; (2008) 'Some remarks on the size of bodies and black holes' [Details] | |

(2007) | 'The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach' T. Baumgarte, N. Ó Murchadha and H. Pfeiffer; (2007) 'The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach' [Details] | |

(2007) | 'Geometry and regularity of moving punctures' M. Hannam, S. Husa, D. Pollney, B. Bruegmann and N. Ó Murchadha, ; (2007) 'Geometry and regularity of moving punctures' [Details] | |

(2007) | 'Where do moving punctures go?' M. Hannam, S. Husa, N. Ó Murchadha, B. Brugmann, J. Gonzalez and U. Sperhake; (2007) 'Where do moving punctures go?' [Details] | |

(2006) | 'Embedding spherical slices in a Schwarzschild solution' N. Ó Murchadha and K. Roszkowski; (2006) 'Embedding spherical slices in a Schwarzschild solution' [Details] | |

(2005) | 'The physical gravitational degrees of freedom' E. Anderson, J. Barbour, B. Foster, B. Kelleher and N. Ó Murchadha; (2005) 'The physical gravitational degrees of freedom' [Details] | |

(2005) | 'Readings of the Lichnerowicz ¿ York equation' N. Ó Murchadha; (2005) 'Readings of the Lichnerowicz ¿ York equation' [Details] | |

(2004) | 'A comment on Liu and Yau¿s positive quasi-local mass' N. Ó Murchadha, L. Szabados, K. Tod,; (2004) 'A comment on Liu and Yau¿s positive quasi-local mass' [Details] | |

(2004) | 'Non CMC conformal data sets ¿' J. Isenberg and N. Ó Murchadha,; (2004) 'Non CMC conformal data sets ¿' [Details] | |

(2004) | 'The Jang equation, apparent horizons, and the Penrose Inequality' E. Malec and N. Ó Murchadha; (2004) 'The Jang equation, apparent horizons, and the Penrose Inequality' [Details] | |

(2003) | 'Constant mean curvature slices' E. Malec and N. Ó Murchadha; (2003) 'Constant mean curvature slices' [Details] | |

(2003) | 'Scale-invariant gravity: geometrodynamics' E. Anderson, J. Barbour, B. Foster and N. Ó Murchadha; (2003) 'Scale-invariant gravity: geometrodynamics' [Details] | |

(2002) | 'Relativity without relativity' J. Barbour, B. Foster and N. Ó Murchadha; (2002) 'Relativity without relativity' [Details] | |

(2002) | 'Constrained hamiltonians and local square-root actions' N. Ó Murchadha; (2002) 'Constrained hamiltonians and local square-root actions' [Details] | |

(2000) | 'Existence and uniqueness of the BCT gauge' D. Garfinkle, C. Gundlach, J. Isenberg and N. Ó Murchadha,; (2000) 'Existence and uniqueness of the BCT gauge' [Details] | |

(1999) | 'Bounds on 2m/R for static spherical objects' J. Guven and N. Ó Murchadha; (1999) 'Bounds on 2m/R for static spherical objects' [Details] | |

(1999) | 'Flat foliations of spherically symmetric geometries' J. Guven and N. Ó Murchadha; (1999) 'Flat foliations of spherically symmetric geometries' [Details] | |

(1998) | 'Spherical scalar waves and gravity - redshift and backreaction' E. Malec, N. Ó Murchadha and T. Chmaj,; (1998) 'Spherical scalar waves and gravity - redshift and backreaction' [Details] | |

(1998) | 'Late time behaviour of the maximal slicing of the Schwarzschild black hole' R. Beig and N. Ó Murchadha,; (1998) 'Late time behaviour of the maximal slicing of the Schwarzschild black hole' [Details] | |

(1997) | 'Sufficient Conditions for Apparent Horizons in Spherically Symmetric General Relativity [X4017]' Guven, J.; Ó Murchadha, N.; (1997) 'Sufficient Conditions for Apparent Horizons in Spherically Symmetric General Relativity [X4017]' [Details] | |

