Built on

T. H. R. Skyrme, “A unified field theory of mesons and baryons” Nucl. Phys. 31 (1962) 556-569
1962
Earlier work this paper cites.
G. H. Derrick, “Comments on Nonlinear Wave Equations as Models for Elementary Particles” J. Math. Phys. 5 (1964) 1252-1254
1964
Earlier work this paper cites.
C. Deffayet, S. Deser, and G. Esposito-Farese, “Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors” Phys. Rev. D80 (2009) 064015, arxiv:0906.1967 [hep-th]
Original
1967
Earlier work this paper cites.
A. I. Vainshtein, “To the problem of nonvanishing gravitation mass” Phys. Lett. B 39 (1972) 393-394
1972
Earlier work this paper cites.
D. B. Fairlie and J. Govaerts, “Euler hierarchies and universal equations” J. Math. Phys. 33 (1992) 3543-3566 [arXiv hep-th/9204074]
1992
Earlier work this paper cites.
D. B. Fairlie, J. Govaerts, and A. Morozov “Universal field equations with covariant solutions” Nucl. Phys. B373 (1992) 214-232 [arXiv hep-th/9110022]
1992
Earlier work this paper cites.

Similar

D. B. Fairlie and J. Govaerts, “Linearisation of Universal Field Equations” J. Phys. A26 (1993) 3339-3347 [arXiv:hep-th/9212005]
1993
Cited alongside, same era.
J. A. Wheeler, “Geons” Phys. Rev. 97 (1955) 511-536. Also see P. R. Anderson and D. R. Brill, “Gravitational Geons Revisited” Phys. Rev. D56 (1997) 4824-4833, arXiv:gr-qc/9610074
1997
Cited alongside, same era.
G. R. Dvali, G. Gabadadze, and M. Porrati, “4-D gravity on a brane in 5-D Minkowski space” Phys. Lett. B 485 (2000) 208 [arXiv:hep-th/0005016]; M. A. Luty, M. Porrati and R. Rattazzi, “Strong interactions and stability in the DGP model” JHEP 0309 (2003) 029 [arXiv:hep-th/0303116]; A. Nicolis and R. Rattazzi, “Classical and quantum consistency of the DGP model” JHEP 0406 (2004) 059 [arXiv:hep-th/0404159]
2004
Cited alongside, same era.
C. Deffayet, G. Esposito-Farese, and A. Vikman, “Covariant Galileon” Phys. Rev. D79 (2009) 084003, arXiv:0901.1314 [hep-th]
Original
2009

Then

D. Fairlie, “Comments on Galileons” J. Phys. A44 (2011) 305201, arXiv:1102.1594 [hep-th]
Original
2011
Later among the works it cites.
G. L. Goon, K. Hinterbichler, M. Trodden, “Stability and superluminality of spherical DBI galileon solutions” Phys. Rev. D83 (2011) 085015 arXiv:1008.4580 [hep-th]
Original
2011
Later among the works it cites.
G. W. Horndeski, “Second-order scalar-tensor field equations in a four-dimensional space” Int. J. Theor. Physics 10 (1974) 363-384. Also see C. Deffayet, Xian Gao, D. A. Steer, and G. Zahariade, “From k-essence to generalised Galileons” Phys. Rev. D84 (2011) 064039 arXiv:1103.3260 [hep-th]
Original
2011
Later among the works it cites.
R. Jackiw and S.-Y. Pi, “Tutorial on Scale and Conformal Symmetries in Diverse Dimensions” J. Phys. A44 (2011) 223001, arXiv:1101.4886 [math-ph], and references therein
Original
2011
Later among the works it cites.

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2012

Geons of Galileons

Curtright, Thomas L., Fairlie, David B.

Understand

We suggest that galileon theories should have an additional self-coupling of the fields to the trace of their own energy-momentum tensor.

We explore the classical features of one such model, in flat 4D spacetime, with emphasis on solutions that are scalar analogues of gravitational geons.
We discuss the stability of these scalar geons, and some of their possible signatures, including shock fronts.

Built on

T. H. R. Skyrme, “A unified field theory of mesons and baryons” Nucl. Phys. 31 (1962) 556-569
1962
Earlier work this paper cites.
G. H. Derrick, “Comments on Nonlinear Wave Equations as Models for Elementary Particles” J. Math. Phys. 5 (1964) 1252-1254
1964
Earlier work this paper cites.
C. Deffayet, S. Deser, and G. Esposito-Farese, “Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors” Phys. Rev. D80 (2009) 064015, arxiv:0906.1967 [hep-th]
Original
1967
Earlier work this paper cites.
A. I. Vainshtein, “To the problem of nonvanishing gravitation mass” Phys. Lett. B 39 (1972) 393-394
1972
Earlier work this paper cites.
D. B. Fairlie and J. Govaerts, “Euler hierarchies and universal equations” J. Math. Phys. 33 (1992) 3543-3566 [arXiv hep-th/9204074]
1992
Earlier work this paper cites.
D. B. Fairlie, J. Govaerts, and A. Morozov “Universal field equations with covariant solutions” Nucl. Phys. B373 (1992) 214-232 [arXiv hep-th/9110022]
1992
Earlier work this paper cites.

