Scalar Field Gravastars: Derivation of Junction Conditions, Shell Stability, and Gravitational Wave Signatures

The gravastar model requires, as an external postulate, a thin shell of zero surface energy density separating a de Sitter interior from a Schwarzschild exterior. We show that this condition is not an assumption but a derived result when the interior is sourced by a static, spherically symmetric scalar field. Starting from the exact identity ρ + 3P = −2V (ϕ), we establish that any non-negative scalar potential enforces Strong Energy Condition violation throughout the interior. The regularity condition ∂rϕ|r=0 = 0 forces w = −1 at the core and the de Sitter geometry follows from the Einstein equations without additional postulate. Applying the Israel junction formalism, we prove that the mass relation M = 4π 3 V0R3 enforced by the scalar Einstein equations implies vanishing surface energy density σ = 0 at the unique equilibrium radius determined by the scalar field dynamics. The shell is radially stable and non-radially stable with surface sound speed c 2 s > 0, subject to the causality constraint. The physical parameter window 16/(243πM2 ) < V0 < 3/(32πM2 ) gives configurations more compact than any Buchdahl perfectfluid star and outside the Schwarzschild radius. The tidal Love number k2 < 0 throughout the physical parameter space, giving a negative tidal deformability Λ < 0 — an anti-tidal response unique to objects with repulsive de Sitter interiors, providing a three-way discriminant among black holes (Λ = 0), neutron stars (Λ > 0), and scalar gravastars (Λ < 0), testable by the Einstein Telescope. All results are confirmed by numerical solution of the full coupled TOV+Klein-Gordon system. PACS: 04.70.Bw, 04.30.Db, 04.40.Dg