(1997) | 'Necessary Conditions for Apparent Horizons and Singularities in Spherical General Relativity [X4018]' Guven, J.; Ó Murchadha, N.; (1997) 'Necessary Conditions for Apparent Horizons and Singularities in Spherical General Relativity [X4018]' [Details] | |

(1997) | 'Geometric Bounds in Spherically Symmetric General Relativity [X4016]' Guven, J.; Ó Murchadha, N.; (1997) 'Geometric Bounds in Spherically Symmetric General Relativity [X4016]' [Details] | |

(1996) | 'Trapped surfaces in cosmological spacetimes' E. Malec and N. Ó Murchadha; (1996) 'Trapped surfaces in cosmological spacetimes' [Details] | |

(1996) | 'The Momentum Constraint of General Relativity and Spatial Conformal Isometries [X4012]' Beig, R.; Ó Murchadha, N.; (1996) 'The Momentum Constraint of General Relativity and Spatial Conformal Isometries [X4012]' [Details] | |

(1996) | 'The Constant Mean Curvature Slices and Trapped Surfaces in Asymptotically Flat Spherical Spacetimes [X4014]' Iriondo, M.; Malec, E.; Ó Murchadha, N.; (1996) 'The Constant Mean Curvature Slices and Trapped Surfaces in Asymptotically Flat Spherical Spacetimes [X4014]' [Details] | |

(1996) | 'Vacuum Spacetimes With Future Trapped Surfaces [X4015]' Beig, R.; Ó Murchadha, N.; (1996) 'Vacuum Spacetimes With Future Trapped Surfaces [X4015]' [Details] | |

(1996) | 'Trapped Surfaces in Cosmological Spacetimes [X4013]' Malec, E.; Ó Murchadha, N.; (1996) 'Trapped Surfaces in Cosmological Spacetimes [X4013]' [Details] | |

(1995) | 'The Constraints in Spherically Symmetric Gravity. I. Optical Scalars [X4010]' Guven, J.; Ó Murchadha, N.; (1995) 'The Constraints in Spherically Symmetric Gravity. I. Optical Scalars [X4010]' [Details] | |

(1995) | 'The Constraints in Spherically Symmetric Gravity. II. Identifying the Configuration Space [X4011]' Guven, J.; Ó Murchadha, N.; (1995) 'The Constraints in Spherically Symmetric Gravity. II. Identifying the Configuration Space [X4011]' [Details] | |

(1995) | 'Weakly Decaying Static and Stationary Solutions to the Einstein Equations [X4009]' Kennefick, D.; Ó Murchadha, N.; (1995) 'Weakly Decaying Static and Stationary Solutions to the Einstein Equations [X4009]' [Details] | |

(1994) | 'Trapped surfaces in vacuum spacetimes'' R. Beig and N. Ó Murchadha; (1994) 'Trapped surfaces in vacuum spacetimes'' [Details] | |

(1994) | 'Trapped Surfaces and the Penrose Inequality in Spherically Symmetric Spacetimes [X4007]' Malec, E.; Ó Murchadha, N.; (1994) 'Trapped Surfaces and the Penrose Inequality in Spherically Symmetric Spacetimes [X4007]' [Details] | |

(1994) | 'Optical Scalars and Singularity Avoidance in Spherical Spacetimes [X4008]' Malec, E.; Ó Murchadha, N.; (1994) 'Optical Scalars and Singularity Avoidance in Spherical Spacetimes [X4008]' [Details] | |

(1994) | 'Trapped Surfaces in Spherical Expanding Open Universes [X4006]' Brauer, U.; Malec, E.; Ó Murchadha, N.; (1994) 'Trapped Surfaces in Spherical Expanding Open Universes [X4006]' [Details] | |

(1994) | 'Trapped Surfaces in Vacuum Spacetimes [X4005]' Beig, R.; Ó Murchadha, N.; (1994) 'Trapped Surfaces in Vacuum Spacetimes [X4005]' [Details] | |

