# CQG+ Insight: The problem of perturbative charged massive scalar field in the Kerr-Newman-(anti) de Sitter black hole background

Written by Dr Georgios V Kraniotis, a theoretical physicist at the University of
Ioannina in the physics department.

# Solving in closed form the Klein-Gordon-Fock equation on curved black hole spacetimes

Dr Georgios V Kraniotis (University of Ioannina)

A new exciting era in the exploration of spacetime
The investigation of the interaction of a scalar particle with the gravitational field is of importance in the attempts to construct quantum theories on curved spacetime backgrounds. The general relativistic form that models such interaction is the so called Klein-Gordon-Fock (KGF) wave equation named after its three independent inventors. The discovery of a Higgs-like scalar particle at CERN in conjuction with the recent spectacular observation of gravitational waves (GW) from the binary black hole mergers GW150914 and GW151226 by LIGO collaboration, adds a further impetus for probing the interaction of scalar degrees of freedom with the strong gravitational field of a black hole.

Kerr black hole perturbations and the separation of the Dirac’s equations was a central theme in the investigations of Teukolsky and Chandrasekhar [1].

All the above motivated our research recently published in CQG on the scalar charged massive field perturbations for the most general four dimensional curved spacetime background of a rotating, charged black hole, in the presence of the cosmological constant $\Lambda$ [2].

Where interesting physics meets profound mathematics
The KGF equation is the relativistic version of the Schrödinger equation and thus is one of the fundamental equations in physics.

In our recent CQG paper, we examined Continue reading