References

1 Abbott, L.F., and Deser, S., “Stability of gravity with a cosmological constant”, Nucl. Phys. B, 195, 76–96, (1982).
2 Aguirregabiria, J.M., Chamorro, A., and Virbhadra, K.S., “Energy and angular momentum of charged rotating black holes”, Gen. Relativ. Gravit., 28, 1393–1400, (1996). [External Linkgr-qc/9501002v3].
3 Aichelburg, P.C., “Remark on the superposition principle for gravitational waves”, Acta Phys. Austriaca, 34, 279–284, (1971).
4 Allemandi, G., Francaviglia, M., and Raiteri, M., “Energy in Einstein–Maxwell theory and the first law of isolated horizons via the Noether theorem”, Class. Quantum Grav., 19, 2633–2655, (2002). [External Linkgr-qc/0110104].
5 Alvarez-Gaumé, L., and Nelson, P., “Riemann surfaces and string theories”, in de Wit, B., Fayet, P., and Grisaru, M., eds., Supersymmetry, Supergravity, Superstrings ’86, Proceedings of the 4th Trieste Spring School, held at the ICTP, Trieste, Italy 7 – 15 April 1986, pp. 419–510, (World Scientific, Singapore, 1986).
6 Anco, S.C., “Mean-curvature flow and quasilocal mass for 2-surfaces in Hamiltonian general relativity”, J. Math. Phys., 48, 052502, 1–32, (2007). [External LinkDOI], [External Linkgr-qc/0402057v2].
7 Anco, S.C., “Spinor Derivation of Quasilocal Mean Curvature Mass in General Relativity”, Int. J. Theor. Phys., 47, 684–695, (2008). [External LinkDOI], [External LinkADS].
8 Anco, S.C., and Tung, R.-S., “Covariant Hamiltonian boundary conditions in general relativity for spatially bounded spacetime regions”, J. Math. Phys., 43, 5531–5566, (2002). [External Linkgr-qc/0109013v4].
9 Anco, S.C., and Tung, R.-S., “Properties of the symplectic structure of general relativity for spatially bounded spacetime regions”, J. Math. Phys., 43, 3984–4019, (2002). [External Linkgr-qc/0109014v6].
10 Anderson, J.L., Principles of Relativity Physics, (Academic Press, New York, 1967).
11 Andersson, F., and Edgar, S.B., “Curvature-free asymmetric metric connections in Kerr–Schild spacetimes”, J. Math. Phys., 39, 2859–2861, (1998).
12 Andersson, L., Mars, M., and Simon, W., “Local Existence of Dynamical and Trapping Horizons”, Phys. Rev. Lett., 95, 111102, (2005). [External LinkDOI], [External Linkgr-qc/0506013v2].
13 Ansorg, M., and Petroff, D., “Black holes surrounded by uniformly rotating rings”, Phys. Rev. D, 72, 024019, 1–12, (2005). [External LinkDOI], [External Linkgr-qc/0505060v4].
14 Ansorg, M., and Petroff, D., “Negative Komar mass of single objects in regular, asymptotically flat spacetimes”, Class. Quantum Grav., 23, L81–L87, (2006). [External LinkDOI], [External Linkgr-qc/0607091v2].
15 Ansorg, M., and Pfister, H., “A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter”, Class. Quantum Grav., 25, 035009, 1–17, (2008). [External LinkDOI], [External LinkarXiv:0708.4196v4].
16 Arnowitt, R., Deser, S., and Misner, C.W., “Energy and the Criteria for Radiation in General Relativity”, Phys. Rev., 118, 1100–1104, (1960).
17 Arnowitt, R., Deser, S., and Misner, C.W., “Coordinate Invariance and Energy Expressions in General Relativity”, Phys. Rev., 122, 997–1006, (1961).
18 Arnowitt, R., Deser, S., and Misner, C.W., “Wave Zone in General Relativity”, Phys. Rev., 121, 1556–1566, (1961).
19 Arnowitt, R., Deser, S., and Misner, C.W., “The dynamics of general relativity”, in Witten, L., ed., Gravitation: An Introduction to Current Research, pp. 227–265, (Wiley, New York; London, 1962). [External LinkDOI], [External LinkADS], [External Linkgr-qc/0405109].
20 Aronson, B., and Newman, E.T., “Coordinate systems associated with asymptotically shear-free null congruences”, J. Math. Phys., 13, 1847–1851, (1972).
21 Ashtekar, A., “Asymptotic structure of the gravitational field at spatial infinity”, in Held, A., ed., General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein, vol. 2, pp. 37–69, (Plenum Press, New York, 1980).
22 Ashtekar, A., “On the boundary conditions for gravitational and gauge fields at spatial infinity”, in Flaherty, F.J., ed., Asymptotic Behavior of Mass and Spacetime Geometry, Proceedings of the conference, held at Oregon State University, Corvallis, Oregon, USA, October 17 – 21, 1983, Lecture Notes in Physics, vol. 202, pp. 95–109, (Springer, Berlin; New York, 1984).
23 Ashtekar, A., Lectures on Non-Perturbative Canonical Gravity, Advanced Series in Astrophysics and Cosmology, vol. 6, (World Scientific, Singapore, 1991).
24 Ashtekar, A., Beetle, C., and Lewandowski, J., “Mechanics of rotating isolated horizons”, Phys. Rev. D, 64, 044016, 1–17, (2001). [External LinkDOI], [External Linkgr-qc/0103026v2].
