# Eric Poisson

Professor, Third Year Coordinator
Email:
epoisson@uoguelph.ca
Phone number:
519-824-4120 x53653
Office:
MacN 452
Summary:

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I obtained a BSc degree in physics from Laval University in 1987, a MSc degree in theoretical physics from the University of Alberta in 1989, and a PhD in theoretical physics from the University of Alberta in 1991. My thesis work was carried out under the supervision of Werner Israel; the topic was the internal structure of black holes.

After obtaining my PhD I spent three years (1991-1994) as a post-doctoral fellow at the California Institute of Technology, where I worked under the supervision of Kip Thorne. And before coming to Guelph in 1995, I spent a year (1994-1995) at Washington University in St. Louis, working under the supervision of Clifford Will.

• I am an affiliate member of the Perimeter Institute for Theoretical Physics, a privately funded research institute based in Waterloo, Canada.
• I served as President of the International Society on General Relativity and Gravitation, for a three-year term from 2016 to 2019; I will serve as Past-President until 2022
• I am a member of the Editorial Board of Physical Review D, a leading publication in gravitational and particle physics.
• I was a member of the Editorial Board (Divisional Associate Editor for Astrophysics) of the prestigious research journal Physical Review Letters, from 2009 to 2016. I was also a member of the Editorial Board of Classical and Quantum Gravity, a leading publication in gravitational physics, from 2009 to 2017.

• In 2005 I was awarded the Herzberg Medal by the Canadian Association of Physicists, for outstanding achievement by a physicist aged 40 or less.
• In 2008 I was elected Fellow of the American Physical Society, “for important contributions to the theory of gravitational radiation from compact bodies orbiting black holes, to the theory of back-reaction of the emitted radiation on their motions, and to understanding the implications for gravitational-wave detection."

The research activities of the Guelph Gravitation Group have recently been divided into two broad streams. The first stream is concerned with the physics of black holes and neutron stars in tidal environments. The second is concerned with the gravitational self-force.

Compact bodies in tidal environments. What happens to a black hole or a neutron star when it is not isolated, but placed in the presence of other bodies which exert tidal forces on it? To answer this question requires a description of the tidal environment, a computation of the gravitational perturbation created by the external bodies, and the extraction of physical, measurable consequences. Among the most exciting of those is the effect of the tidal coupling on the phasing of gravitational waves; a measurement of this effect will allow a black hole or a neutron star to be observationally distinguished from other types of compact bodies.

Gravitational self-force. The term "gravitational self-force" refers to the motion of a small-mass body around a much larger body, in a treatment that goes beyond the test-mass description. In this treatment, the small mass creates a (small but significant) perturbation in the gravitational field of the large body. The perturbation affects the motion of the small body --- the motion is no longer geodesic, but accelerated, and the body is said to move in response to its own gravitational self-force. The perturbation also propagates outward in the form of gravitational waves. What is the nature of the self-forced motion, and what information concerning the strong-field dynamics can be extracted from the gravitational waves? These are the questions that my research group and I have been exploring.

A description of recent research projects carried out with the members of my research group follows below.

### Self-force and fluid resonances

The gravitational self-force acting on a particle orbiting a massive central body has thus far been computed for vacuum spacetimes involving a black hole. In this work, post-doctoral fellows Soichiro Isoyama, Raissa Mendes, and I continue an ongoing effort to study the self-force in nonvacuum situations. We replace the black hole by a material body consisting of a perfect fluid, and determine the impact of the fluid's dynamics on the self-force and resulting orbital evolution. We show that as the particle inspirals toward the fluid body, its gravitational perturbations trigger a number of normal modes of the fluid-gravity system, which produce resonant features in the conservative and dissipative components of the self-force. As a proof-of-principle, we demonstrate this phenomenon in a simplified framework in which gravity is mediated by a scalar potential satisfying a wave equation in Minkowski spacetime.

