Klein-Gordon and Schr\"{o}dinger solutions in Lovelock quantum gravity

TL;DR

This paper explores wave function solutions to Klein-Gordon and Schrödinger equations in Lovelock gravity, deriving key formulas and analyzing black hole properties and quantum modes.

Contribution

It introduces novel solutions and connections between wave functions, black hole thermodynamics, and Lovelock gravity, including the derivation of the Smarr formula from topological density.

Findings

Klein-Gordon solutions yield Wheeler-de Witt Hamiltonian and quasinormal modes.

Connection established between potential and black hole temperature.

Airy function influences Schrödinger wave function evolution.

Abstract

This study investigates the application of wave functions to explore various solutions of the Klein-Gordon and Schr\"{o}dinger equations within the framework of Lovelock gravity. We also present the derived Smarr formula from the topological density. The Klein-Gordon solution leads to the Wheeler-de Witt Hamiltonian and quasinormal modes, and we demonstrate the connection between the potential and the black hole temperature within the Schwarzschild limit. Additionally, we discuss different solutions of the Schr% \"{o}dinger equation, with one solution highlighting the influence of the Airy solution on the wave function's evolution over time.