[Paper Review] Gravastars in $f(\mathbb{T},\mathcal{T})$ gravity

Shounak Ghosh, A. D. Kanfon+4 more|arXiv (Cornell University)|Mar 5, 2020

Cosmology and Gravitation Theories75 references9 citations

TL;DR

This paper proposes a singularity-free gravastar model in $f(\mathbb{T},\mathcal{T})$ gravity, where the interior de Sitter core, stiff fluid shell ($p=\rho$), and Schwarzschild exterior are matched via thin-shell junction conditions. The model yields exact solutions with positive surface energy density, increasing entropy, and finite, physically valid metric functions, demonstrating that $f(\mathbb{T},\mathcal{T})$ gravity supports stable, horizon-free compact objects without curvature singularities.

ABSTRACT

We propose a stellar model under the $f(\mathbb{T},\mathcal{T})$ gravity following Mazur-Mottola's conjecture [Mazur (2001), Mazur (2004)] known as gravastar which is generally believed as a viable alternative to black hole. The gravastar consists of three regions, viz., (I) Interior region, (II) Intermediate shell region, and (III) Exterior region. The pressure within the interior core region is assumed to be equal to the constant negative matter-energy density which provides a constant repulsive force over the thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma and following the Zel'dovich's conjecture of stiff fluid [Zeldovich (1972)] it is also assumed that the pressure which is directly proportional to the matter-energy density according to Zel'dovich's conjecture, does cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum and it can be described by the Schwarzschild solution. Under all these specifications we find out a set of exact and singularity-free solutions of the gravastar presenting several physically valid features within the framework of alternative gravity, namely $f(\mathbb{T},\mathcal{T})$ gravity [Harko (2014)], where the part of the gravitational Lagrangian in the corresponding action is taken as an arbitrary function of torsion scalar $\mathbb{T}$ and the trace of the energy-momentum tensor $\mathcal{T}$.

Motivation & Objective

• To construct a stable, singularity-free stellar model as an alternative to black holes within modified gravity.
• To investigate the viability of the gravastar structure in $f(\mathbb{T},\mathcal{T})$ gravity, a theory combining torsion scalar $\mathbb{T}$ and trace of energy-momentum tensor $\mathcal{T}$.
• To ensure physical consistency by satisfying energy conditions and junction conditions at the thin shell interface.
• To explore how the inclusion of $\mathbb{T}$ and $\mathcal{T}$ modifies the gravastar structure compared to general relativity.

Proposed method

• Adopt the Mazur-Mottola gravastar model with three regions: interior de Sitter core ($p = -\rho$), stiff fluid shell ($p = \rho$), and exterior vacuum ($p = \rho = 0$).
• Use the $f(\mathbb{T},\mathcal{T})$ gravity framework, where the gravitational Lagrangian is an arbitrary function of torsion scalar $\mathbb{T}$ and trace $\mathcal{T}$, to derive modified field equations.
• Apply the thin-shell approximation to match the interior and exterior spacetimes using Darmois-Israel junction conditions at $r = r_1$ and $r = r_2$.
• Solve the field equations analytically under the assumption of constant energy density and pressure in the interior, and stiff fluid behavior in the shell.
• Derive expressions for metric functions $e^{\lambda(r)}$ and $e^{\nu(r)}$, proper thickness $\ell$, surface energy density, and entropy within the shell.
• Verify physical validity by ensuring positivity of surface energy density, pressure, and entropy, and by confirming $\frac{2M}{r} < 1$ and $\rho_c(2\pi - Q)R^2 < \frac{1}{2}$.

Experimental results

Research questions

• RQ1 Can a gravastar model be consistently formulated in $f(\mathbb{T},\mathcal{T})$ gravity without curvature singularities?
• RQ2 How do the inclusion of torsion scalar $\mathbb{T}$ and trace $\mathcal{T}$ affect the structure and stability of the gravastar?
• RQ3 Do the junction conditions yield positive surface energy density and pressure, satisfying weak and dominant energy conditions?
• RQ4 Is the entropy within the shell monotonically increasing, indicating thermodynamic stability?
• RQ5 What are the exact expressions for mass, thickness, and energy of the shell in this modified gravity framework?

Key findings

• The interior region exhibits constant negative pressure and energy density, ensuring a repulsive de Sitter core without central singularity.
• The metric functions $e^{\lambda(r)}$ and $e^{\nu(r)}$ are continuous and finite at $r=0$, confirming regularity at the origin.
• The proper thickness $\ell$ of the shell increases gradually from the inner to outer boundary, indicating a denser outer shell.
• The matter density and pressure in the shell are positive and increase with radial coordinate $r$, with energy proportional to $r$.
• Entropy $S$ increases monotonically with $r$, reaching a maximum at the outer surface, supporting thermodynamic stability.
• Surface energy density and pressure remain positive across the shell, satisfying both weak and dominant energy conditions.