Built on

S.W. Wei, Y.C. Zou, Y.X. Liu and R.B. Mann, “Curvature radius and Kerr black hole shadow,” JCAP 1908
Original
1904
Earlier work this paper cites.
R. Shaikh, “Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
K. Akiyama et al
Original
1906
Earlier work this paper cites.
H.S. Liu, Z.F. Mai, Y.Z. Li and H. Lü, “Quasi-topological electromagnetism: dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality,” arXiv:1907.10876 [hep-th]
Original
1907
Earlier work this paper cites.
R.A. Konoplya, T. Pappas and A. Zhidenko, “Einstein-scalar-Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows,” arXiv:1907.10112 [gr-qc]
Original
1907
Earlier work this paper cites.
M. Wang, S. Chen and J. Jing, “Effect of gravitational wave on shadow of a Schwarzschild black hole,” arXiv:1908.04527 [gr-qc]
Original
1908
Earlier work this paper cites.
A. Das, A. Saha and S. Gangopadhyay, “Shadow of charged black holes in Gauss-Bonnet gravity,” arXiv:1909.01988 [gr-qc]
Original
1909
Earlier work this paper cites.
M. Zhang and M. Guo, “Black hole shadow and black hole thermodynamics,” arXiv:1909.07033 [gr-qc]
Original
1909
Earlier work this paper cites.
H.S. Liu, H. Lü, L. Ma and W.D. Tan, “Holographic complexity bounds,” arXiv:1910.10723 [hep-th]
Original
1910
Earlier work this paper cites.
J.L. Synge, “The escape of photons from gravitationally intense stars,” Mon. Not. Roy. Astron. Soc. 131
1966
Earlier work this paper cites.
J.M. Bardeen, in Proceedings of the International Conference GR5, Tbilisi, U.S.S.R. (1968), p. 174
1968
Earlier work this paper cites.
J.P. Luminet, “Image of a spherical black hole with thin accretion disk,” Astron. Astrophys. 75
1979
Earlier work this paper cites.
A. García A, H. Salazar and J.F. Plebánski, “Type- D D solutions of the Einstein and Born-Infeld nonlinear-electrodynamics equations,” Nuovo Cimento B 84
1984
Earlier work this paper cites.
M.J. Duff, H. Lü and C.N. Pope, “The black branes of M theory,” Phys. Lett. B 382
1996
Earlier work this paper cites.
M. Cvetič and A.A. Tseytlin, “Nonextreme black holes from nonextreme intersecting M-branes,” Nucl. Phys. B 478
1996
Earlier work this paper cites.
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, “STU black holes and string triality,” Phys. Rev. D 54
1996
Earlier work this paper cites.

Similar

M. Cvetič, M.J. Duff, P. Hoxha, J.T. Liu, H. Lü, J.X. Lu, R. Martinez-Acosta, C.N. Pope, H. Sati, T.A. Tran, “Embedding AdS black holes in ten-dimensions and eleven-dimensions,” Nucl. Phys. B 558
1999
Cited alongside, same era.
A. De Vries, “The apparent shape of a rotating charged black hole, closed photon orbits and the bifurcation set A 4 A_{4} ,” Class. Quant. Grav. 17
2000
Cited alongside, same era.
C.M. Claudel, K.S. Virbhadra and G.F.R. Ellis, “The Geometry of photon surfaces,” J. Math. Phys. 42
2001
Cited alongside, same era.
S.E. Vazquez and E.P. Esteban, “Strong field gravitational lensing by a Kerr black hole,” Nuovo Cim. B 119
2004
Cited alongside, same era.
K.G. Zloshchastiev, On co-existence of black holes and scalar field,
2005
Cited alongside, same era.

Then

X.H. Feng, H. Lü and Q. Wen, Scalar hairy black holes in general dimensions,
Original
2014
Later among the works it cites.
J.W. Moffat, “Modified gravity black holes and their observable shadows,” Eur. Phys. J. C 75
Original
2015
Later among the works it cites.
P.V.P. Cunha, C.A.R. Herdeiro, E. Radu and H.F. Runarsson, “Shadows of Kerr black holes with scalar hair,” Phys. Rev. Lett. 115
Original
2015
Later among the works it cites.
A. Abdujabbarov, M. Amir, B. Ahmedov and S.G. Ghosh, “Shadow of rotating regular black holes,” Phys. Rev. D 93
Original
2016
Later among the works it cites.
Z. Younsi, A. Zhidenko, L. Rezzolla, R. Konoplya and Y. Mizuno, “New method for shadow calculations: Application to parametrized axisymmetric black holes,” Phys. Rev. D 94

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2019

On the Size of a Black Hole: The Schwarzschild is the Biggest

Lu, H., Lyu, Hong-Da

Understand

We consider static black holes in Einstein gravity and study parameters characterizing the black hole size, namely the radii of the horizon $R_+$, photon sphere $R_{\rm ph}$ and black hole shadow $R_{\rm sh}$.

