[1] B. P. Abbott et al. [LIGO Scientific Collaboration and Virgo Collaboration], Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102.
[2] K. Akiyama et al., First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. Lett. 875 (2019) L1 [1906.11238].
[3] J.L. Synge, The escape of photons from gravitationally intense stars, Monthly Notices Roy Astron. Soc. 131 (1966) 463.
[4] V. Cardoso, A.S. Miranda, E. Berti, H. Witek and V.T. Zanchin, Geodesic stability, Lyapunov exponents, and quasinormal modes, Phys. Rev. D 79 (2009) 064016 [0812.1806].
[5] S. Hod, Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation, Phys. Rev. D 80 (2009) 064004 [0909.0314].
[6] P.V.P. Cunha, E. Berti and C.A.R. Herdeiro, Light ring stability in ultra-compact objects, Phys. Rev. Lett. 119 (2017) 251102 [1708.04211].
[7] V. Cardoso, L.C.B. Crispino, C.F.B. Macedo, H. Okawa and P. Pani, Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects, Phys. Rev. D 90 (2014) 044069 [1406.5510].
[8] C.-M. Claudel, K. Virbhadra and G. Ellis, The Geometry of photon surfaces, J. Math. Phys. 42 (2001) 818 [gr-qc/0005050].
[9] V. Perlick, On totally umbilic submanifolds of semi-riemannian manifolds, Nonlinear Analysis 63 (2005) e511 [gr-qc/0512066].
[10] G.W. Gibbons and C.M. Warnick, Aspherical Photon and Anti-Photon Surfaces, Phys. Lett. B 763 (2016) 169 [1609.01673].
[11] C. Cederbaum, Uniqueness of photon spheres in static vacuum asymptotically flat spacetimes, Contemp. Math 653 (2015) 86 [1406.5475].
[12] C. Cederbaum and G.J. Galloway, Uniqueness of photon spheres in electro-vacuum spacetimes, Class. Quant. Grav. 33 (2016) 075006 [1508.00355].
[13] M. Rogatko, Uniqueness of photon sphere for Einstein-Maxwell-dilaton black holes with arbitrary coupling constant, Phys. Rev. D 93 (2016) 064003 [1602.03270].
[14] S. Yazadjiev, Uniqueness of the static spacetimes with a photon sphere in Einstein-scalar field theory, Phys. Rev. D 91 (2015) 123013 [1501.06837].
[15] Y. Koga and T. Harada, Stability of null orbits on photon spheres and photon surfaces, Phys. Rev. D 100 (2019) 064040 [1907.07336].
[16] Y. Koga, T. Igata and K. Nakashi, Photon surfaces in less symmetric spacetimes, 2011.10234.
[17] Y. Koga and T. Harada, Correspondence between sonic points of ideal photon gas accretion and photon spheres, Phys. Rev. D 94 (2016) 044053 [1601.07290].
[18] Y. Koga and T. Harada, Rotating accretion flows in D dimensions: sonic points, critical points and photon spheres, Phys. Rev. D 98 (2018) 024018 [1803.06486].
[19] Y. Koga, Photon surfaces in spherically, planar and hyperbolically symmetric spacetimes of D-dimensions: Sonic point/photon sphere correspondence, Phys. Rev. D 99 (2019) 064034 [1901.02592].
[20] Y. Koga, Photon surfaces as pure tension shells: Uniqueness of thin shell wormholes, Phys. Rev. D 101 (2020) 104022 [2003.10859].
[21] R.M. Wald, General Relativity, The University of Chicago Press, Chicago (1984).
[22] J. Keir, Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars, Classical Quantum Gravity 33 (2016) 135009 [1404.7036].
[23] V. Cardoso, L.C.B. Crispino, C.F.B. Macedo, H. Okawa and P. Pani, Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects, Phys. Rev. D 90 (2014) 044069 [1406.5510].
[24] E. Chaverra and O. Sarbach, Radial accretion flows on static spherically symmetric black holes, Class. Quantum Grav. 32 (2015) 155006 [1501.01641].
[25] E. Poisson, A Relativist’s Toolkit, Cambridge University Press, Cambridge, England (2004).
[26] M. Ban˜ados, C. Teitelboim and J. Zanelli, Black Hole in Three-Dimensional Spacetime, Phys. Rev. Lett. 69 (1992) 1840 [1009.3749].
[27] H. Kodama and A. Ishibashi, Master equations for perturbations of generalized static black holes with charge in higher dimensions, Prog. Theor. Phys. Suppl. 111 (2004) 29 [0308128].
[28] G.R. Jensen, Homogeneous einstein spaces of dimension four, J. Differ. Geom. 3 (1969) 309.
[29] J. Fine and B. Premoselli, Examples of compact einstein four-manifolds with negative curvature, J. Amer. Math. Soc. 33 (2020) 991 [1802.00608].
[30] D. Alekseevsky, I. Dotti and C. Ferraris, Homogeneous ricci positive 5-manifolds, Pac. J. Math. 175 (1996) 1.
[31] B. Grajales and L. Grama, NON-DIAGONAL INVARIANT EINSTEIN METRICS ON REAL FLAG MANIFOLDS, 1907.02626.
[32] A.L. Besse, Einstein Manifolds (Classics in Mathematics), Springer-Verlag, Berlin (1986).
[33] H. Bondi, On spherically symmetrical accretion, Monthly Notices Roy Astron. Soc. 112 (1952) 195.
[34] F. Michel, Accretion of matter by condensed objects, Astrophysics and Space Science 15 (1972) 153.