25 Ashtekar, A., Beetle, C., and Lewandowski, J., “Geometry of generic isolated horizons”, Class. Quantum Grav., 19, 1195–1225, (2002). [External Linkgr-qc/0111067v2].
26 Ashtekar, A., Bombelli, L., and Reula, O.A., “The covariant phase space of asymptotically flat gravitational fields”, in Francaviglia, M., and Holm, D., eds., Mechanics, Analysis and Geometry: 200 Years after Lagrange, pp. 417–450, (North-Holland, Amsterdam; New York, 1991).
27 Ashtekar, A., Fairhurst, S., and Krishnan, B., “Isolated horizons: Hamiltonian evolution and the first law”, Phys. Rev. D, 62, 104025, 1–29, (2000). [External LinkDOI], [External Linkgr-qc/0005083v3].
28 Ashtekar, A., and Galloway, J.G., “Some uniqueness results for dynamical horizons”, Adv. Theor. Math. Phys., 95, 1–30, (2005). [External Linkgr-qc/0503109v4].
29 Ashtekar, A., and Geroch, R., “Quantum theory of gravitation”, Rep. Prog. Phys., 37, 1211–1256, (1974).
30 Ashtekar, A., and Hansen, R.O., “A unified treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity”, J. Math. Phys., 19, 1542–1566, (1978).
31 Ashtekar, A., and Horowitz, G.T., “Energy-momentum of isolated systems cannot be null”, Phys. Lett., 89A, 181–184, (1982).
32 Ashtekar, A., and Krishnan, B., “Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws”, Phys. Rev. Lett., 89, 261101, (2002). [External Linkgr-qc/0207080v3].
33 Ashtekar, A., and Krishnan, B., “Dynamical horizons and their properties”, Phys. Rev. D, 68, 104030, 1–25, (2003). [External LinkDOI], [External Linkgr-qc/0308033v4].
34 Ashtekar, A., and Krishnan, B., “Isolated and Dynamical Horizons and Their Applications”, Living Rev. Relativity, 7, lrr-2004-10, (2004). URL (cited on 17 November 2008):
http://www.livingreviews.org/lrr-2004-10.
35 Ashtekar, A., and Magnon, A., “Asymptotically anti-de Sitter spacetimes”, Class. Quantum Grav., 1, L39–L44, (1984).
36 Ashtekar, A., and Romano, J.D., “Spatial infinity as a boundary of spacetime”, Class. Quantum Grav., 9, 1069–1100, (1992).
37 Ashtekar, A., and Streubel, M., “Symplectic geometry of radiative modes and conserved quantities at null infinity”, Proc. R. Soc. London, Ser. A, 376, 585–607, (1981).
38 Ashtekar, A., and Winicour, J., “Linkages and Hamiltonians at null infinity”, J. Math. Phys., 23, 2410–2417, (1982).
39 Balachandran, A.P., Chandar, L., and Momen, A., “Edge States in Canonical Gravity”, arXiv e-print, (1995). [External Linkgr-qc/9506006v2].
40 Balachandran, A.P., Momen, A., and Chandar, L., “Edge states in gravity and black hole physics”, Nucl. Phys. B, 461, 581–596, (1996). [External Linkgr-qc/9412019v2].
41 Balasubramanian, V., and Kraus, P., “A stress tensor for anti-de-Sitter gravity”, Commun. Math. Phys., 208, 413–428, (1999). [External Linkhep-th/9902121v5].
42 Bardeen, J.M., Carter, B., and Hawking, S.W., “The four laws of black hole mechanics”, Commun. Math. Phys., 31, 161–170, (1973). Related online version (cited on 21 February 2005):
External Linkhttp://projecteuclid.org/euclid.cmp/1103858973.
43 Barrabès, C., Gramain, A., Lesigne, E., and Letelier, P.S., “Geometric inequalities and the hoop conjecture”, Class. Quantum Grav., 9, L105–L110, (1992).
44 Barrabès, C., Israel, W., and Letelier, P.S., “Analytic models of nonspherical collapse, cosmic censorship and the hoop conjecture”, Phys. Lett. A, 160, 41–44, (1991).
45 Bartnik, R., “The mass of an asymptotically flat manifold”, Commun. Pure Appl. Math., 39, 661–693, (1986).
46 Bartnik, R., “A new definition of quasi-local mass”, in Blair, D.G., and Buckingham, M.J., eds., The Fifth Marcel Grossmann Meeting on recent developments in theoretical and experimental general relativity, gravitation and relativistic field theories, Proceedings of the meeting held at The University of Western Australia, 8 – 13 August 1988, pp. 399–401, (World Scientific, Singapore; River Edge, NJ, 1989).
47 Bartnik, R., “New definition of quasilocal mass”, Phys. Rev. Lett., 62, 2346–2348, (1989).
48 Bartnik, R., “Quasi-spherical metrics and prescribed scalar curvature”, J. Differ. Geom., 37, 31–71, (1993).
49 Bartnik, R., “Mass and 3-metrics of non-negative scalar curvature”, in Tatsien, L., ed., Proceedings of the International Congress of Mathematicians, Beijing, China 20 – 28 August 2002, vol. II, pp. 231–240, (World Scientific, Singapore, 2002). [External Linkmath.DG/0304259].
50 Baskaran, D., Lau, S.R., and Petrov, A.N., “Center of mass integral in canonical general relativity”, Ann. Phys. (N.Y.), 307, 90–131, (2003). [External Linkgr-qc/0301069v2].
