Wave equations on the linear mass Vaidya metric

Abstract

We discuss the near singularity region of the linear mass Vaidya metric. In particular we investigate the structure in the numerical solutions for the scattering of scalar and electromagnetic metric perturbations from the singularity. In addition to directly integrating the full wave-equation, we use the symmetry of the metric to reduce the problem to that of an ODE. We observe that, around the total evaporation point, quasi-normal like oscillations appear, indicating that this may be an interesting model for the description of the end-point of black hole evaporation.

Vaidya geometries and scalar fields with null gradients

“…A null dust appears frequently in classical and quantum gravity, in Vaidya spacetimes [1,2], pp-waves [6][7][8], Robinson-Trautman geometries [9], twisting solutions of the Einstein-Maxwell equations [9][10][11], in studies of classical and quantum gravitational collapse, horizon formation, mass inflation [12][13][14][15][16][17][18][19][20][21], black hole evaporation [22][23][24], and canonical Hamiltonians [4,6,25]. Colliding scalar field-null dust solutions were studied in [26,27].…”

Emmy's letter to Santa Claus (and a reply): Vaidya geometries and scalar fields with null gradients

“…A null dust appears frequently in classical and quantum gravity, in Vaidya spacetimes [3,4], pp-waves [8-10], Robinson-Trautman geometries [11], twisting solutions of the Einstein-Maxwell equations [11][12][13], in studies of classical and quantum gravitational collapse, horizon formation, mass inflation [14][15][16][17][18][19][20][21][22][23], black hole evaporation [24][25][26], and canonical Hamiltonians [1,8,27].…”