Birkhoff’s theorem in f(R) theory of gravity

• Published in: European physical journal plus Vol. 133; no. 9; p. 376
• Main Authors: Ravindranath, P. J., Aditya, Y., Reddy, D. R. K., Subba Rao, M. V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2018; Springer Nature B.V
• Subjects: Applied and Technical Physics; Applied mathematics; Atomic; Black holes; Complex Systems; Condensed Matter Physics; Dark energy; Einstein equations; Gravitation theory; Gravity; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Relativity; Tensors; Theorems; Theoretical; Theory of relativity
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2018-12241-5

. Birkhoff’s theorem in general relativity states that every spherically symmetric solution of Einstein field equations in vacuum is either static or Schwarzschild. This theorem has been established in the scalar-tensor theories of gravity by Reddy (J. Phys. A 6 , 1867 (1973)). In this paper, we prove this theorem in f ( R ) theory of gravity (where R Ricci scalar) when the scalaron Φ ( R ) of the theory is time-independent only. However, no attention is given to the order of the f ( R ) theory. Here it is important to note that the Birkhoff theorem in f ( R ) gravity states only that if R is time-independent, the spherical solution is static (not Schwarzschild).