Volume 130, number 4,5 PHYSICS LETTERS A 11 July 1988 SURFACE PHENOMENA IN GENERAL RELATIVISTIC STELLAR MODELS: CRITICAL MASS AND STABILITY L. HERRERA ‘, J. JIMENEZ Departamento de FIsica, Facultadde Ciencias, Universidad Central de Venezuela, Caracas, Venezuela and M. ESCULPI Departamento de Fisica Aplicada, Facultadde IngenierIa, Universidad Central de Venezulela, Caracas, Venezuela Received 14 March 1988; accepted for publication 11 May 1988 Communicated by J.P. Vigier The influence of surface phenomena on general relativistic stellar models is investigated, with particular emphasis on the critical mass value and the adiabatic stability. It will be shown, in a particular model, that for a given radius, the maximum value of the total mass (compatible with a static, singularity-free configuration) is a decreasing function of the surface tension coefficient. It will also be shown that the inclusion of surface phenomena enhances the adiabatic instability of the model in the high density regime. In the study of stellar structures and gravitational collapse, both in newtonian and relativistic calculations, surface phenomena are systematically excluded. This omission is partially justified by the simple fact that, as the size of a body increases, the surface effects increase much slower than the volume effects [1]. However, this approximation is likely to fail, at least in certain situations of stellar evolution. We have in mind, for ex- ample, the occurrence of a phase transition to the pion condensed state, which is expected to happen when the central density exceeds the nuclear density [2—4],and which could give rise to interesting surface phenomena [5]. Besides this particular example, we feel it is worth exploring how the surface phenomena affect the stellar structure and the stellar stability. Thus, let us consider a non-static distribution of matter which is spherically symmetric. In Schwarzschild coordinates the metric can be written as ds 2=evdr2_eAdr2_r2(dO2+sin2Odb~) Denoting differentiation with respect to r by a dot and with respect to r by a prime, with (~, r; 0, ~) = (0, 1, 2, 3), the Einstein field equations read —87tT 0 0= —r2+e~(r2—)~’r~) , (1) —8irT 1’ = —r 2+e~(r2+ v’r~) , (2) ~ v’2—~’v’)+2(v’—2’)r~] (3) —8~tT 01=—r’)~. (4) Postal address: Apartado 80793, Caracas 1080 A, Venezuela. 0375-9601/88/$ 03.50 © Elsevier Science Publishers B.V. 211 (North-Holland Physics Publishing Division)