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The properties of geodesics flow are studied in a Friedmann-Robertson-Walker metric perturbed due to the inhomogeneities of matter. The basic, averaged Jacobi equation is derived, which reveals that the low density regions (voids) are able…
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the "forward" temporal direction to a positive variation of the…
The emergent gravity paradigm interprets gravitational field equations as describing the thermodynamic limit of the underlying statistical mechanics of microscopic degrees of freedom of the spacetime. The connection is established by…
Recent observations show that our universe is accelerating by dark energy, so it is important to investigate the thermodynamical properties of it. The Undulant Universe is a model with equation of state $\omega(a)=-\cos(b\ln a)$ for dark…
Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity TdS=dE+PdV (where the variations are interpreted as changes due to virtual displacement along the affine…
With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the…
Rindler worldsheets are known to acquire a Carrollian structure at infinite acceleration, marking their tensionless limit. This work extends the same paradigm to time-evolving worldsheets in the background target spacetime spanning the…
During a de Sitter stage of expansion the spectator fields of different spin are constrained by the critical density bound and by further requirements determined by their specific physical nature. The evolution of spectator electric fields…
We describe ideal incompressible hydrodynamics on the hyperbolic plane which is an infinite surface of constant negative curvature. We derive equations of motion, general symmetries and conservation laws, and then consider turbulence with…
Classical thermodynamics contains familiar geometric relations associated with cyclic processes, most notably the identification of mechanical work with the area enclosed by a trajectory in the $(P,V)$ plane. We show that the area laws for…
Assuming that an accelerated observer with four-velocity ${\bf u}_{\rm R}$ in a curved spacetime attributes the standard Bekenstein-Hawking entropy and Unruh temperature to his "local Rindler horizon", we show that the $\rm \it change$ in…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null…
Dynamical properties of a generic null surface are known to have a thermodynamic interpretation. Such an interpretation is completely based on an analogy between the usual law of thermodynamics and structure of gravitational field equation…
The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is…
The relation between the thermodynamical and cosmological arrows of time is usually viewed in the context of the initial conditions of the Universe. It is a necessary but not sufficient condition for ensuring the thermodynamical arrow. We…
A link between the possibility of extending a geodessically incomplete kinked spacetime to a spacetime which is geodesically complete and the energy conditions is discussed for the case of a cylindrically-symmetric spacetime kink. It is…
By following the spirit of Verlinde's entropic force proposal arXiv:1001.0785, we give the differential and integral form of the first law of thermodynamics on the holographic screen enclosing a spherical symmetric black hole. It is…
In the Cadassian universe, one can explain the acceleration of the universe without introducing dark energy component. However, the dynamical equations of this model can not be directly obtained from the action principle. Recently, works on…
Three decades ago, Ted Jacobson surprised us with a very appealing approach to classical gravity. According to him, the gravitational field equations are the consequence of the first law of thermodynamics applied to a Rindler observer.…