51 Baston, R.J., “The index of the 2-twistor equations”, Twistor Newsletter, 1984(17), 31–32, (1984).
52 Beetle, C., “Approximate Killing Fields as an Eigenvalue Problem”, arXiv e-print, (2008). [External LinkarXiv:0808.1745 [gr-qc]].
53 Beig, R., “Integration of Einstein’s equations near spatial infinity”, Proc. R. Soc. London, Ser. A, 391, 295–304, (1984).
54 Beig, R., “Time symmetric initial data and Penrose’s quasi-local mass”, Class. Quantum Grav., 8, L205–L209, (1991).
55 Beig, R., “The classical theory of canonical general relativity”, in Ehlers, J., and Friedrich, H., eds., Canonical Gravity: From Classical to Quantum, Proceedings of the 117th WE Heraeus Seminar, Bad Honnef, Germany, 13 – 17 September 1993, Lecture Notes in Physics, vol. 434, pp. 59–80, (Springer, Berlin; New York, 1994).
56 Beig, R., and Ó Murchadha, N., “The Poincaré group as the symmetry group of canonical general relativity”, Ann. Phys. (N.Y.), 174, 463–498, (1987).
57 Beig, R., and Schmidt, B.G., “Einstein’s equations near spatial infinity”, Commun. Math. Phys., 87, 65–80, (1982).
58 Beig, R., and Szabados, L.B., “On a global conformal invariant of initial data sets”, Class. Quantum Grav., 14, 3091–3107, (1997). [External Linkgr-qc/9706078].
59 Bekenstein, J.D., “Black Holes and Entropy”, Phys. Rev. D, 7, 2333–2346, (1973).
60 Bekenstein, J.D., “Generalized second law of thermodynamics in black-hole physics”, Phys. Rev. D, 9, 3292–3300, (1974).
61 Bekenstein, J.D., “Universal upper bound on the entropy-to energy ratio for bounded systems”, Phys. Rev. D, 23, 287–298, (1981).
62 Bekenstein, J.D., “Black holes and everyday physics”, Gen. Relativ. Gravit., 14, 355–359, (1982).
63 Bekenstein, J.D., “On Page’s examples challenging the entropy bound”, arXiv e-print, (2000). [External Linkgr-qc/0006003v3].
64 Bekenstein, J.D., and Mayo, A.E., “Black hole polarization and new entropy bounds”, Phys. Rev. D, 61, 024022, 1–8, (1999). [External LinkDOI], [External Linkgr-qc/9903002v2].
65 Belinfante, F.J., “On the spin angular momentum of mesons”, Physica, VI(9), 887–898, (1939). [External LinkDOI], [External LinkADS].
66 Belinfante, F.J., “On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields”, Physica, VII, 449–474, (1940). [External LinkDOI], [External LinkADS].
67 Ben-Dov, I., “Penrose inequality and apparent horizons”, Phys. Rev. D, 70, 124031, 1–11, (2004). [External LinkDOI], [External Linkgr-qc/0408066v2].
68 Bergmann, P.G., “Observables in general relativity”, Rev. Mod. Phys., 33, 510–514, (1961).
69 Bergmann, P.G., “The general theory of relativity”, in Flügge, S., ed., Handbuch der Physik. Vol. IV: Prinzipien der Elektrodynamik und Relativitätstheorie, pp. 203–242, (Springer, Berlin; New York, 1962).
70 Bergmann, P.G., and Thomson, R., “Spin and angular momentum in general relativity”, Phys. Rev., 89, 400–407, (1953).
71 Bergqvist, G., “Positivity and definitions of mass”, Class. Quantum Grav., 9, 1917–1922, (1992).
72 Bergqvist, G., “Quasilocal mass for event horizons”, Class. Quantum Grav., 9, 1753–1766, (1992).
73 Bergqvist, G., “Energy of small surfaces”, Class. Quantum Grav., 11, 3013–3023, (1994).
74 Bergqvist, G., “On the Penrose inequality and the role of auxiliary spinor fields”, Class. Quantum Grav., 14, 2577–2583, (1997).
75 Bergqvist, G., “Vacuum momenta of small spheres”, Class. Quantum Grav., 15, 1535–1538, (1998).
76 Bergqvist, G., and Ludvigsen, M., “Quasi-local mass near a point”, Class. Quantum Grav., 4, L29–L32, (1987).
77 Bergqvist, G., and Ludvigsen, M., “Spinor propagation and quasilocal momentum for the Kerr solution”, Class. Quantum Grav., 6, L133–L136, (1989).
78 Bergqvist, G., and Ludvigsen, M., “Quasilocal momentum and angular momentum in Kerr spacetime”, Class. Quantum Grav., 8, 697–701, (1991).
79 Bernstein, D.H., and Tod, K.P., “Penrose’s quasi-local mass in a numerically computed space-time”, Phys. Rev. D, 49, 2808–2820, (1994).
80 BizoÅ„, P., and Malec, E., “On Witten’s positive-energy proof for weakly asymptotically flat spacetimes”, Class. Quantum Grav., 3, L123–L128, (1986). [External LinkDOI].
81 Blau, M., and Rollier, B., “Brown–York energy and radial geodesics”, Class. Quantum Grav., 25, 105004, 1–7, (2008). [External LinkDOI], [External LinkarXiv:0708.0321v3].
82 Bondi, H., “Gravitational waves in general relativity”, Nature, 186, 535, (1960). [External LinkDOI], [External LinkADS].
