Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell

Paul R. Anderson , Shohreh Gholizadeh Siahmazgi , Raymond D. Clark , Alessandro Fabbri (1)

1 IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie

A method is given to compute the stress-energy tensor for a massless minimally coupled scalar field in a spacetime where a black hole forms from the collapse of a spherically symmetric null shell in four dimensions. Part of the method involves matching the modes for the in vacuum state to a complete set of modes in Schwarzschild spacetime. The other part involves subtracting from the unrenormalized expression for the stress-energy tensor when the field is in the in vacuum state, the corresponding expression when the field is in the Unruh state and adding to this the renormalized stress-energy tensor for the field in the Unruh state. The method is shown to work in the two-dimensional case where the results are known.

Mots clés: Formal aspects of field theory; field theory in curved space; tensor: energy-momentum; field theory: scalar; space-time: Schwarzschild; coupling: scalar; dimension: 4; symmetry: rotation; coupling: minimal; dimension: 2; vacuum state; black hole: formation; gravitation: collapse; quantization; shell model; renormalization

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Paul R. Anderson, Shohreh Gholizadeh Siahmazgi, Raymond D. Clark, Alessandro Fabbri. Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell. Physical Review D, 2020, 102 (12), pp.125035. ⟨10.1103/PhysRevD.102.125035⟩. ⟨hal-02953138⟩