### Tidal deformation of a slowly rotating compact body

Graduate student Philippe Landry and I are investigating the tidal deformation of compact bodies in general relativity, allowing the body to rotate. We keep the tidal environment generic, and account for the coupling betwen the tidal and rotational perturbations. The body's response to the external field is measured in part by the familiar gravitational Love numbers, but we find that the coupling between the body's rotation and the tidal environment requires the introduction of an additional set of Love numbers. In a recent development, we discovered that the tidal response of the body is time-dependent even when the tidal field is stationary.

### Relativistic theory of surficial Love numbers

A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated several years ago by Damour and Nagar. Graduate student Philippe Landry and I revisited this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refined the definition of surficial Love numbers proposed by Damour and Nagar, and formulated it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we developed a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derived a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and showed that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplified the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

### Self-force in nonvacuum spacetimes

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. Former graduate student Peter Zimmerman and I provided a foundation for such extensions, and carried out a concrete formulation of the gravitational self-force in two specific cases. In the first we considered a particle with scalar charge moving in a background spacetime that contains a background scalar field. In the second we considered a particle with electric charge moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields.

### Self-force around a five-dimensional black hole

Former undergraduate student Matt Beach, my colleague Bernie Nickel, and I computed the electromagnetic self-force acting on a charged particle held in place outside a five-dimensional black hole. The self-force is repulsive at large distances, and its behaviour is related to a model according to which the force results from a gravitational interaction between the black hole and the distribution of electrostatic field energy attached to the particle. The model, however, is shown to become inadequate at small distances from the black hole, where the self-force changes sign and becomes attractive.

### Self-force as a cosmic censor

Former graduate student Peter Zimmerman, postdoctoral fellow Ian Vega, PhD student Roland Hass, and I examined Hubeny's scenario according to which a charged black hole can absorb a particle and be driven toward a final state in which its charge exceeds the mass, signalling the destruction of the black hole. Our analysis incorporates the particle's electromagnetic self-force and the energy radiated to infinity in the form of electromagnetic waves. With these essential ingredients, our sampling of the parameter space reveals no instances of an overcharged final state, and we conjecture that the self-force acts as a cosmic censor, preventing the destruction of a black hole by the absorption of a charged particle. We argue, on the basis of the third law of black-hole mechanics, that this conclusion is robust and should apply to attempts to overspin a Kerr black hole.

### Self-force in Schwarschild-de Sitter spacetime

Former graduate student Joseph Kuchar, postdoctoral fellow Ian Vaga, and I computed the self-force acting on an electric charge at rest in Schwarzschild-de Sitter spacetime, allowing the cosmological constant to be either positive or negative. In the case of a positive cosmological constant, we showed that the self-force is always positive, representing a repulsion from the black hole, and monotonically decreasing with increasing distance from the black hole. The spectrum of results is richer in the case of a negative cosmological constant. Here the self-force is not always positive and not always monotonically decreasing. The self-force also approaches a constant asymptotic value when the charge is moved to large cosmological distances; this feature can be explained in terms of an interaction between the charge and the conformal boundary at infinity, which acts as a grounded conductor.

