AdS Gravastar: Horizonless Compact Object

• AdS gravastar is a horizonless compact object replacing traditional black hole singularities with an interior AdS/dS core, serving as a regular alternative in gravitational models.
• It is constructed by matching an interior region with a de Sitter or AdS core to an exterior AdS-Schwarzschild or BTZ geometry via a thin shell using precise junction conditions.
• Their stability and distinctive dual CFT signatures, including echo phenomena in two-point correlators, provide actionable insights for probing quantum gravity effects.

An AdS gravastar is a horizonless compact object whose core structure replaces the singularity of standard black holes with a region of anti-de Sitter (AdS) or de Sitter spacetime, typically enveloped by a thin shell matched to an exterior AdS-Schwarzschild or BTZ geometry. AdS gravastars are constructed to evade event horizon formation and curvature singularities, serving as regular alternatives to classical black holes, particularly in the context of quantum-gravity motivated regularizations and holographic studies. Their stability, global structure, and signatures in dual conformal field theory (CFT) have become central topics in current gravitational research.

1. Construction and Geometric Structure

AdS gravastar models are built by segmenting spacetime into three distinct regions characterized by their equations of state and metric properties. In the $(2+1)$-dimensional case (Rahaman et al., 2011), the coordinates $(t, r, \theta)$ parametrize the static, circularly symmetric line element: $$ds^2 = -e^{2\gamma(r)} dt^2 + e^{2\mu(r)} dr^2 + r^2 d\theta^2$$ The regions are:

1. Interior (Region I): For $0 \leq r < r_1$, the energy density and pressure satisfy $\rho = -p = \rho_c$, with the metric functions $$e^{2\gamma_I} = e^{-2\mu_I} = 1 + (-\Lambda - 2\pi \rho_c) r^2$$. The mass function is $M(r) = \pi \rho_c r^2$.
2. Shell (Region II): For $r_1 \leq r < r_2$, stiff fluid equation of state $\rho = p$, and metric functions involving nontrivial solutions to a nonlinear ODE for $\gamma(r)$. In the thin-shell limit, explicit forms involve integration constants and a positive “junction cosmological constant” $\Lambda_0 > 0$.
3. Exterior (Region III): For $r > r_2$, the metric reduces to the BTZ solution with negative cosmological constant ($\Lambda < 0$),

$$ds^2 = -(-M_0 - \Lambda r^2) dt^2 + (-M_0 - \Lambda r^2)^{-1} dr^2 + r^2 d\theta^2$$

and a vacuum equation of state $\rho = p = 0$.

In $(d+1)$ dimensions, AdS gravastars are constructed by excising $r < r_0$ from an AdS-Schwarzschild spacetime and grafting in a de Sitter interior (Chen et al., 1 Dec 2025):

• Exterior: $f_+(r) = r^2 + 1 - \mu/r^{d-2}$.
• Interior: $f_-(r) = 1 - \Lambda_{\text{eff}} r^2$, with $\Lambda_{\text{eff}}$ a linear combination of core energy density and AdS curvature.

Matching across the shell at $r=r_0$ exploits Israel junction conditions, with induced metrics continuous and extrinsic curvature discontinuity sourcing the shell’s tension $\bar P$.

2. Junction Conditions and Shell Properties

The shell at the core-exterior interface is analyzed using the Darmois–Israel formalism. The surface stress-energy tensor $S^i{}_j$ in $(2+1)$D reads: $$S^i{}_j = -\frac{1}{8\pi} \left( \kappa^i{}_j - \delta^i{}_j \kappa^k{}_k \right)$$ with line energy density $\sigma$ and line pressure $\mathcal{P}$ determined by the jump in extrinsic curvature at the shell radius: $$\sigma = -\frac{1}{8\pi R} \left[ \sqrt{-\Lambda_0 R^2 + (B-2\Lambda R^2)} - \sqrt{1+(-\Lambda-2\pi\rho_c)R^2} \right]$$

$$\mathcal{P} = \frac{1}{8\pi} \left[ \frac{-\Lambda_0 R}{\sqrt{-\Lambda_0 R^2 + (B-2\Lambda R^2)}} - \frac{(-\Lambda-2\pi\rho_c)R}{\sqrt{1+(-\Lambda-2\pi\rho_c)R^2}} \right]$$

The requirement $\Lambda_0 > 0$ ensures inward tension, essential for stability.

