Stable gravastar with large surface redshift in Einstein's gravity with two scalar fields

Abstract

We propose a class of models, in which stable gravastar with large surface redshift becomes a solution. In recent decades, gravastars have become a plausible substitute for black holes. Researchers have explored stable gravastar models in various alternative gravity theories, in addition to the conventional framework of general relativity. In this paper, we present a stellar model within the framework of Einstein's gravity with two scalar fields, in accordance with the conjecture proposed by Mazur and Mottola [Proc. Nat. Acad. Sci. 101 (2004), 9545-9550]. In the model, the two scalar fields do not propagate by imposing constraints in order to avoid ghosts. The gravastar comprises two distinct regions, namely: (a) the interior region and (b) the exterior region. We assume the interior region consists of the de Sitter spacetime, and the exterior region is the Schwarzschild one. The two regions are connected with each other by the shell region. On the shell, we assume that the metric is given by a polynomial function of the radial coordinate r. The function has six constants. These constants are fixed by the smooth junction conditions, i.e., the interior region with the interior layer of the shell and the exterior region with the exterior layer of the shell. From these boundary conditions, we are able to write the coefficients of the scalar fields in terms of the interior radius and exterior radius. To clarify the philosophy of this study, we also give two examples of spacetimes that asymptote as the de Sitter spacetime for small r and as the Schwarzschild spacetime for large r. Exploration is focused on the physical attribute of the shell region, specifically, its proper length. The gravastar model's stability has frequently been examined by analyzing the relationship between surface redshift and shell thickness, a comparison we also undertake with previous models. Especially, we show that there exists a stable gravastar with a large surface redshift prohibited by the instability in the previous works. Furthermore, by checking the effective equation of state parameters, we show that the gravastar geometry realized in this paper by using two scalar fields could be difficult to generate with ordinary fluid.