[35] P. Mach, E. Malec and J. Karkowski, Dependence on the cosmological constant, exact isothermal solutions, and applications to cosmology, Phys. Rev. D 88 (2013) 084056 [1309.1252].
[36] J. Karkowski and E. Malec, Bondi accretion onto cosmological black holes, Phys. Rev. D 87 (2013) 044007 [1211.3618].
[37] F.S. Guzman and F.D. Lora-Clavijo, Exploring the effects of pressure on the radial accretion of dark matter by a Schwarzschild supermassive black hole, Mon. Not. R. Astron. Soc. 415 (2011) 225 [1103.5497].
[38] B. Carter, G.W. Gibbons, D.N.C. Lin and M.J. Perry, Black Hole Emission Process in the High Energy Limit, Astronomy and Astrophysics 52 (1976) 427.
[39] S. Chandrasekhar, The Mathematical Theory of Black Holes, Oxford University Press, New York (1983).
[40] H. Abraham, N. Bilic and T.K. Das, Acoustic horizons in axially symmetric relativistic accretion, Classical and Quantum Gravity 23 (2006) 2371 [gr-qc/0509057].
[41] T.K. Das, N. Bilic and S. Dasgupta, Black-Hole Accretion Disc as an Analogue Gravity Model, JCAP 0706 (2007) 009 [astro-ph/0604477].
[42] P. Barai, T.K. Das and P.J. Wiita, Dependence of general relativistic accretion on black hole spin, Astrophys. J. 613 (2004) L49.
[43] M.A. Abramowicz, A. Lanza and M.J. Percival, Accretion disks around Kerr black holes: vertical equilibrium revisited, Astrophys. J. 479 (1997) 179.
[44] M. Tsuchiya, C.-M. Yoo, Y. Koga and T. Harada, Sonic Point and Photon Surface, Phys. Rev. D 102 (2020) 044057 [2003.10125].
[45] P. Kanti, B. Kleinhaus and J. Kunz, Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory, Phys. Rev. Lett. 107 (2011) 271101 [1108.3003].
[46] P. Kanti, B. Kleinhaus and J. Kunz, Stable Lorentzian wormholes in dilatonic Einstein-Gauss-Bonnet theory, Phys. Rev. D 85 (2012) 044007 [1111.4049].
[47] T. Harko, F.S.N. Lobo, M.K. Mak and S.V. Sushkov, Modified-gravity wormholes without exotic matter, Phys. Rev. D 87 (2013) 067504 [1301.6878].
[48] M. Rogatko, Uniqueness of higher-dimensional phantom field wormholes, Phys. Rev. D 97 (2018) 024001 [1801.01987].
[49] S. Yazadjiev, Uniqueness theorem for static wormholes in Einstein-phantom scalar field theory, Phys. Rev. D 96 (2017) 044045 [1707.03654].
[50] M. Rogatko, Uniqueness of higher-dimensional Einstein-Maxwell-phantom dilaton wormholes, Phys. Rev. D 97 (2018) 064023 [1803.08296].
[51] M.S. Morris and K.S. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395.
[52] D. Hochberg and M. Visser, Null Energy Condition in Dynamic Wormholes, Phys. Rev. Lett. 81 (1998) 746 [gr-qc/9802048].
[53] M. Visser, Traversable wormholes from surgically modified Schwarzschild spacetimes, Nucl.Phys. B328 (1989) 203 [0809.0927].
[54] W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cimento 44B (1966) 1.
[55] C. Barcelo and M. Visser, Brane surgery: energy conditions, traversable wormholes, and voids, Nucl. Phys. B584 (2000) 415 [0004022].
[56] T. Kokubu and T. Harada, Negative tension branes as stable thin shell wormholes, Class. Quant. Grav. 32 (2015) 205001 [1411.5454].
[57] L. Randall and R. Sundrum, An alternative to Compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064].
[58] L. Randall and R. Sundrum, Large mass Hierarchy from a Small Extra Dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221].
[59] R. Capovilla and J. Guven, GEOMETRY OF DEFORMATIONS OF RELATIVISTIC MEMBRANES, Phys. Rev. D 51 (1995) 6736 [9411060].
[60] W. Kinnersley and M. Walker, Uniformly Accelerating Charged Mass in General Relativity, Phys. Rev. D 2 (1970) 1359.
[61] W. Smith and R. Mann, Formation of Topological Black holes from Gravitational Collapse, Phys. Rev. D 56 (1997) 4942 [gr-qc/9703007].
[62] T. Shiromizu, Y. Tomikawa, K. Izumi and H. Yoshino, Area bound for a surface in a strong gravity region, Prog. Theor. Exp. Phys. 2017 (2017) 033E01 [1701.00564].
[63] H. Yoshino, K. Izumi, T. Shiromizu and Y. Tomikawa, Extension of photon surfaces and their area: Static and stationary spacetimes, Prog. Theor. Exp. Phys. 2017 (2017) 063E01 [1704.04637].
[64] H. Yoshino, K. Izumi, T. Shiromizu and Y. Tomikawa, Transversely trapping surfaces: Dynamical version, Prog. Theor. Exp. Phys. 2020 (2020) 023E02 [1909.08420].
[65] M. Siino, Causal concept for black hole shadows, Class. Quant. Grav. 38 (2020) 025005 [1908.02921].
[66] K.V. Kobialko and D.V. Gal’tsov, Photon regions and umbilic conditions in stationary axisymmetric spacetimes, Eur. Phys. J. C 80 (2020) 527 [2002.04280].
[67] S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, England (1973).
論文の公開元へ