## Papers in refereed journals

1. B. Bonga and E. Poisson, Coulombic contribution to the flux of angular momentum in general relativity, Phys. Rev. D 99, 064024, 14 pages (2019).
2. B. Bonga, E. Poisson, and H. Yang, Self-torque and angular momentum balance for a spinning charged sphere, Am. J. Phys. 86, 839{848 (2018).
3. D.M. Podkowka, R.F.P. Mendes, and E. Poisson, Trace of the energy-momentum tensor and macroscopic properties of neutron stars, Phys. Rev. D 98, 064057, 9 pages (2018).
4. E. Poisson and E. Corrigan, Nonrotating black hole in a post-Newtonian tidal environment.II., Phys. Rev. D 97, 124048, 33 pages (2018).
5. E. Corrigan and E. Poisson, EZ gauge is singular on the event horizon, Class. Quantum Grav. 35, 137001, 8 pages (2018).
6. K. Davidson and E. Poisson, Self-force as a probe of global structure, Phys. Rev. D 97, 104030, 10 pages (2018).
7. E. Poisson and J. Dou¸cot, Gravitomagnetic tidal currents in rotating neutron stars, Phys. Rev. D 95, 044023, 19 pages (2017).
8. L. Lehner, R. C. Myers, E. Poisson, and R. D. Sorkin, Gravitational action with null boundaries, Phys. Rev. D 94, 084046, 36 pages (2016).
9. K. Chatziioannou, E. Poisson, N. Yunes, Improved next-to-leading order tidal heating and torquing of a Kerr black hole, Phys. Rev. D 94, 084043, 13 pages (2016).
10. S. Isoyama, R.F.P. Mendes, and E. Poisson, Self-force and fluid resonances, Class. Quantum Grav. 33, 085002, 34 pages (2016).
11. P. Landry and E. Poisson, Dynamical response to a stationary tidal field, Phys. Rev. D 92, 124041, 11 pages (2015).
12. P. Landry and E. Poisson, Gravitomagnetic response of an irrotational body to an applied tidal field, Phys. Rev. D 91, 104026, 13 pages (2015).
13. P. Landry and E. Poisson, Tidal deformation of a slowly rotating material body. External metric, Phys. Rev. D 91, 104018, 15 pages (2015).
14. E. Poisson, Tidal deformation of a slowly rotating black hole, Phys. Rev. D 91, 044004, 27 pages, Editor’s Suggestion (2015).
15. P. Zimmerman and E. Poisson, Gravitational self-force in nonvacuum spacetimes, Phys. Rev. D 90, 084030, 17 pages (2014).
16. P. Landry and E. Poisson, Relativistic theory of surficial Love numbers, Phys. Rev. D 89, 124011, 10 pages (2014).
17. M.J.S. Beach, E. Poisson, and B.G. Nickel, Self-force on a charge outside a five-dimensional black hole, Phys. Rev. D 89, 124014, 20 pages (2014).
18. P. Landry and E. Poisson, Relativistic theory of surficial Love numbers, Phys. Rev. D 89, 124011, 10 pages (2014).
19. P. Fromholz, E. Poisson, and C.M. Will, The Schwarzschild metric: It’s the coordinates, stupid!, Am. J. Phys. 82, 295–300 (2014).
20. J. Kuchar, E. Poisson, and I. Vega, Electromagnetic self-force on a static charge in Schwarzschild-de Sitter spacetimes, Class. Quantum Grav. 30, 235033, 13 pages (2013).
21. K. Chatziioannou, E. Poisson, and N. Yunes, Tidal heating and torquing of a Kerr black hole to nextto-leading order in the tidal coupling, Phys. Rev. D 87, 044022, 16 pages (2013).
22. P. Zimmerman, I. Vega, E. Poisson, and R. Haas, Self-force as a cosmic censor , Phys. Rev. D 87, 041501(R), 6 pages (2013).
23. M. Casals, E. Poisson, and I. Vega, Regularization of static self-forces, Phys. Rev. D 86, 064033, 23 pages (2012).
24. S. Isoyama and E. Poisson, Self-force as probe of internal structure, Class. Quantum Grav. 29, 155012, 17 pages (2012).
25. I. Vega, E. Poisson, and R. Massey, Intrinsic and extrinsic geometries of a tidally deformed black hole, Class. Quantum Grav. 28, 175006, 26 pages (2011).
26. Eric Poisson, Adam Pound, and Ian Vega, The motion of point particles in curved spacetime, Living Rev. Relativity 14, Online article: http://www.livingreviews.org/lrr-2011-7 (2011).
27. C.G. Gray and E. Poisson, When action is not least for orbits in general relativity, Am. J. Phys. 79, 43–55 (2011).
28. E. Poisson and I. Vlasov, Geometry and dynamics of a tidally deformed black hole, Phys. Rev. D 81, 024029, 42 pages (2010).
29. S. Comeau and E. Poisson, Tidal interaction of a small black hole in the field of a large Kerr black hole, Phys. Rev. D 80, 087501, 4 pages (2009).
30. T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers, Phys. Rev. D 80, 084018, 30 pages (2009).
31. E. Poisson, Tidal interaction of black holes and Newtonian viscous bodies, Phys. Rev. D 80, 064029, 11 pages (2009).
32. S. Taylor and E. Poisson, Nonrotating black hole in a post-Newtonian tidal environment, Phys. Rev. D 78, 084016, 26 pages (2008).