83 Bondi, H., van den Burg, M.G.J., and Metzner, A.W.K., “Gravitational waves in general relativity VII. Waves from axi-symmetric isolated systems”, Proc. R. Soc. London, Ser. A, 269, 21–52, (1962). [External LinkDOI], [External LinkADS].
84 Booth, I., and Fairhurst, S., “Canonical phase space formulation of quasilocal general relativity”, Class. Quantum Grav., 20, 4507–4531, (2003). [External Linkgr-qc/0301123v2].
85 Booth, I., and Fairhurst, S., “The First Law for Slowly Evolving Horizons”, Phys. Rev. Lett., 92, 011102, (2004). [External Linkgr-qc/0307087v2].
86 Booth, I., and Fairhurst, S., “Horizon energy and angular momentum from a Hamiltonian perspective”, Class. Quantum Grav., 22, 4515–4550, (2005). [External Linkgr-qc/0505049v2].
87 Booth, I., and Fairhurst, S., “Isolated, slowly evolving, and dynamical trapping horizons: Geometry and mechanics from surface deformations”, Phys. Rev. D, 75, 084019, 1–23, (2007). [External LinkDOI], [External Linkgr-qc/0610032v2].
88 Booth, I., and Fairhurst, S., “Extremality conditions for isolated and dynamical horizons”, Phys. Rev. D, 77, 084005, 1–14, (2008). [External LinkDOI], [External LinkarXiv:0708.2209v3].
89 Booth, I.S., “Metric-based Hamiltonians, null boundaries and isolated horizons”, Class. Quantum Grav., 18, 4239–4264, (2001). [External Linkgr-qc/0105009v2].
90 Booth, I.S., and Creighton, J.D.E., “Quasilocal calculation of tidal heating”, Phys. Rev. D, 62, 067503, 1–4, (2000). [External LinkDOI], [External Linkgr-qc/0003038v2].
91 Booth, I.S., and Mann, R.B., “Moving observers, nonorthogonal boundaries, and quasilocal energy”, Phys. Rev. D, 59, 064021, 1–9, (1999). [External LinkDOI], [External Linkgr-qc/9810009v2].
92 Booth, I.S., and Mann, R.B., “Static and infalling quasilocal energy of charged and naked black holes”, Phys. Rev. D, 60, 124009, 1–22, (1999). [External LinkDOI], [External Linkgr-qc/9907072].
93 Borowiec, A., Ferraris, M., Francaviglia, M., and Volovich, I., “Energy-momentum complex for nonlinear gravitational Lagrangians in the first-order formalism”, Gen. Relativ. Gravit., 26, 637–645, (1994).
94 Bousso, R., “Holography in general space-times”, J. High Energy Phys., 1999(06), 028, (1999). [External Linkhep-th/9906022v2].
95 Bousso, R., “The holographic principle”, Rev. Mod. Phys., 74, 825–874, (2002). [External Linkhep-th/0203101v2].
96 Brady, P.R., Droz, S., Israel, W., and Morsink, S.M., “Covariant double–null dynamics: (2+2)-splitting of the Einstein equations”, Class. Quantum Grav., 13, 2211–2230, (1996). [External Linkgr-qc/9510040].
97 Bramson, B.D., “The alignment of frames of reference at null infinity for asymptotically flat Einstein–Maxwell manifolds”, Proc. R. Soc. London, Ser. A, 341, 451–461, (1975).
98 Bramson, B.D., “Relativistic angular momentum for asymptotically flat Einstein–Maxwell manifolds”, Proc. R. Soc. London, Ser. A, 341, 463–490, (1975).
99 Bramson, B.D., “Physics in cone space”, in Espositio, P., and Witten, L., eds., Asymptotic structure of spacetime, Proceedings of a Symposium on Asymptotic Structure of Space-Time (SOASST), held at the University of Cincinnati, Ohio, June 14 – 18, 1976, pp. 273–359, (Plenum Press, New York, 1977).
100 Bramson, B.D., “The invariance of spin”, Proc. R. Soc. London, Ser. A, 364, 463–490, (1978).
101 Bray, H., Hayward, S., Mars, M., and Simon, W., “Generalized Inverse Mean Curvature Flows in Spacetime”, Commun. Math. Phys., 272, 119–138, (2007). [External LinkDOI], [External Linkgr-qc/0603014].
102 Bray, H.L., “Proof of the Riemannian Penrose inequality using the positive energy theorem”, J. Differ. Geom., 59, 177–267, (2001). [External Linkmath.DG/9911173].
103 Bray, H.L., “Black holes and the Penrose inequality in general relativity”, in Tatsien, L., ed., Proceedings of the International Congress of Mathematicians, Beijing, China 20 – 28 August 2002, vol. II, (World Scientific, Singapore, 2002). [External Linkmath.DG/0304261].
104 Bray, H.L., “Black holes, geometric flows, and the Penrose inequality in general relativity”, Notices AMS, 49, 1372–1381, (2002).
105 Bray, H.L., and ChruÅ›ciel, P.T., “The Penrose Inequality”, in ChruÅ›ciel, P.T., and Friedrich, H., eds., The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity, pp. 39–70, (Birkhäuser, Basel, 2004). [External Linkgr-qc/0312047v2].
106 Brinkmann, H.W., “On Riemann spaces conformal to Euclidean space”, Proc. Natl. Acad. Sci. USA, 9, 1–3, (1923).
107 Brown, J.D., Creighton, J.D.E., and Mann, R., “Temperature, energy, and heat capacity of asymptotically anti-de-Sitter black holes”, Phys. Rev. D, 50, 6394–6403, (1994). [External Linkgr-qc/9405007].
