Hamiltonian Formulation of Scalar Field Collapse in Einstein Gauss Bonnet Gravity

TL;DR

This paper derives a Hamiltonian formulation for scalar field collapse in Einstein-Gauss-Bonnet gravity, facilitating numerical simulations of gravitational collapse in higher dimensions with potential applications to black hole physics.

Contribution

It presents a simplified Hamiltonian constraint and gauge fixing for scalar collapse in Einstein-Gauss-Bonnet gravity, enabling more accessible numerical analysis.

Findings

Hamiltonian formulated for scalar collapse in higher-dimensional gravity.

Gauge fixing leads to equations suitable for numerical simulations.

Generalized mass function appears as a key component in the Hamiltonian.

Abstract

We compute the Hamiltonian for spherically symmetric scalar field collapse in Einstein-Gauss-Bonnet gravity in D dimensions using slicings that are regular across future horizons. We first reduce the Lagrangian to two dimensions using spherical symmetry. We then show that choosing the spatial coordinate to be a function of the areal radius leads to a relatively simple Hamiltonian constraint whose gravitational part is the gradient of the generalized mass function. Next we complete the gauge fixing such that the metric is the Einstein-Gauss-Bonnet generalization of non-static Painleve-Gullstrand coordinates. Finally, we derive the resultant reduced equations of motion for the scalar field. These equations are suitable for use in numerical simulations of spherically symmetric scalar field collapse in Gauss-Bonnet gravity and can readily be generalized to other matter fields minimally coupled to gravity.