33. A. Pound and E. Poisson, Multi-scale analysis of the electromagnetic self-force in a weak gravitational field, Phys. Rev. D 77, 044012, 17 pages (2008).
34. A. Pound and E. Poisson, Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals, Phys. Rev. D 77, 044013, 18 pages (2008).
35. B. Preston and E. Poisson, A light-cone gauge for black-hole perturbation theory, Phys. Rev. D 74, 064010, 13 pages (2006).
36. B. Preston and E. Poisson, Light-cone coordinates based at a geodesic world line, Phys. Rev. D 74, 064009, 10 pages (2006).
37. R. Haas and E. Poisson, Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field, Phys. Rev. D 74, 044009, 29 pages (2006).
38. A. Pound, E. Poisson, and B.G. Nickel, Limitations of the adiabatic approximation to the gravitational self-force, Phys. Rev. D 72, 124001, 9 pages (2005).
39. K. Martel and E. Poisson, Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism, Phys. Rev. D 71, 104003, 13 pages (2005).
40. E. Poisson, Metric of a tidally distorted, nonrotating black hole, Phys. Rev. Lett. 94, 161103, 4 pages (2005).
41. R. Haas and E. Poisson, Mass change and motion of a scalar charge in cosmological spacetimes, Class. Quantum Grav. 22, S739–S752 (2005).
42. E. Poisson, Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation, Phys. Rev. D 70, 084044, 36 pages (2004).
43. E. Poisson, Radiation reaction of point particles in curved spacetime, Class. Quantum Grav. 21, R153–R232 (2004).
44. E. Poisson, The motion of point particles in curved spacetime, Living Rev. Relativity 7, Online article: http://www.livingreviews.org/lrr-2004-6 (2004).
45. S. Detweiler and E. Poisson, Low multipole contributions to the gravitational self-force, Phys. Rev. D 69, 084019, 18 pages (2004).
46. E. Poisson, Retarded coordinates based at a world line, and the motion of a small black hole in an external universe, Phys. Rev. D 69, 084007, 21 pages (2004).
47. K. Martel and E. Poisson, A one-parameter family of time-symmetric initial data for the radial infall of a particle into a Schwarzschild black hole, Phys. Rev. D 66, 084001, 16 pages (2002).
48. E. Poisson, Radiative falloff of a scalar field in a weakly curved spacetime without symmetries , Phys. Rev. D 66, 044008, 17 pages (2002).
49. L.M. Burko, A.I. Harte, and E. Poisson, Mass loss by a scalar charge in an expanding universe, Phys. Rev. D 65, 124006, 11 pages (2002).
50. M.J. Pfenning and E. Poisson, Scalar, electromagnetic, and gravitational self-forces in weakly curved spacetimes, Phys. Rev. D 65, 084001, 30 pages (2002).
51. W.G. Laarakkers and E. Poisson, Radiative falloff in Einstein-Straus spacetime, Phys. Rev. D 64, 084008, 13 pages (2001).
52. K. Martel and E. Poisson, Regular coordinate systems for Schwarzschild and other spherical spacetimes , Am. J. Phys. 69, 476–480 (2001).
53.  W. Tichy, E.E. Flanagan, and E. Poisson, Can the post-Newtonian gravitational waveform of an inspiraling binary be improved by solving the energy balance equation numerically? , Phys. Rev. D 61, 104015, 11 pages (2000).
54. K. Martel and E. Poisson, Gravitational waves from eccentric compact binaries: Reduction in signalto-noise ratio due to nonoptimal signal processing, Phys. Rev. D 60, 124008, 8 pages (1999).
55. P.R. Brady, C.M. Chambers, W.G. Laarakkers, and E. Poisson, Radiative falloff in Schwarzschild-de Sitter spacetime, Phys. Rev. D 60, 064003, 10 pages (1999).
56. S. Droz, D.J. Knapp, E. Poisson, and B.J. Owen, Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform, Phys. Rev. D 59, 124016, 8 pages (1999).
57. W.G. Laarakkers and E. Poisson, Quadrupole moments of rotating neutron stars, Astrophys. J. 512, 282–287 (1999).
58. S.W. Leonard and E. Poisson, Gravitational waves from binary systems in circular orbits: Convergence of a partially-bare multipole expansion, Class. Quantum Grav. 15, 2075–2081 (1998).
59. E. Poisson, Gravitational waves from inspiraling compact binaries: The quadrupole-moment term, Phys. Rev. D 57, 5287–5290 (1998).
60. S.W. Leonard and E. Poisson, Radiative multipole moments of integer-spin fields in curved spacetime, Phys. Rev. D 56, 4789–4814 (1997).
61. S. Droz and E. Poisson, Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates, Phys. Rev. D 56, 4449–4454 (1997).
62. E. Poisson, Erratum and Addendum: Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion, Phys. Rev. D 55, 7980–7981 (1997).
63. L.E. Simone, S.W. Leonard, E. Poisson, and C.M. Will, Gravitational waves from binary systems in circular orbits: Does the post-Newtonian expansion converge? , Class. Quantum Grav. 14, 237–256 (1997).