108 Brown, J.D., Lau, S.R., and York Jr, J.W., “Energy of isolated systems at retarded times as the null limit of quasilocal energy”, Phys. Rev. D, 55, 1977–1984, (1997). [External Linkgr-qc/9609057].
109 Brown, J.D., Lau, S.R., and York Jr, J.W., “Canonical quasilocal energy and small spheres”, Phys. Rev. D, 59, 064028, 1–13, (1999). [External LinkDOI], [External Linkgr-qc/9810003].
110 Brown, J.D., Lau, S.R., and York Jr, J.W., “Action and energy of the gravitational field”, Ann. Phys. (N.Y.), 297, 175–218, (2002). [External Linkgr-qc/0010024v3].
111 Brown, J.D., and York, J.M., “Quasilocal energy in general relativity”, in Gotay, M.J., Marsden, J.E., and Moncrief, V.E., eds., Mathematical Aspects of Classical Field Theory, Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 20 – 26, 1991 at the University of Washington, Seattle, Contemporary Mathematics, vol. 132, pp. 129–142, (American Mathematical Society, Providence, RI, 1992).
112 Brown, J.D., and York Jr, J.W., “Quasilocal energy and conserved charges derived from the gravitational action”, Phys. Rev. D, 47, 1407–1419, (1993). [External Linkgr-qc/9209012].
113 Cahill, M.E., and McVittie, G.C., “Spherical symmetry and mass-energy in general relativity I. General theory”, J. Math. Phys., 11, 1382–1391, (1970).
114 Carlip, S., “Statistical Mechanics and Black Hole Entropy”, arXiv e-print, (1995). [External Linkgr-qc/9509024v2].
115 Carlip, S., “Black hole entropy from conformal field theory in any dimension”, Phys. Rev. Lett., 82, 2828–2831, (1999). [External Linkhep-th/9812013v3].
116 Carlip, S., “Entropy from conformal field theory at Killing horizons”, Class. Quantum Grav., 16, 3327–3348, (1999). [External Linkgr-qc/9906126v2].
117 Carlip, S., “Black hole entropy from conformal field theory”, Nucl. Phys. B (Proc. Suppl.), 88, 10–16, (2000). [External Linkgr-qc/9912118].
118 Carlip, S., “Near-horizon conformal symmetry and black hole entropy”, Phys. Rev. Lett., 88, 241301, (2002). [External Linkgr-qc/0203001].
119 Carlip, S., “Black Hole Thermodynamics and Statistical Mechanics”, in Papantonopoulos, E., ed., Physics of Black Holes: A Guided Tour, Proceedings of the Fourth Aegean School on Black Holes held in Mytilene, Greece, 17 – 22 September 2007, Lecture Notes in Physics, vol. 769, pp. 89–123, (Springer, Berlin; New York, 2009). [External LinkDOI], [External LinkarXiv:0807.4520].
120 Carrera, M., and Giulini, D., “On the influence of global cosmological expansion on the dynamics and kinematics of local systems”, arXiv e-print, (2008). [External LinkarXiv:0810.2712 [gr-qc]].
121 Chang, C.-C., Nester, J.M., and Chen, C.-M., “Pseudotensors and quasi-local energy-momentum”, Phys. Rev. Lett., 83, 1897–1901, (1999). [External Linkgr-qc/9809040v2].
122 Chang, C.-C., Nester, J.M., and Chen, C.-M., “Energy-momentum quasi-localization for gravitating systems”, in Liu, L., Luo, J., Li, X.-Z., and Hsu, J.-P., eds., Gravitation and Astrophysics, Proceedings of the Fourth International Workshop, held at Beijing Normal University, China, October 10 – 15, 1999, pp. 163–173, (World Scientific, Singapore; River Edge, NJ, 2000). [External Linkgr-qc/9912058].
123 Chellathurai, V., and Dadhich, N., “Effective mass of a rotating black hole in a magnetic field”, Class. Quantum Grav., 7, 361–370, (1990).
124 Chen, C.-M., Liu, J.-L., and Nester, J.M., “Quasi-local energy for cosmological models”, Mod. Phys. Lett. A, 22, 2039–2046, (2007). [External LinkarXiv:0705.1080v2].
125 Chen, C.-M., and Nester, J.M., “Quasilocal quantities for general relativity and other gravity theories”, Class. Quantum Grav., 16, 1279–1304, (1999). [External Linkgr-qc/9809020v2].
126 Chen, C.-M., and Nester, J.M., “A symplectic Hamiltonian derivation of quasi-local energy-momentum for GR”, Grav. Cosmol., 6, 257–270, (2000). [External Linkgr-qc/0001088].
127 Chen, C.-M., and Nester, J.M., “Quasi-Local Energy for an Unusual Slicing of Static Spherically Symmetric Metrics”, in Kleinert, H., Jantzen, R.T., and Ruffini, R., eds., The Eleventh Marcel Grossmann Meeting on General Relativity, Proceedings of the MG11 Meeting on General Relativity, Berlin, Germany, 23 – 29 July 2006, pp. 2146–2148, (World Scientific, Singapore; Hackensack, NJ, 2008).
128 Chen, C.-M., Nester, J.M., and Tung, R.-S., “Quasilocal energy-momentum for geometric gravity theories”, Phys. Lett. A, 203, 5–11, (1995). [External Linkgr-qc/9411048v2].