(1993) | 'There Are No [R]^3^ x [S]^1^ Vacuum Gravitational Instantons [X4001]' Ó Murchadha, N.; Shanahan, H.; (1993) 'There Are No [R]^3^ x [S]^1^ Vacuum Gravitational Instantons [X4001]' [Details] | |

(1993) | 'Trapped Surfaces and Spherical Closed Cosmologies [X4002]' Malec, E.; Ó Murchadha, N.; (1993) 'Trapped Surfaces and Spherical Closed Cosmologies [X4002]' [Details] | |

(1993) | 'Is the Universe Open or Closed? [X4004]' Malec, E.; Ó Murchadha, N.; (1993) 'Is the Universe Open or Closed? [X4004]' [Details] | |

(1991) | 'Trapped surfaces due to concentration of gravitationsal radiation' R. Beig and N. Ó Murchadha; (1991) 'Trapped surfaces due to concentration of gravitationsal radiation' [Details] | |

(1990) | 'On maximal surfaces in asymptotically flat spacetimes' R. Bartnik, P. Chrusciel and N. Ó Murchadha; (1990) 'On maximal surfaces in asymptotically flat spacetimes' [Details] | |

(1990) | 'Binding energy for spherical stars' P. Bizon, E. Malec and N. Ó Murchadha; (1990) 'Binding energy for spherical stars' [Details] | |

(1990) | 'Magnetic monopoles and superconducting cosmic strings' J. Mehegan and N. Ó Murchadha; (1990) 'Magnetic monopoles and superconducting cosmic strings' [Details] | |

(1989) | 'Trapped surfaces due to concentration of matter in spherically symmetric geometries'' P. Bizon, E. Malec and N. Ó Murchadha; (1989) 'Trapped surfaces due to concentration of matter in spherically symmetric geometries'' [Details] | |

(1989) | 'The Yamabe theorem and general relativity' N. Ó Murchadha; (1989) 'The Yamabe theorem and general relativity' [Details] | |

(1988) | 'Trapped surfaces in spherical stars'' P. Bizon, E. Malec and N. Ó Murchadha; (1988) 'Trapped surfaces in spherical stars'' [Details] | |

(1987) | 'The Poincar\'e group as symmetry group of canonical general relativity' R. Beig and N. Ó Murchadha, ; (1987) 'The Poincar\'e group as symmetry group of canonical general relativity' [Details] | |

(1987) | 'The bag of gold reopened' N. Ó Murchadha; (1987) 'The bag of gold reopened' [Details] | |

(1987) | 'Average energy density and the size of the universe' N. Ó Murchadha; (1987) 'Average energy density and the size of the universe' [Details] | |

(1986) | 'Total energy-momentum in general relativity'' N. Ó Murchadha; (1986) 'Total energy-momentum in general relativity'' [Details] | |

(1986) | 'How large can a star be?' N. Ó Murchadha; (1986) 'How large can a star be?' [Details] | |

(1986) | 'Global existence of Yang - Mills ¿ Higgs monopoles' J. Burzlaff and N. Ó Murchadha; (1986) 'Global existence of Yang - Mills ¿ Higgs monopoles' [Details] | |

(1985) | 'Search for simplicity' N. Ó Murchadha; (1985) 'Search for simplicity' [Details] | |

(1983) | 'Asymptotic behaviour of gravitational instantons on $R^4$' N. Ó Murchadha; (1983) 'Asymptotic behaviour of gravitational instantons on $R^4$' [Details] | |

(1982) | 'mathematical horses for elementary physics courses' N. Ó Murchadha and C. O'Sullivan; (1982) 'mathematical horses for elementary physics courses' [Details] | |

(1982) | 'Black hole radiation made simple' N. Ó Murchadha; (1982) 'Black hole radiation made simple' [Details] | |

(1981) | 'The boost problem in general relativity' D. Christodoulou and N. Ó Murchadha; (1981) 'The boost problem in general relativity' [Details] | |

(1980) | 'Killing vectors and maximal slicing in general relativity' N. Ó Murchadha; (1980) 'Killing vectors and maximal slicing in general relativity' [Details] | |

