Eur. Phys. J. Plus (2013) 128: 144
https://doi.org/10.1140/epjp/i2013-13144-7

Regular Article

Lie symmetries of the Ricci and energy-momentum tensors

¹ Faculty of Engineering Sciences, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi, Khyber Pakhtunkhwa, Pakistan
² Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad, Pakistan
³ Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
⁴ Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman

^* e-mail: saifullah@qau.edu.pk

Received: 16 July 2013
Revised: 17 October 2013
Accepted: 29 October 2013
Published online: 27 November 2013

Abstract

Though the Ricci and energy-momentum tensors have the same algebraic symmetries and appear in a similar way in the Einstein equations, in that interchanging them and inverting the gravitational coupling leaves the equations invariant, their differential symmetry Lie algebras are not identical in general. For cylindrically symmetric static spacetimes their inter-relationship is studied in this paper. Neither set of symmetries is a subset of the other in general.