64. E. Poisson, Gravitational radiation from infall into a black hole: Regularization of the Teukolsky equation, Phys. Rev. D 55, 639–649 (1997).
65. E. Poisson, Measuring black-hole parameters and testing general relativity using gravitational-wave data from space-based interferometers, Phys. Rev. D 54, 5939–5953 (1996).
66. E. Poisson and M. Visser, Thin-shell wormholes: Linearization stability, Phys. Rev. D 52, 7318–7321 (1995).
67. E. Poisson, Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion, Phys. Rev. D 52, 5719–5723 (1995).
68. L.E. Simone, E. Poisson, and C.M. Will, Head-on collision of compact objects in general relativity: Comparison of post-Newtonian and perturbation approaches, Phys. Rev. D 52, 4481–4496 (1995).
69. E. Poisson and C.M. Will, Gravitational waves from inspiraling compact binaries: Parameter estimation using second-post-Newtonian waveforms, Phys. Rev. D 52, 848–855 (1995).
70. E. Poisson and M. Sasaki, Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections, Phys. Rev. D 51, 5753–5767 (1995).
71. D. Markovi´c and E. Poisson, Classical stability and quantum instability of black-hole Cauchy horizons , Phys. Rev. Lett. 74, 1280–1283 (1995).
72. A. Ori and E. Poisson, Death of cosmological white holes, Phys. Rev. D 50, 6150–6157 (1994).
73. C. Cutler, D. Kennefick, and E. Poisson, Gravitational radiation reaction for bound motion around a Schwarzschild black hole, Phys. Rev. D 50, 3816–3835 (1994).
74. E. Poisson, Gravitational-wave astronomy, J. Roy. Astron. Can. 87, 234–243 (1993).
75. E. Poisson, Gravitational radiation from a particle in circular orbit around a black hole. IV: Analytical results for the slowly rotating case, Phys. Rev. D 48, 1860–1863 (1993).
76. A. Apostolatos, D. Kennefick, A. Ori, and E. Poisson, Gravitational radiation from a particle in circular orbit around a black hole. III: Stability of circular orbits under radiation reaction, Phys. Rev. D. 47, 5376–5388 (1993).
77. C. Cutler, T.A. Apostolatos, L. Bildsten, L.S. Finn, E.E. Flanagan, D. Kennefick, D.M. Markovic, A. Ori, E. Poisson, G.J. Sussman, and K.S. Thorne, The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries, Phys. Rev. Lett. 70, 2984–2987 (1993).
78. C. Barrabes, P.R. Brady, and E. Poisson, Death of white holes, Phys. Rev. D 47, 2383–2387 (1993).
79. C. Cutler, L.S. Finn, E. Poisson, and G.J. Sussman, Gravitational radiation from a particle in circular orbit around a black hole. II: Numerical results for the nonrotating case, Phys. Rev. D 47, 1511-1518 (1993).
80. E. Poisson, Gravitational radiation from a particle in circular orbit around a black hole. I: Analytical results for the nonrotating case, Phys. Rev. D 47, 1497–1510 (1993).
81. R. Balbinot and E. Poisson, Mass inflation: The semiclassical regime, Phys. Rev. Lett. 70, 13–16 (1993).
82. P.R. Brady and E. Poisson, Cauchy-horizon instability for Reissner-Nordstr¨om black holes in de Sitter space, Class. Quantum. Grav. 9, 121–125 (1992).
83. R. Balbinot, P.R. Brady, W. Israel and E. Poisson, How singular are black hole interiors? , Phys. Lett. A 161, 223–226 (1991).
84. P.R. Brady, J. Louko and E. Poisson, Stability of a shell around a black hole, Phys. Rev. D 44, 1891–1894 (1991).
85. E. Poisson, Quadratic gravity as hair tonic for black holes, Class. Quantum Grav. 8, 639–650 (1991).
86. E. Poisson, Quadratic gravity and the black hole singularity, Phys. Rev. D 43, 3923–3928 (1991).
87. C. Barrabes, W. Israel, and E. Poisson, Collision of lightlike shells and mass inflation inside black holes, Class. Quantum Grav. 7, L273-L278 (1990).
88. E. Poisson, A look inside black holes, J. Roy. Astron. Soc. Can. 84, 191–198 (1990).
89. E. Poisson and W. Israel, The internal structure of black holes, Phys. Rev. D 41, 1796–1801 (1990).
90. R. Balbinot and E. Poisson, On the stability of the Schwarzschild - de Sitter model, Phys. Rev. D 41, 395–402 (1990).
91. E. Poisson and W. Israel, Eschatology of the black hole interior , Phys. Lett. B233, 74–78 (1989).
92. S. Pineault and E. Poisson, Encounters between degenerate stars and extra-solar comet clouds, Astrophys. J. 347, 1141–1154 (1989).
93. E. Poisson and W. Israel, Inner-horizon instability and mass-inflation in black holes , Phys. Rev. Lett. 63, 1663–1666 (1989).
94. E. Poisson and W. Israel, Structure of the black hole nucleus, Class. Quantum Grav. 5, L201–L205 (1988).