129 Chen, C.-M., Nester, J.M., and Tung, R.-S., “Spinor Formulations for Gravitational Energy-Momentum”, arXiv e-print, (2002). [External Linkgr-qc/0209100v2].
130 Chen, C.-M., Nester, J.M., and Tung, R.-S., “Hamiltonian boundary term and quasilocal energy flux”, Phys. Rev. D, 72, 104020, 1–13, (2005). [External LinkDOI], [External Linkgr-qc/0508026].
131 Christodoulou, D., and Yau, S.-T., “Some remarks on the quasi-local mass”, in Isenberg, J.A., ed., Mathematics and General Relativity, Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held June 22 – 28, 1986, Contemporary Mathematics, vol. 71, pp. 9–14, (American Mathematical Society, Providence, RI, 1988).
132 ChruÅ›ciel, P.T., “Boundary conditions at spacelike infinity from a Hamiltonian point of view”, in Bergmann, P.G., and de Sabbata, V., eds., Topological Properties and Global Structure of Space-time, Proceedings of a NATO Advanced Study Institute, held May 12–22, 1985, in Erice, Italy, NATO ASI Series B, vol. 138, pp. 49–59, (Plenum Press, New York, 1986).
133 ChruÅ›ciel, P.T., “A remark on the positive-energy theorem”, Class. Quantum Grav., 3, L115–L121, (1986).
134 Chruściel, P.T., Jezierski, J., and Kijowski, J., Hamiltonian Field Theory in the Radiating Regime, Lecture Notes in Physics, vol. m70, (Springer, Berlin; New York, 2002).
135 ChruÅ›ciel, P.T., Jezierski, J., and MacCallum, M.A.H., “Uniqueness of scalar field energy and gravitational energy in the radiating regime”, Phys. Rev. Lett., 80, 5052–5055, (1998). [External Linkgr-qc/9801073].
136 ChruÅ›ciel, P.T., Jezierski, J., and MacCallum, M.A.H., “Uniqueness of the Trautman–Bondi mass”, Phys. Rev. D, 58, 084001, 1–16, (1998). [External LinkDOI], [External Linkgr-qc/9803010].
137 ChruÅ›ciel, P.T., Maerten, D., and Tod, P., “Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times”, J. High Energy Phys., 2006(11), 084, 1–43, (2006). [External LinkDOI], [External Linkgr-qc/0606064v2].
138 ChruÅ›ciel, P.T., and Nagy, G., “A Hamiltonian mass of asymptotically anti-de Sitter space-times”, Class. Quantum Grav., 18, L61–L68, (2001). [External Linkhep-th/0011270v2].
139 ChruÅ›ciel, P.T., and Tod, P., “An angular momentum bound at null infinity”, arXiv e-print, (2007). [External LinkarXiv:0706.4057 [gr-qc]].
140 Coleman, S., “Non-Abelian plane waves”, Phys. Lett. B, 70, 59–60, (1977). [External LinkDOI].
141 Cook, G.B., and Whiting, B.F., “Approximate Killing vectors on S2”, Phys. Rev. D, 76, 041501, 1–5, (2007). [External LinkDOI], [External LinkarXiv:0706.0199].
142 Corvino, J., “Scalar curvature deformation and a gluing construction for the Einstein constraint equations”, Commun. Math. Phys., 214, 137–189, (2000).
143 Corvino, J., and Schoen, R.M., “On the Asymptotics for the Vacuum Einstein Constraint Equations”, arXiv e-print, (2003). [External Linkgr-qc/0301071].
144 Corvino, J., and Wu, H., “On the center of mass of isolated systems”, Class. Quantum Grav., 25, 085008, 1–18, (2008). [External LinkDOI], [External LinkADS].
145 Creighton, J.D.E., and Mann, R., “Quasilocal thermodynamics of dilaton gravity coupled to gauge fields”, Phys. Rev. D, 52, 4569–4587, (1995). [External Linkgr-qc/9505007].
146 Crnkovic, C., and Witten, E., “Covariant description of canonical formalism in geometrical theories”, in Hawking, S.W., and Israel, W., eds., Three Hundred Years of Gravitation, pp. 676–684, (Cambridge University Press, Cambridge; New York, 1987).
147 d’ Inverno, R.A., and Smallwood, J., “Covariant 2+2 formalism of the initial-value problem in general relativity”, Phys. Rev. D, 22, 1233–1247, (1980).
148 Dain, S., personal communication, (September 2003).
149 Dain, S., “Angular Momentum–Mass Inequality for Axisymmetric Black Holes”, Phys. Rev. Lett., 96, 101101, 1–3, (2006). [External LinkDOI], [External Linkgr-qc/0511101].
150 Dain, S., “Proof of the (local) angular momentum–mass inequality for axisymmetric black holes”, Class. Quantum Grav., 23, 6845–6855, (2006). [External Linkgr-qc/0511087].
151 Dain, S., “A variational principle for stationary, axisymmetric solutions of Einstein’s equations”, Class. Quantum Grav., 23, 6857–6871, (2006). [External Linkgr-qc/0508061v2].
152 Dain, S., “The Inequality Between Mass and Angular Momentum for Axially Symmetric Black Holes”, Int. J. Mod. Phys. D, 17, 519–523, (2008). [External LinkDOI], [External LinkarXiv:0707.3118].
153 Dain, S., “Proof of the angular momentum–mass inequality for axisymmetric black holes”, J. Differ. Geom., 79, 33–67, (2008). [External Linkgr-qc/0606105v3].
