Erratum to: General spherically symmetric elastic stars in relativity

Generating elastic solutions of the Einstein field equations from the Schwarzschild vacuum solution

“…The pressure tensor p ab can be expressed as p ab = p 1 e 1a e 1b + p 2 e 2a e 2b + p 3 e 3a e 3b (113) and the principal pressures p 1 , p 2 , p 3 satisfy p 1 + p 2 + p 3 = 3p. Following [24] (see also [18], [19]) the energy-momentum tensor for elastic matter can also be written as…”

“…These expressions allow to write the components of the energy-momentum tensor in the following way (using a process presented in [18], [19])…”

“…where ρ is the energy density, p 1 the radial and p 2 the tangential pressure. Note that the last expressions depending on the eigenvalues are obtained from (114) in an analogous way as explained in Subsection 2.1 (or in [17], [18], [19]). The weak energy condition is satisfied for certain ranges of r, however ρ − p 2 < 0, so that the dominant energy condition is not satisfied.…”

“…In Section 3 are summarized the main conclusions of this work. The Appendix contains a brief review of the relativistic theory of elasticity, based on the formulations presented in [4], [8] and [18], [19].…”

Compact objects from gravitational collapse: an analytical toy model

“…In fact, static regular perfect fluid compact sources in general relativity have been used to model very dense objects such as neutron stars for a long time now (see for example [1] or [2] and references therein). Furthermore a theory of rela e-mail: daniele.malafarina@nu.edu.kz b e-mail: psj@tifr.res.in ativistic elasticity provides the first step towards a physically meaningful description of the inner structure of such objects [3].…”