Shell physical quantities include:

• Thickness: $\ell \approx \epsilon/\sqrt{B-2\Lambda_0 R^2}$, where $\epsilon$ is the radial shell width.
• Energy: $$E_{\text{shell}} \approx \epsilon R / [C - (1/(2\Lambda))\sqrt{B-2\Lambda R^2}]^2$$ (thin-shell limit).
• Entropy: $$S \propto [\ln|2\Lambda C - \sqrt{B-2\Lambda r^2}|]_{R}^{R+\epsilon}$$, using Mazur–Mottola’s local-temperature prescription.

3. Mass–Radius Relations and Stability Criteria

The gravastar’s mass is encoded in the interior region; for the $(2+1)$D case, $M_{\text{gravastar}} = \pi \rho_c r_1^2$ (Rahaman et al., 2011). In $4$D scalar-field gravastar models, the exterior Schwarzschild radius is $R_S=2GM=(1-2\beta)r_0$, with the shell situated at $R=y_0>R_S$ (Cadoni et al., 2023). Regular horizonless solutions with an AdS core smoothly interpolate to Minkowski + Schwarzschild + $1/r^2$ at infinity.

Stability demands inward-directed shell tension ($\mathcal{P}>0$) and negative energy density ($\sigma<0$), with radial perturbations stabilized if $d\sigma/dR<0$. Satisfaction of weak and null energy conditions is observed for suitable parameter windows. Non-singular construction requires $e^{2\gamma_I}>0$ throughout the core, eliminating horizons and curvature singularities.

A plausible implication is that by ensuring $\Lambda_0>0$ in the shell, the stabilizing properties of AdS gravastars are robust against small radial perturbations and no horizons or singularities form for admissible parameter choices.

4. AdS/CFT Correspondence and Dual CFT Signatures

AdS gravastars induce characteristic features in the dual CFT via the AdS/CFT correspondence (Chen et al., 1 Dec 2025). The retarded two-point functions $G_R(t, \theta)$ incorporate new singularities not seen in standard black-hole spacetimes.

• Bulk-cone singularities: Arise for $t_n = n T(u_*)$, where $T(u_*)$ is the time along bulk null geodesics connecting boundary points grazing the photon sphere.
• New singularities due to the horizonless core: $t_{n,p} = n T(u_*) + p \tilde T(u_*)$, signifying repeated traversal between shell and inner turning points in the horizonless geometry.
• Echo phenomenon: Late-time echoes in $G_R(t)$ occur at intervals $\Delta t_{\text{echo}} = 2\int_{r_s}^{r_c} dr/f(r)$, corresponding to multiple wave reflections between the shell $r_s$ and the photon sphere $r_c$.

These echo trains in the CFT correlator are direct signatures of the horizonless geometry and vanish in the presence of a horizon, thus offering a potential probe of quantum-gravity corrections and horizon regularization mechanisms.

5. Scalar Field Constructions and Smooth Versus Thin-Shell Models

In $4$D, AdS gravastar solutions have been realized employing a real scalar field minimally coupled to gravity with arbitrary potential $V(\phi)$ (Cadoni et al., 2023). The action is: $$S = \int d^4x \sqrt{-g} \left[ \frac{1}{2\kappa} R - \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi - V(\phi) \right]$$

• Smooth AdS core models: Achieved via generating-function techniques yielding horizonless solutions with regular AdS interior and Schwarzschild asymptotics. No shell matching is necessary.
• Non-smooth (thin-shell) gravastars: Admit more general interior (de Sitter-like) matched to scalar vacuum exteriors via perfect-fluid shell, with explicitly calculated shell stress-energy. Surface quantities $\sigma$ and $p$ are positive in certain parameter regimes.

This suggests that scalar gravastars present a broad family of horizonless compact objects, able to interpolate between AdS, de Sitter, and Schwarzschild exteriors, either through smooth or shell-based constructions. Mass–radius relations and energy conditions furnish diagnostics for physical viability and stability.

6. Physical Implications and Observational Prospects

AdS gravastars represent regular alternatives to classical black holes, eliminating singularities and event horizons, and producing unique observational signatures through dual field theories. Their properties include:

• Horizon-free structure: No curvature singularity at $r=0$ or event horizon in the exterior.
• Shell: Carries negative line energy but positive pressure; junction cosmological constant $\Lambda_0>0$ is required for compatibility and stability.
• Echoes and bulk-cone diagnostics: In CFT correlators, extra singularities and late-time echoes distinguish gravastars from classical black holes—offering theoretical observational handles in quantum gravity contexts.

These objects underpin prospective models for quantum gravity regularizations, provide precise targets for AdS/CFT research, and illuminate the fine structure of ultracompact objects, with ongoing exploration of their stability, formation, and holographic imprints (Rahaman et al., 2011, Chen et al., 1 Dec 2025, Cadoni et al., 2023).