Brans-Dicke Theory and Thermodynamical Laws on Apparent and Event Horizons

Abstract

In this work, we have described the Brans-Dicke theory of gravity and given a particular solution by choosing a power law form of scalar field $\varphi$ and constant $\omega$. If we assume first law and entropy formula on apparent horizon then we recover Friedmann equations. Next, assuming first law of thermodynamics, the validity conditions of GSL on event horizon are presented. Also without use first law, if we impose the entropy relation on the horizon, then we also obtain the condition of validity of GSL on event horizon. The validity of GSL completely depends on the model of BD scalar field solutions. We have justified that on the apparent horizon the two process are equivalent, but on the event horizon they are not equivalent. If first law is valid on the event horizon then GSL may be satisfied in BD solution, but if first law is not satisfied then GSL is not satisfied in BD solution. So first law always favours GSL on event horizon. In our effective approach, the first law and GSL is always satisfied in apparent horizon, which do not depend on BD theory of gravity.

6 pages, 2 figures

References in corpus (13)

• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Generalized Second Law of Thermodynamics in Quintom Dominated Universe
• Thermodynamics of Apparent Horizon in Brane World Scenario
• Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
• Thermodynamics and classification of cosmological models in the Horava-Lifshitz theory of gravity
• The generalized second law of thermodynamics in generalized gravity theories
• Thermodynamics of Apparent Horizon in Brane World Scenarios
• The Holographic Model of Dark Energy and Thermodynamics of Non-Flat Accelerated Expanding Universe
• The generalized second law in phantom dominated universes in the presence of black holes
• Thermodynamics on the apparent horizon in generalized gravity theories
• Generalized second law in modified theory of gravity
• Schwarzschild black hole and the generalized second law in phantom-dominated universe
• Role of Brans-Dicke Theory with or without self-interacting potential in cosmic acceleration

Cited by in corpus (3)

• A study of generalized second law of thermodynamics in modified f(R) Horava-Lifshitz gravity
• Brans-Dicke Cosmology: Thermodynamic viability
• Study of Thermodynamic Quantities in Generalized Gravity Theories