154 Dain, S., Lousto, C.O., and Takahashi, R., “New conformally flat initial data for spinning black holes”, Phys. Rev. D, 65, 104038, 1–7, (2002). [External LinkDOI], [External Linkgr-qc/0201062].
155 Dain, S., and Moreschi, O.M., “General existence proof for rest frame systems in asymptotically flat spacetime”, Class. Quantum Grav., 17, 3663–3672, (2000). [External Linkgr-qc/0203048].
156 Deser, S., Franklin, J.S., and Seminara, D., “Graviton–graviton scattering, Bel–Robinson and energy (pseudo)–tensors”, Class. Quantum Grav., 18, 2815–2821, (1999). [External Linkgr-qc/9905021].
157 Dougan, A.J., “Quasi-local mass for spheres”, Class. Quantum Grav., 9, 2461–2475, (1992).
158 Dougan, A.J., and Mason, L.J., “Quasilocal mass constructions with positive energy”, Phys. Rev. Lett., 67, 2119–2122, (1991).
159 Dray, T., “Momentum flux at null infinity”, Class. Quantum Grav., 2, L7–L10, (1985).
160 Dray, T., and Streubel, M., “Angular momentum at null infinity”, Class. Quantum Grav., 1, 15–26, (1984).
161 Dubois-Violette, M., and Madore, J., “Conservation laws and integrability conditions for gravitational and Yang-Mills equations”, Commun. Math. Phys., 108, 213–223, (1987).
162 Eardley, D.M., “Global problems in numerical relativity”, in Smarr, L.L., ed., Sources of Gravitational Radiation, Proceedings of the Battelle Seattle Workshop, July 24 – August 4, 1978, pp. 127–138, (Cambridge University Press, Cambridge; New York, 1979).
163 Eastwood, M., and Tod, K.P., “Edth – a differential operator on the sphere”, Math. Proc. Camb. Phil. Soc., 92, 317–330, (1982).
164 Epp, R.J., “Angular momentum and an invariant quasilocal energy in general relativity”, Phys. Rev. D, 62, 124018, 1–30, (2000). [External LinkDOI], [External Linkgr-qc/0003035].
165 Exton, A.R., Newman, E.T., and Penrose, R., “Conserved quantities in the Einstein–Maxwell theory”, J. Math. Phys., 10, 1566–1570, (1969).
166 Fan, X.-Q., Shi, Y., and Tam, L.-F., “Large-sphere and small-sphere limits of the Brown–York mass”, arXiv e-print, (2007). [External LinkarXiv:0711.2552 [math.DG]].
167 Farinelli, S., and Schwartz, G., “On the spectrum of the Dirac operator under boundary conditions”, J. Geom. Phys., 28, 67–84, (1998).
168 Fatibene, L., Ferraris, M., Francaviglia, M., and Raiteri, M., “Noether charges, Brown–York quasilocal energy, and related topics”, J. Math. Phys., 42, 1173–1195, (2001). [External Linkgr-qc/0003019].
169 Favata, M., “Energy localization invariance of tidal work in general relativity”, Phys. Rev. D, 63, 064013, 1–14, (2001). [External LinkDOI], [External Linkgr-qc/0008061].
170 Ferraris, M., and Francaviglia, M., “Covariant first-order Lagrangians, energy-density and superpotentials in general relativity”, Gen. Relativ. Gravit., 22, 965–985, (1990).
171 Ferraris, M., and Francaviglia, M., “Conservation laws in general relativity”, Class. Quantum Grav., 9, S79–S95, (1992).
172 Flanagan, É.É., “Hoop conjecture for black-hole horizon formation”, Phys. Rev. D, 44, 2409–2420, (1991).
173 Flanagan, É.É., Marolf, D., and Wald, R.M., “Proof of classical versions of the Bousso entropy bound and of the generalized second law”, Phys. Rev. D, 62, 084035, 1–11, (2000). [External LinkDOI], [External Linkhep-th/9908070v4].
174 Fouxon, I., Betschart, G., and Bekenstein, J.D., “Bound on viscosity and the generalized second law of thermodynamics”, Phys. Rev. D, 77, 024016, 1–11, (2008). [External LinkDOI], [External LinkarXiv:0710.1429v2].
175 Francaviglia, M., and Raiteri, M., “Hamiltonian, energy and entropy in general relativity with non-orthogonal boundaries”, Class. Quantum Grav., 19, 237–258, (2002). [External Linkgr-qc/0107074].
176 Frauendiener, J., “Geometric description of energy-momentum pseudotensors”, Class. Quantum Grav., 6, L237–L241, (1989).
177 Frauendiener, J., “On an integral formula on hypersurfaces in general relativity”, Class. Quantum Grav., 14, 2413–3423, (1997). [External Linkgr-qc/9511036].
178 Frauendiener, J., “On the Penrose inequality”, Phys. Rev. Lett., 87, 101101, (2001). [External Linkgr-qc/0105093].
179 Frauendiener, J., “Conformal Infinity”, Living Rev. Relativity, 7, lrr-2004-1, (2004). URL (cited on 17 November 2008):
http://www.livingreviews.org/lrr-2004-1.
180 Frauendiener, J., and Sparling, G.A.J., “On the symplectic formalism for general relativity”, Proc. R. Soc. London, 436, 141–153, (1992).
181 Frauendiener, J., and Szabados, L.B., “The kernel of the edth operators on higher-genus spacelike 2-surfaces”, Class. Quantum Grav., 18, 1003–1014, (2001). [External Linkgr-qc/0010089].