## Conference proceedings

1. E. Poisson, Constructing the self-force, in Mass and Motion in General Relativity (Fundamental Theories of Physics), edited by Luc Blanchet, Alessandro Spallicci, abd Bernard Whiting (Springer, 2011).
2. E. Poisson, The gravitational self-force, in General relativity and gravitation. Proceedings of the 17th International Conference, edited by P. Florides, B. Nolan, and A. Ottewill (World Scientific, New Jersey, 2005).
3. W.G. Laarakkers and E. Poisson, Radiative falloff in black-hole spacetimes, in General relativity and relativistic astrophysics; Eighth Canadian conference, edited by C.P. Burgess and R.C. Myers (American Institute of Physics, Melville, 1999).
4. E. Poisson, Gravitational waves from inspiraling compact binaries: Accuracy of the post-Newtonian waveforms, in Second Workshop on Gravitational Wave Data Analysis, edited by M. Davier and P. Hello (Editions Frontieres, 1998).
5. E. Poisson, Black-hole interiors and strong cosmic censorship, in Internal Structure of Black Holes and Spacetime Singularities, edited by Lior M. Burko and Amos Ori (Institute of Physics, Bristol, 1997).
6. E. Poisson, Gravitational waves from coalescing compact binaries, in The Sixth Canadian Conference on General Relativity and Relativistic Astrophysics, edited by S.P. Braham, J.D. Gegenberg, and R.J. McKellar (Fields Institute Communications, American Mathematical Society, Providence, 1997).
7. E. Poisson, Radiation reaction for bound motion in Schwarzschild, in Proceedings of the Fifth Canadian Conference on General Relativity and Relativistic Astrophysics, edited by R.B. Mann and R.G. McLenaghan (World Scientific, Singapore, 1994).
8. E. Poisson, Semi-classical gravity and the black hole singularity, in Gravitation: A Banff summer institute, edited by R. Mann and P. Wesson (World Scientific, Singapore, 1991).
9. E. Poisson, Quantum effects near the black hole singularity, in Proceedings of the third Canadian conference on general relativity and relativistic astrophysics, edited by A. Coley, F. Cooperstock, and Tupper (World Scientific, Singapore, 1990).

