# COSMOLOGICAL CONS(tant → erved charge)

## The road to black hole thermodynamics with Λ

by  Dmitry Chernyavsky and Kamal Hajian

What are volume and pressure in black hole thermodynamics? That is the question!

What do the gas in a balloon and a black hole have in common? For a regular CQG reader the answer should be obvious; both can be described within the framework of thermodynamics. However we know that the gas in balloon is characterised by volume and pressure, as well as other  thermodynamic quantities. So, a natural question arises about analogues of the volume and pressure for a black hole.
Answering this question, black hole physicists have noticed that if the universe is filled with a non-zero cosmological constant Λ, this mysterious entity can be absorbed in the energy-momentum tensor of matter, and its contribution resembles a perfect fluid with a pressure proportional to Λ. Continuing with this analogy, one can also introduce a ‘thermodynamic volume’ for a black hole. For instance, the appropriate volume which satisfies the first law of thermodynamics for the Schwarzschild black hole is equal to the volume of a ball with the same radius, but in flat space! Using the notions of the black hole pressure P and volume V, it is standard to vary the cosmological constant generalising the first law of black hole thermodynamics by V δP.

Dmitry Chernyavsky and Kamal Hajian Sevan lake in Armenia where we started to think about the cosmological conserved charge instead of cosmological constant.

# 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