Similar

D. B. Fairlie and J. Govaerts, “Linearisation of Universal Field Equations” J. Phys. A26 (1993) 3339-3347 [arXiv:hep-th/9212005]
1993
Cited alongside, same era.
J. A. Wheeler, “Geons” Phys. Rev. 97 (1955) 511-536. Also see P. R. Anderson and D. R. Brill, “Gravitational Geons Revisited” Phys. Rev. D56 (1997) 4824-4833, arXiv:gr-qc/9610074
1997
Cited alongside, same era.
G. R. Dvali, G. Gabadadze, and M. Porrati, “4-D gravity on a brane in 5-D Minkowski space” Phys. Lett. B 485 (2000) 208 [arXiv:hep-th/0005016]; M. A. Luty, M. Porrati and R. Rattazzi, “Strong interactions and stability in the DGP model” JHEP 0309 (2003) 029 [arXiv:hep-th/0303116]; A. Nicolis and R. Rattazzi, “Classical and quantum consistency of the DGP model” JHEP 0406 (2004) 059 [arXiv:hep-th/0404159]
2004
Cited alongside, same era.
C. Deffayet, G. Esposito-Farese, and A. Vikman, “Covariant Galileon” Phys. Rev. D79 (2009) 084003, arXiv:0901.1314 [hep-th]
Original
2009

Then

D. Fairlie, “Comments on Galileons” J. Phys. A44 (2011) 305201, arXiv:1102.1594 [hep-th]
Original
2011
Later among the works it cites.
G. L. Goon, K. Hinterbichler, M. Trodden, “Stability and superluminality of spherical DBI galileon solutions” Phys. Rev. D83 (2011) 085015 arXiv:1008.4580 [hep-th]
Original
2011
Later among the works it cites.
G. W. Horndeski, “Second-order scalar-tensor field equations in a four-dimensional space” Int. J. Theor. Physics 10 (1974) 363-384. Also see C. Deffayet, Xian Gao, D. A. Steer, and G. Zahariade, “From k-essence to generalised Galileons” Phys. Rev. D84 (2011) 064039 arXiv:1103.3260 [hep-th]
Original
2011
Later among the works it cites.
R. Jackiw and S.-Y. Pi, “Tutorial on Scale and Conformal Symmetries in Diverse Dimensions” J. Phys. A44 (2011) 223001, arXiv:1101.4886 [math-ph], and references therein
Original
2011
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

S. Endlich, K. Hinterbichler, L. Hui, A. Nicolis, and J. Wang, “Derrick’s theorem beyond a potential” JHEP 05 (2011) 73, arXiv:1002.4873 [hep-th]; A. Padilla, P.M. Saffin, and S.-Y. Zhou, “Multi-galileons, solitons and Derrick’s theorem” Phys. Rev. D83 (2011) 045009, arXiv:1008.0745 [hep-th]

Original

2011

Cited alongside, same era.

For a recent review, C. de Rham, “Galileons in the Sky” arXiv:1204.5492 [astro-ph.CO]

Original

Cited in the paper.

G. Gabadadze, K. Hinterbichler, and D. Pirtskhalava, “Classical Duals of Derivatively Self-Coupled Theories” arXiv:1202.6364 [hep-th]

Original

Cited in the paper.

Also note that A 2 A_{2} follows from coupling ϕ \phi to the trace of the manifestly chargeless tensor ( ∂ μ ∂ ν − δ μ ν ∂ α ∂ α ) ϕ β ϕ β \left(\partial_{\mu}\partial_{\nu}-\delta_{\mu\nu}\partial_{\alpha}\partial_{\alpha}\right)\phi_{\beta}\phi_{\beta}

Cited in the paper.

For C < 0 C<0 , to see cancellation between the individually divergent galileon and trace interaction energies for small r r requires leading and next-to-leading terms in the expansion: ϕ ′ ∼ r → 0 − 2 λ κ r + κ C 4 λ 2 + O ⁡ ( r ) \ \phi^{\prime}\underset{r\rightarrow 0}{\sim}\tfrac{-2\lambda}{\kappa r}+\tfrac{\kappa C}{4\lambda^{2}}+O\left(r\right)

Cited in the paper.

The multivalued behavior of any solution for C critical < C < 0 C_{\text{critical}}<C<0 makes the determination of the total energy ambiguous, at best, for these cases. This is an unresolved issue

Cited in the paper.

P. G. O. Freund and Y. Nambu, “Scalar field coupled to the trace of the energy-momentum tensor” Phys. Rev. 174 (1968) 1741-1743. Also see Appendix II in R. H. Kraichnan, “Special-Relativistic Derivation of Generally Covariant Gravitation Theory” Phys. Rev. 98 (1955) 1118-1122. The history of this idea is traced in K. Hinterbichler, “Theoretical Aspects of Massive Gravity” Rev. Mod. Phys. 84 (2012) 671-710, arXiv:1105.3735 [hep-th]

Original

2012

Closest in time.