Built on

M. Fierz, W. Pauli, On Relativistic Wave Equations for Particles of Arbitrary Spin in an Electromagnetic Field , Proc. Roy. Soc. Lond. A 173
1939
Earlier work this paper cites.
R. Courant, D. Hilbert, Methods of Mathematical Physics , Vol.2, Wiley-Interscience, Inc., New York (1962) pp. 590 and 596
Original
1962
Earlier work this paper cites.
H. van Dam, M. J. G. Veltman, Massive and Massless Yang-Mills and Gravitational Field , Nucl. Phys. B 22
1970
Earlier work this paper cites.
V. I. Zakharov, Linearized Gravitation Theory and the Graviton Mass , JETP Lett. 12
1970
Earlier work this paper cites.
B. Zumino, Effective Lagrangians and Broken Symmetries , Brandeis Univ. Lectures on Elementary Particles and Quantum Field Theory, MIT Press Cambridge (Mass. , S. Deser, M. Grisaru and H. Pendleton eds.), Vol. 2
1970
Earlier work this paper cites.
A. I. Vainshtein, To the Problem of Nonvanishing Graviton Mass , Phys. Lett. B 39
1972
Earlier work this paper cites.
D. Boulware, S. Deser, Can Gravitation Have a Finite Range? , Phys. Rev. D 6
1972
Earlier work this paper cites.
P. Van Nieuwenhuizen, On Ghost-Free Tensor Lagrangians and Linearized Gravitation , Nucl. Phys. B 60
1973
Earlier work this paper cites.
F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, General Relativity with Spin and Torsion: Foundations and Prospects , Rev. Mod. Phys. 48
1976
Earlier work this paper cites.
H. Chen, J. M. Nester, H. -J. Yo, Acausal PGT Modes and the Nonlinear Constraint Effect , A. Phys. Pol. B, 29
1998
Earlier work this paper cites.
J-P. Bruneton, On Causality and Superluminal Behavior in Classical Field Theories: Applications to k-Essence Theories and MOND-like Theories of Gravity , Phys. Rev. D 75
2007
Earlier work this paper cites.
N. Afshordi, D. J. H. Chung, G. Geshnizjani, Cuscuton: A Causal Field Theory with an Infinite Speed of Sound , Phys. Rev. D 75
2007
Earlier work this paper cites.
E. Babichev, C. Deffayet, R. Ziour, The Recovery of General Relativity in Massive Gravity via the Vainshtein Mechanism , Phys. Rev. D 82
Original
2010
Earlier work this paper cites.

Similar

P. Chen, Gauge Theory of Gravity with de Sitter Symmetry as a Solution to the Cosmological Constant Problem and the Dark Enegry Puzzle , Mod. Phys. Lett. A 25
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C. de Rham, G. Gabadadze, A. J. Tolley, Resummation of Massive Gravity , Phys. Rev. Lett. 106
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Original
2011
Cited alongside, same era.
G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava, A. J. Tolley, Massive Cosmologies , Phys. Rev. D 84

Then

S. F. Hassan, R. A. Rosen, Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity , JHEP 04
Original
2012
Later among the works it cites.
S. Hassan, A. Schmidt-May, M. von Strauss, Proof of Consistency of Nonlinear Massive Gravity in the Stúckelberg Formulation , Phys. Lett. B 715
Original
2012
Later among the works it cites.
A. E. Gumrukcuoglu, C. Lin, S. Mukohyama, Cosmological Perturbations of Self-Accelerating Universe in Nonlinear Massive Gravity , JCAP 03
Original
2012
Later among the works it cites.
K. Hinterbichler, R. A. Rosen, Interacting Spin-2 Fields , JHEP 1207
Original
2012
Later among the works it cites.
K. Nomura, J. Soda, When is Multimetric Gravity Ghost-free? , Phys. Rev. D 86

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2013

An Analysis of Characteristics in Non-Linear Massive Gravity

Izumi, Keisuke, Ong, Yen Chin

Understand

We study the Cauchy problem in a special case of non-linear massive gravity: the two-tensor "f-g" theory.

Despite being ghost-free, it has recently been argued that the theory is inherently problematic due to the existence of superluminal shock waves.
Furthermore it is claimed that acausal characteristic can arise for any choice of background.
In order to further understand the causal structure of the theory, we carefully perform a detailed analysis of the characteristic equations and show that the theory does admit a well-posed Cauchy problem, i.e., there exist hypersurfaces that are not characteristic hypersurface.

Built on

M. Fierz, W. Pauli, On Relativistic Wave Equations for Particles of Arbitrary Spin in an Electromagnetic Field , Proc. Roy. Soc. Lond. A 173
1939
Earlier work this paper cites.
R. Courant, D. Hilbert, Methods of Mathematical Physics , Vol.2, Wiley-Interscience, Inc., New York (1962) pp. 590 and 596
Original
1962
Earlier work this paper cites.
H. van Dam, M. J. G. Veltman, Massive and Massless Yang-Mills and Gravitational Field , Nucl. Phys. B 22
1970
Earlier work this paper cites.
V. I. Zakharov, Linearized Gravitation Theory and the Graviton Mass , JETP Lett. 12
1970
Earlier work this paper cites.
B. Zumino, Effective Lagrangians and Broken Symmetries , Brandeis Univ. Lectures on Elementary Particles and Quantum Field Theory, MIT Press Cambridge (Mass. , S. Deser, M. Grisaru and H. Pendleton eds.), Vol. 2
1970
Earlier work this paper cites.
A. I. Vainshtein, To the Problem of Nonvanishing Graviton Mass , Phys. Lett. B 39
1972
Earlier work this paper cites.
D. Boulware, S. Deser, Can Gravitation Have a Finite Range? , Phys. Rev. D 6
1972
Earlier work this paper cites.
P. Van Nieuwenhuizen, On Ghost-Free Tensor Lagrangians and Linearized Gravitation , Nucl. Phys. B 60
1973
Earlier work this paper cites.
F. W. Hehl, P. von der Heyde, G. D. Kerlick, J. M. Nester, General Relativity with Spin and Torsion: Foundations and Prospects , Rev. Mod. Phys. 48
1976
Earlier work this paper cites.
H. Chen, J. M. Nester, H. -J. Yo, Acausal PGT Modes and the Nonlinear Constraint Effect , A. Phys. Pol. B, 29
1998
Earlier work this paper cites.
J-P. Bruneton, On Causality and Superluminal Behavior in Classical Field Theories: Applications to k-Essence Theories and MOND-like Theories of Gravity , Phys. Rev. D 75
2007
Earlier work this paper cites.
N. Afshordi, D. J. H. Chung, G. Geshnizjani, Cuscuton: A Causal Field Theory with an Infinite Speed of Sound , Phys. Rev. D 75
2007
Earlier work this paper cites.
E. Babichev, C. Deffayet, R. Ziour, The Recovery of General Relativity in Massive Gravity via the Vainshtein Mechanism , Phys. Rev. D 82
Original
2010
Earlier work this paper cites.