182 Friedrich, H., “Gravitational fields near space-like and null infinity”, J. Geom. Phys., 24, 83–163, (1998).
183 Friedrich, H., and Nagy, G., “The Initial Boundary Value Problem for Einstein’s Vacuum Field Equation”, Commun. Math. Phys., 201, 619–655, (1999). [External LinkDOI], [External LinkADS].
184 Frolov, V.P., “Embedding of the Kerr–Newman black hole surface in Euclidean space”, Phys. Rev. D, 73, 064021, 1–5, (2006). [External LinkDOI], [External Linkgr-qc/0601104].
185 Gallo, E., Lehner, L., and Moreschi, O.M., “A note on computations of angular momentum and its flux in numerical relativity”, Class. Quantum Grav., 26, 048002, 1–9, (2009). [External LinkDOI], [External LinkarXiv:0810.0666v3].
186 Garfinkle, D., and Mann, R., “Generalized entropy and Noether charge”, Class. Quantum Grav., 17, 3317–3324, (2000). [External Linkgr-qc/0004056v2].
187 Geroch, R., “Spinor Structure of Space-Times in General Relativity. I”, J. Math. Phys., 9, 1739–1744, (1968). [External LinkDOI].
188 Geroch, R., “Energy extraction”, Ann. N.Y. Acad. Sci., 224, 108–117, (1973).
189 Geroch, R., “Asymptotic structure of space-time”, in Esposito, F.P., and Witten, L., eds., Asymptotic Structure of Spacetime, Proceedings of a Symposium on Asymptotic Structure of Space-Time (SOASST), held at the University of Cincinnati, Ohio, June 14 – 18, 1976, pp. 1–105, (Plenum Press, New York, 1977).
190 Geroch, R., Held, A., and Penrose, R., “A spacetime calculus based on pairs of null directions”, J. Math. Phys., 14, 874–881, (1973).
191 Geroch, R., and Winicour, J., “Linkages in general relativity”, J. Math. Phys., 22, 803–812, (1981).
192 Giachetta, G., and Sardanashvily, G., “Stress-Energy-Momentum Tensors in Lagrangian Field Theory. Part 1. Superpotentials”, arXiv e-print, (1995). [External Linkgr-qc/9510061].
193 Giachetta, G., and Sardanashvily, G., “Stress-Energy-Momentum Tensors in Lagrangian Field Theory. Part 2. Gravitational Superpotential”, arXiv e-print, (1995). [External Linkgr-qc/9511040].
194 Gibbons, G.W., “The isoperimetric and Bogomolny inequalities for black holes”, in Willmore, T.J., and Hitchin, N.J., eds., Global Riemannian Geometry, pp. 194–202, (Ellis Horwood; Halsted Press, Chichester; New York, 1984).
195 Gibbons, G.W., “Collapsing shells and the isoperimetric inequality for black holes”, Class. Quantum Grav., 14, 2905–2915, (1997). [External Linkhep-th/9701049].
196 Gibbons, G.W., and Hawking, S.W., “Action integrals and partition functions in general relativity”, Phys. Rev. D, 15, 2752–2756, (1977).
197 Gibbons, G.W., Hawking, S.W., Horowitz, G.T., and Perry, M.J., “Positive mass theorem for black holes”, Commun. Math. Phys., 88, 295–308, (1983).
198 Gibbons, G.W., and Holzegel, G., “The positive mass and isoperimetric inequalities for axisymmetric black holes in four and five dimensions”, Class. Quantum Grav., 23, 6459–6478, (2006). [External Linkgr-qc/0606116].
199 Gibbons, G.W., and Hull, C.M., “A Bogomolny bound for general relativity and solutions in N=2 supergravity”, Phys. Lett. B, 109, 190–194, (1982).
200 Gibbons, G.W., Hull, C.M., and Warner, N.P., “The stability of gauged supergravity”, Nucl. Phys. B, 218, 173–190, (1983).
201 Goldberg, J.N., “Conservation laws in general relativity”, Phys. Rev., 111, 315–320, (1958).
202 Goldberg, J.N., “Invariant transformations, conservation laws, and energy-momentum”, in Held, A., ed., General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein, vol. 1, pp. 469–489, (Plenum Press, New York, 1980).
203 Goldberg, J.N., “Conserved quantities at spatial and null infinity: The Penrose potential”, Phys. Rev. D, 41, 410–417, (1990).
204 Goldberg, J.N., and Soteriou, C., “Canonical general relativity on a null surface with coordinate and gauge fixing”, Class. Quantum Grav., 12, 2779–2797, (1995).
205 Gour, G., “Entropy bounds for charged and rotating systems”, Class. Quantum Grav., 20, 3403–3412, (2003). [External Linkgr-qc/0302117].
206 Gourgoulhon, E., “Generalized Damour–Navier–Stokes equation applied to trapping horizons”, Phys. Rev. D, 72, 104007, 1–16, (2005). [External LinkDOI], [External Linkgr-qc/0508003v2].
207 Gourgoulhon, E., and Jaramillo, J.L., “Area evolution, bulk viscosity, and entropy principles for dynamical horizons”, Phys. Rev. D, 74, 087502, 1–4, (2006). [External LinkDOI], [External LinkADS], [External Linkgr-qc/0607050v2].
208 Güven, R., “Solutions for gravity coupled to non-Abelian plane waves”, Phys. Rev. D, 19, 471–472, (1979).