### E. Poisson and C.W. Will, Gravity: Newtonian, post-Newtonian, Relativistic (Cambridge, Cambridge University Press, 2014).

Honorable mention, Textbook/Physical Sciences and Mathematics, 2015 PROSE Awards (The American Publishers Awards for Professional and Scholarly Excellence)

This textbook, published by Cambridge University Press, explores approximate solutions to general relativity and their consequences. It offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. The book explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. It concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present challenging tests of the material covered in the main text.

### Reviews

This remarkable book gives a superb pedagogical treatment of topics that are crucial for modern astrophysics and gravitational-wave science, but (sadly) are generally omitted from textbooks on general relativity, or treated much too briefly. With enthusiasm, I recommend this book to all astrophysicists, gravitational physicists, and students of these subjects.
Kip S. Thorne, California Institute of Technology

This book is likely to become the bedside reading of all students and working scientists interested in Newtonian and Einsteinian gravity. Pedagogically written using fully modern notation, the book contains an extensive description of the post-Newtonian approximation, and is replete with useful results on gravitational waves and the motion of bodies under gravity.
Luc Blanchet, Institut d'Astrophysique de Paris

### Contents

1. Foundations of Newtonian gravity
1. Newtonian gravity. 2. Equations of Newtonian gravity. 3. Newtonian field equations. 4. Equations of hydrodynamics. 5. Spherical and nearly spherical bodies. 6. Motion of extended fluid bodies. 7. Bibliographical notes. 8. Exercises.
2. Structure of self-gravitating bodies
1. Equations of internal structure. 2. Equilibrium structure of spherical bodies. 3. Rotating self-gravitating bodies. 4. General theory of deformed bodies. 5. Tidally deformed bodies. 6. Bibliographical notes. 7. Exercises.
3. Newtonian orbital dynamics
1. Celestial mechanics from Newton to Einstein. 2. Two bodies: Kepler's problem. 3. Perturbed Kepler problem. 4. Case studies of perturbed Keplerian motion. 5. More bodies. 6. Lagrangian formulation of Newtonian dynamics. 7. Bibliographical notes. 8. Exercises.
4. Minkowski spacetime
1. Spacetime. 2. Relativistic hydrodynamics. 3. Electrodynamics. 4. Point particles in spacetime. 5. Bibliographical notes. 6. Exercises.
5. Curved spacetime
1. Gravitation as curved spacetime. 2. Mathematics of curved spacetime. 3. Physics in curved spacetime. 4. Einstein field equations. 5. Linearized theory. 6. Spherical bodies and Schwarzschild spacetime. 7. Bibliographical notes. 8. Exercises.
6. Post-Minkowskian theory: formulation
1. Landau-Lifshitz formulation of general relativity. 2. Relaxed Einstein equations. 3. Integration of the wave equation. 4. Bibliographical notes. 5. Exercises.
7. Post-Minkowskian theory: implementation
1. Assembling the tools. 2. First iteration. 3. Second iteration: near zone. 3. Second iteration: wave zone. 4. Bibliographical notes. 5. Exercises.
8. Post-Newtonian theory: fundamentals
1. Equations of post-Newtonian theory. 2. Classic approach to post-Newtonian theory. 3. Coordinate transformations. 4. Post-Newtonian hydrodynamics. 5. Bibliographical notes. 6. Exercises.
9. Post-Newtonian theory: system of isolated bodies
1. From fluid configurations to isolated bodies. 2. Inter-body metric. 3. Motion of isolated bodies. 4. Motion of compact bodies. 5. Motion of spinning bodies. 6. Point particles. 7. Bibliographical notes. 8. Exercises.
10. Post-Newtonian celestial mechanics, astrometry and navigation
1. Post-Newtonian two-body problem. 2. Motion of light in post-Newtonian theory. 3. Post-Newtonian gravity in timekeeping and navigation. 4. Spinning bodies. 5. Bibliographical notes. 6. Exercises.
11. Gravitational waves
1. Gravitational-wave field and polarizations. 2. The quadrupole formula. 3. Beyond the quadrupole formula: Waves at 1.5PN order. 4. Gravitational waves emitted by a two-body system. 5. Gravitational waves and laser interferometers. 6. Bibliographical notes. 7. Exercises.
1. Radiation reaction in electromagentism. 2. Radiative losses in gravitating systems. 3. Radiative losses in slowly-moving systems. 4. Astrophysical implications of radiative losses. 5. Radiation-reaction potentials. 6. Radiation reaction of fluid systems. 7. Radiation reaction of N-body systems. 8. Radiation reaction in alternative gauges. 9. Orbital evolution under radiation reaction. 10. Bibliographical notes. 11. Exercises.
13. Alternative theories of gravity
1. Metric theories and the strong equivalence principle. 2. Parametrized post-Newtonian framework. 3. Experimental tests of gravitational theories. 4. Gravitational radiation in alternative theories of gravity. 5. Scalar-tensor gravity. 6. Bibliographical notes. 7. Exercises.