(1977) | 'Positivity of energy and stationary solutions in general relativity' N. Ó Murchadha,; (1977) 'Positivity of energy and stationary solutions in general relativity' [Details] | |

(1976) | 'Initial value problem of general relativity III' J. Isenberg, N. Ó Murchadha and J. W. York; (1976) 'Initial value problem of general relativity III' [Details] | |

(1976) | 'Maximal slicings' M. Cantor, A. Fischer, J. Marsden, N. Ó Murchadha and J. W. York; (1976) 'Maximal slicings' [Details] | |

(1976) | 'Nonmaximal solutions to the initial value constraints' N. Ó Murchadha; (1976) 'Nonmaximal solutions to the initial value constraints' [Details] | |

(1976) | 'Gravitational potentials' N. Ó Murchadha and J. W. York; (1976) 'Gravitational potentials' [Details] | |

(1974) | 'Initial value problem of general relativity I' N. Ó Murchadha and J. W. York, ; (1974) 'Initial value problem of general relativity I' [Details] | |

(1974) | 'Initial value problem of general relativity II' N. Ó Murchadha and J. W. York; (1974) 'Initial value problem of general relativity II' [Details] | |

(1974) | 'Gravitational energy'' N. Ó Murchadha and J. W. York; (1974) 'Gravitational energy'' [Details] | |

(1973) | 'Existence and uniqueness of solutions to the Hamiltonian constraint of general relativity'' N. Ó Murchadha and J. W. York,; (1973) 'Existence and uniqueness of solutions to the Hamiltonian constraint of general relativity'' [Details] |

### Conference Contributions

Year | Publication | |
---|---|---|

(2009) | 12th Marcel Grossman Conference,N. Ó Murchadha; (2009) Annual member of the International Coordinating Committee. [Conference Organising Committee Member], 12th Marcel Grossman Conference, Paris, France , 12-JUL-09 - 18-JUL-09 | |

(2006) | 11th Marcel Grossman Conference,N. Ó Murchadha; (2006) Annual member of the International Coordinating Committee. [Conference Organising Committee Member], 11th Marcel Grossman Conference, Berlin , 23-JUL-06 - 29-JUL-06 | |

(2004) | GR17,N. Ó Murchadha; (2004) On both the organising committee and the scientific committee. [Conference Organising Committee Member], GR17, Dublin , 18-JUL-04 - 23-JUL-04 | |

(2003) | 10th Marcel Grossman Conference,N. Ó Murchadha; (2003) Annual member of the International Coordinating Committee. [Conference Organising Committee Member], 10th Marcel Grossman Conference, Rio de Janeiro, Brazil , 20-JUL-03 - 26-JUL-03 |

## Professional Activities

### Associations

Assocation | Function | From / To | |
---|---|---|---|

Radio na Gaeltachta | Regular appearances on Radio na Gaeltachta to discuss science | 01-JAN-80 / 28-MAY-10 | |

Classical and Quantum Gravity | Editorial Board | 01-JUN-04 / 28-MAY-10 |

### Employment

Employer | Position | From / To | |
---|---|---|---|

Princeton University | Research Associate | 01-JAN-73 / 01-SEP-73 | |

UNC Chapel Hill | Research Associate | 01-SEP-73 / 01-SEP-75 | |

U. C. Cardiff | Research Associate | 01-OCT-75 / 01-OCT-76 | |

UCC | Associate Professor | 01-OCT-76 / 28-MAY-10 |

### Education

Year | Instituion | Qualification | Subject | |
---|---|---|---|---|

1968 | UCC | B.Sc. | '' | |

1973 | Princeton University | MA | '' | |

1973 | Princeton University | PHD | '' |

### Other Activities

Description | |
---|---|

I have been a regular contributor on Radio na Gaeltachta to discuss science since the 1980s. | |

External Research Funding - National - Exchequer. Indicate Status: P1. Title of Research Project: Analytic support of numerical relativity. Total amount of grant: 173,799e. Period of Grant: 09/06 to 09/09. |