[Paper Review] Gravitational collapse of dustlike matter with heat flux

Rituparno Goswami|ArXiv.org|Jul 9, 2007

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper presents a new class of spherically symmetric solutions to Einstein's equations for dustlike matter with radial heat flux, demonstrating that dissipative processes induce a spacetime shear and cause a bounce before singularity formation. The bounce, driven by negative effective inertial mass due to heat flow, can occur before trapped surface formation, leading to explosion-like behavior for certain initial data sets.

ABSTRACT

We present a new class of solutions to Einstein equations for the spherical collapse of dustlike matter coupled with heat flux. In this family of solutions spacetime shear is necessarily non-zero. Also these solutions have an interesting property that there is always a bounce before the singularity, which is caused entirely due to the dissipative processes. We show there exist open sets of initial data for which the bounce occurs before any trapped surface formation, making the star explode away to infinity. We also discuss the role of heat flow in generating spacetime shear and in modifying the effective inertial mass of the matter cloud.

Motivation & Objective

• To generalize Lemaitre-Tolman-Bondi solutions by incorporating radial heat flux and allowing non-zero spacetime shear.
• To investigate whether dissipative processes can prevent singularity formation in gravitational collapse.
• To examine the role of heat flow in generating spacetime shear and modifying effective inertial mass.
• To determine conditions under which bounce occurs before trapped surface formation, avoiding black hole outcomes.
• To explore classical resolution of singularities via heat flux without requiring quantum gravity.

Proposed method

• Derives a spherically symmetric metric with time and radial dependence, using gauge freedom to eliminate the $g_{tr}$ component and set the fluid 4-velocity to $u^i = e^{- u} abla^i t$.
• Models the energy-momentum tensor as $T^{ik} = \rho u^i u^k + q^i u^k + u^i q^k$, with heat flux $q^i = Q(t,r) \delta^i_r$ orthogonal to the 4-velocity.
• Introduces the function $v(t,r) = R(t,r)/r$ to distinguish the center ($v=1$) from the singularity ($v=0$), enabling analysis of collapse dynamics.
• Solves the Einstein equations under the assumption of dustlike matter and radial heat flux, deriving an equation of motion for $v(t,r)$ that includes dissipative terms.
• Analyzes the effective inertial mass density as $\rho(1 - \alpha)$, where $\alpha$ depends on temperature, density, thermal conductivity, and relaxation time, showing it can exceed 1 and become negative.
• Uses junction conditions to match the interior solution with an exterior generalized Vaidya spacetime, modeling mass and energy loss via outgoing radiation.

Experimental results

Research questions

• RQ1 Can gravitational collapse of dustlike matter with heat flux avoid singularity formation through dissipative effects?
• RQ2 How does radial heat flux generate spacetime shear in spherically symmetric collapse, even from initially homogeneous conditions?
• RQ3 What is the role of effective inertial mass reduction due to heat flow in halting collapse before $R=0$?
• RQ4 Under what initial data conditions does the bounce occur before trapped surface formation, leading to explosion rather than black hole formation?
• RQ5 Can classical general relativity resolve singularities via heat flux without invoking quantum gravity?

Key findings

• The collapse always undergoes a bounce before the spacetime singularity due to dissipative processes, even in the absence of pressure.
• Spacetime shear is necessarily non-zero in the presence of heat flux, contradicting the shearfree assumption in standard Oppenheimer-Snyder collapse.
• The effective inertial mass density becomes negative as collapse proceeds, due to heat flow increasing $\alpha > 1$, which generates a repulsive force halting collapse.
• For open sets of initial data, the bounce occurs before any trapped surface forms, implying the star can explode to infinity instead of forming a black hole.
• The presence of heat flux delays trapped surface formation, and when combined with mass loss to a Vaidya exterior, can prevent horizon formation altogether.
• The model provides a classical mechanism for singularity avoidance via heat conduction, offering a potential alternative to quantum gravity in resolving singularities.