### Errors, typographical and otherwise

A number of errors were reported by readers. They have our gratitude. List of corrections.

### E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge, Cambridge University Press, 2004).

This textbook, published by Cambridge University Press, fills a gap in the existing literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most successful and relevant applications of general relativity. Topics covered include congruences of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity.

You can order the book from Amazon.com
Read Eric Sheldon's review in Contemporary Physics

### Contents

1. Fundamentals
1- Vectors, dual vectors, and tensors. 2- Covariant differentiation. 3- Geodesics. 4- Lie differentiation. 5- Killing vectors. 6- Local flatness. 7- Metric determinant. 8- Levi-Civita tensor. 9- Curvature. 10- Geodesic deviation. 11- Fermi normal coordinates. 12- Bibliographical notes. 13- Problems.
2. Geodesic congruences
1- Energy conditions. 2- Kinematics of a deformable medium. 3- Congruence of timelike geodesics. 4- Congruence of null geodesics. 5- Bibliographical notes. 6- Problems.
3. Hypersurfaces
1- Description of hypersurfaces. 2- Integration on hypersurfaces. 3- Gauss-Stokes theorem. 4- Differentiation of tangent tensor fields. 5- Gauss-Codazzi equations. 6- Initial-value problem. 7- Junction conditions and thin shells. 8- Oppenheimer-Snyder collapse. 9- Thin-shell collapse. 10- Slowly rotating shell. 11- Null shells. 12- Bibliographical notes. 13- Problems.
4. Lagrangian and Hamiltonian formulations of general relativity
1- Lagrangian formulation. 2- Hamiltonian formulation. 3- Mass and angular momentum. 4- Bibliographical notes. 5- Problems.
5. Black holes
1- Schwarzschild black hole. 2- Reissner-Nordstrom black hole. 3- Kerr black hole. 4- General properties of black holes. 5- The laws of black-hole mechanics. 6- Bibliographical notes. 7- Problems.

### Errors, typographical and otherwise

Name Role
Michael LaHaye MSc Candidate

## Alumni

### PhD Students

• John Ryan Westernacher-Schneider (2019)
• Philippe Landry (2017)
• Jonah Miller (2017)
• Peter Zimmerman (2015)
• Roland Haas (2008)
• Karl Martel (2004)

### MSc Students

• Eamonn Corrigan (2018)
• Karl Davidson (2018)
• Dylan Podkowka (2018)
• John Ryan Westernacher-Schnieider (2015)
• Philippe Landry (2014)
• Joseph Kuchar (2013)
• Ryan Massey (2011)
• Peter Zimmerman (2011)
• Taylor Binnington (2009)
• Simon Comeau (2008)
• Stephanne Taylor (2008)