Built on

T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev
1957
Earlier work this paper cites.
C. V. Vishveshwara, “Stability of the schwarzschild metric,” Phys. Rev
1970
Earlier work this paper cites.
D. Lovelock, “The Einstein tensor and its generalizations,” J. Math. Phys
1971
Earlier work this paper cites.
F. H. Stillinger, “Axiomatic basis for spaces with noninteger dimension,” Journal of Mathematical Physics
1977
Earlier work this paper cites.
T. Appelquist and A. Chodos, “The Quantum Dynamics of Kaluza-Klein Theories,” Phys. Rev
1983
Earlier work this paper cites.
D. G. Boulware and S. Deser, “String Generated Gravity Models,” Phys. Rev. Lett
1985
Earlier work this paper cites.
F. Mueller-Hoissen, “Spontaneous Compactification With Quadratic and Cubic Curvature Terms,” Phys. Lett
1985
Earlier work this paper cites.
C. Teitelboim and J. Zanelli, “Dimensionally continued topological gravitation theory in Hamiltonian form,” Class. Quant. Grav
1987
Earlier work this paper cites.
N. Deruelle, “On the Approach to the Cosmological Singularity in Quadratic Theories of Gravity: The Kasner Regimes,” Nucl. Phys
1989
Earlier work this paper cites.
N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, “The Hierarchy problem and new dimensions at a millimeter,” Phys.Lett
1998
Earlier work this paper cites.
N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, and N. Kaloper, “Infinitely large new dimensions,” Phys. Rev. Lett
2000
Earlier work this paper cites.
S. Alexeyev, A. Toporensky, and V. Ustiansky, “The Nature of singularity in Bianchi I cosmological string gravity model with second order curvature corrections,” Phys. Lett
2001
Earlier work this paper cites.
A. Ishibashi and H. Kodama, “Stability of higher dimensional Schwarzschild black holes,” Prog. Theor. Phys
2003
Earlier work this paper cites.
V. E. Tarasov, “Gravitational Field of Fractal Distribution of Particles,” Celest. Mech. Dyn. Astron
2006
Earlier work this paper cites.
E. Elizalde, A. N. Makarenko, V. V. Obukhov, K. E. Osetrin, and A. E. Filippov, “Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein-Gauss-Bonnet gravity,” Phys. Lett
2007
Earlier work this paper cites.
D. Kastor, “Komar Integrals in Higher (and Lower) Derivative Gravity,” Class.Quant.Grav
Original
2008
Earlier work this paper cites.

Similar

C. Garraffo and G. Giribet, “The Lovelock Black Holes,” Mod. Phys. Lett
Original
2008
Cited alongside, same era.
S. A. Pavluchenko, “General features of Bianchi-I cosmological models in Lovelock gravity,” Phys. Rev
Original
2009
Cited alongside, same era.
F. Canfora, A. Giacomini, R. Troncoso, and S. Willison, “General Relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum,” Phys. Rev
Original
2009
Cited alongside, same era.
T. Takahashi and J. Soda, “Instability of Small Lovelock Black Holes in Even-dimensions,” Phys. Rev
Original
2009
Cited alongside, same era.
Cambridge University Press, Cambridge, UK, 2010
T.Padmanabhan, Gravitation: Foundations and Frontiers · 2010

Then

S. Chakraborty and T. Padmanabhan, “Evolution of Spacetime arises due to the departure from Holographic Equipartition in all Lanczos-Lovelock Theories of Gravity,” Phys.Rev
Original
2014
Later among the works it cites.
K.-i. Maeda and N. Ohta, “Cosmic acceleration with a negative cosmological constant in higher dimensions,” JHEP
Original
2014
Later among the works it cites.
F. Canfora, A. Giacomini, and S. A. Pavluchenko, “Cosmological dynamics in higher-dimensional Einstein-Gauss-Bonnet gravity,” Gen. Rel. Grav
Original
2014
Later among the works it cites.
V. E. Tarasov, “Fractional Quantum Field Theory: From Lattice to Continuum,” Adv. High Energy Phys
2014
Later among the works it cites.
R. Gannouji and N. Dadhich, “Stability and existence analysis of static black holes in pure Lovelock theories,” Class. Quant. Grav

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2016

1/r potential in higher dimensions

Chakraborty, Sumanta, Dadhich, Naresh

Understand

In Einstein gravity, gravitational potential goes as $1/r^{d-3}$ in $d$ non-compactified spacetime dimensions, which assumes the familiar $1/r$ form in four dimensions.

On the other hand, it goes as $1/r^{\alpha}$, with $\alpha=(d-2m-1)/m$, in pure Lovelock gravity involving only one $m$th order term of the Lovelock polynomial in the gravitational action.
The latter offers a novel possibility of having $1/r$ potential for the non-compactified dimension spectrum given by $d=3m+1$.
Thus it turns out that in the two prototype gravitational settings of isolated objects, like black holes and the universe as a whole --- cosmological models, the Einstein gravity in four and $m$th order pure Lovelock gravity in $3m+1$ dimensions behave in a similar fashion as far as gravitational interactions are considered.

Built on

T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev
1957
Earlier work this paper cites.
C. V. Vishveshwara, “Stability of the schwarzschild metric,” Phys. Rev
1970
Earlier work this paper cites.
D. Lovelock, “The Einstein tensor and its generalizations,” J. Math. Phys
1971
Earlier work this paper cites.
F. H. Stillinger, “Axiomatic basis for spaces with noninteger dimension,” Journal of Mathematical Physics
1977
Earlier work this paper cites.
T. Appelquist and A. Chodos, “The Quantum Dynamics of Kaluza-Klein Theories,” Phys. Rev
1983
Earlier work this paper cites.
D. G. Boulware and S. Deser, “String Generated Gravity Models,” Phys. Rev. Lett
1985
Earlier work this paper cites.
F. Mueller-Hoissen, “Spontaneous Compactification With Quadratic and Cubic Curvature Terms,” Phys. Lett
1985
Earlier work this paper cites.
C. Teitelboim and J. Zanelli, “Dimensionally continued topological gravitation theory in Hamiltonian form,” Class. Quant. Grav
1987
Earlier work this paper cites.
N. Deruelle, “On the Approach to the Cosmological Singularity in Quadratic Theories of Gravity: The Kasner Regimes,” Nucl. Phys
1989
Earlier work this paper cites.
N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, “The Hierarchy problem and new dimensions at a millimeter,” Phys.Lett
1998
Earlier work this paper cites.
N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, and N. Kaloper, “Infinitely large new dimensions,” Phys. Rev. Lett
2000
Earlier work this paper cites.
S. Alexeyev, A. Toporensky, and V. Ustiansky, “The Nature of singularity in Bianchi I cosmological string gravity model with second order curvature corrections,” Phys. Lett
2001
Earlier work this paper cites.
A. Ishibashi and H. Kodama, “Stability of higher dimensional Schwarzschild black holes,” Prog. Theor. Phys
2003
Earlier work this paper cites.
V. E. Tarasov, “Gravitational Field of Fractal Distribution of Particles,” Celest. Mech. Dyn. Astron
2006
Earlier work this paper cites.
E. Elizalde, A. N. Makarenko, V. V. Obukhov, K. E. Osetrin, and A. E. Filippov, “Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein-Gauss-Bonnet gravity,” Phys. Lett
2007
Earlier work this paper cites.
D. Kastor, “Komar Integrals in Higher (and Lower) Derivative Gravity,” Class.Quant.Grav
Original
2008
Earlier work this paper cites.