We find a sequence of inequalities $\frac32 R_+\, \le\, R_{\rm ph}\, \le \,\frac{1}{\sqrt3} R_{\rm sh}\,\le\, 3 M$, where $M$ is the black hole mass.
These are consistent with and beyond the previously known upper bounds in literature.
The Schwarzschild black hole saturates all the inequalities, making it the biggest of all for given mass.

Built on

S.W. Wei, Y.C. Zou, Y.X. Liu and R.B. Mann, “Curvature radius and Kerr black hole shadow,” JCAP 1908
Original
1904
Earlier work this paper cites.
R. Shaikh, “Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
K. Akiyama et al
Original
1906
Earlier work this paper cites.
H.S. Liu, Z.F. Mai, Y.Z. Li and H. Lü, “Quasi-topological electromagnetism: dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality,” arXiv:1907.10876 [hep-th]
Original
1907
Earlier work this paper cites.
R.A. Konoplya, T. Pappas and A. Zhidenko, “Einstein-scalar-Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows,” arXiv:1907.10112 [gr-qc]
Original
1907
Earlier work this paper cites.
M. Wang, S. Chen and J. Jing, “Effect of gravitational wave on shadow of a Schwarzschild black hole,” arXiv:1908.04527 [gr-qc]
Original
1908
Earlier work this paper cites.
A. Das, A. Saha and S. Gangopadhyay, “Shadow of charged black holes in Gauss-Bonnet gravity,” arXiv:1909.01988 [gr-qc]
Original
1909
Earlier work this paper cites.
M. Zhang and M. Guo, “Black hole shadow and black hole thermodynamics,” arXiv:1909.07033 [gr-qc]
Original
1909
Earlier work this paper cites.
H.S. Liu, H. Lü, L. Ma and W.D. Tan, “Holographic complexity bounds,” arXiv:1910.10723 [hep-th]
Original
1910
Earlier work this paper cites.
J.L. Synge, “The escape of photons from gravitationally intense stars,” Mon. Not. Roy. Astron. Soc. 131
1966
Earlier work this paper cites.
J.M. Bardeen, in Proceedings of the International Conference GR5, Tbilisi, U.S.S.R. (1968), p. 174
1968
Earlier work this paper cites.
J.P. Luminet, “Image of a spherical black hole with thin accretion disk,” Astron. Astrophys. 75
1979
Earlier work this paper cites.
A. García A, H. Salazar and J.F. Plebánski, “Type- D D solutions of the Einstein and Born-Infeld nonlinear-electrodynamics equations,” Nuovo Cimento B 84
1984
Earlier work this paper cites.
M.J. Duff, H. Lü and C.N. Pope, “The black branes of M theory,” Phys. Lett. B 382
1996
Earlier work this paper cites.
M. Cvetič and A.A. Tseytlin, “Nonextreme black holes from nonextreme intersecting M-branes,” Nucl. Phys. B 478
1996
Earlier work this paper cites.
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, “STU black holes and string triality,” Phys. Rev. D 54
1996
Earlier work this paper cites.

Similar

M. Cvetič, M.J. Duff, P. Hoxha, J.T. Liu, H. Lü, J.X. Lu, R. Martinez-Acosta, C.N. Pope, H. Sati, T.A. Tran, “Embedding AdS black holes in ten-dimensions and eleven-dimensions,” Nucl. Phys. B 558
1999
Cited alongside, same era.
A. De Vries, “The apparent shape of a rotating charged black hole, closed photon orbits and the bifurcation set A 4 A_{4} ,” Class. Quant. Grav. 17
2000
Cited alongside, same era.
C.M. Claudel, K.S. Virbhadra and G.F.R. Ellis, “The Geometry of photon surfaces,” J. Math. Phys. 42
2001
Cited alongside, same era.
S.E. Vazquez and E.P. Esteban, “Strong field gravitational lensing by a Kerr black hole,” Nuovo Cim. B 119
2004
Cited alongside, same era.
K.G. Zloshchastiev, On co-existence of black holes and scalar field,
2005
Cited alongside, same era.