Saugata Mitra

In this work, static traversable wormholes are investigated in the context of [ ] gravity theory. Considering [ ] model (in which [ ] and [ ] are constants) and assuming [ ], a new shape function is obtained which is not asymptotically flat, but satisfies all the conditions of a shape function. Also in this case, all energy conditions (except strong energy conditions) are satisfied. Assuming [ ] and shape function [ ], a new energy density function is obtained. Finally, a comparative study of ECs is investigated for different shape functions under the assumption [ ] and [ ] (where [ ], [ ] and [ ] are constants) and we have seen that the presence of exotic matter is not required in most of the cases.

In this work, we have studied the traversable wormhole geometries in [ ] gravity theory, where [ ] denotes the Ricci scalar and [ ] is the trace of the energy–momentum tensor. Firstly, two new shape functions are obtained for some assumed generating function. Also, some new generating functions are obtained in wormhole geometry for some well-known shape functions and redshift functions. Energy conditions are examined in each wormhole solution and it is found that a particular type of wormhole satisfies all the energy conditions in a region.

Universal thermodynamics for FRW model of the Universe bounded by apparent/event horizon has been considered for massive gravity theory. Assuming Hawking temperature and using the unified first law of thermodynamics on the horizon, modified entropy on the horizon has been determined. For simple perfect fluid with constant equation of state, generalized second law of thermodynamics and thermodynamical equilibrium have been examined on both the horizons.

A study of Universal thermodynamics is done in Lanczos-Lovelock gravity. The Universe is chosen as FRW model bounded by apparent or event horizon. The unified first law is examined, assuming extended Hawking temperature on the horizon. As a result there is a modification of Bekenstein entropy on the horizons. Further the validity of generalized second law of thermodynamics and thermodynamical equilibrium are also investigated for perfect fluid (with constant equation of state), modified chaplygin gas model and holographic dark energy model.

The present work deals with a detailed study of universal thermodynamics in different modified gravity theories. The validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe bounded by a horizon (apparent/event) in f(R)-gravity, Einstein-Gauss-Bonnet gravity, RS-II brane scenario and DGP brane model has been investigated. In the perspective of recent observational evidences, the matter in the Universe is chosen as interacting holographic dark energy model. The entropy on the horizons are evaluated from the validity of the unified first law and as a result there is a correction (in integral form) to the usual Bekenstein entropy. The other thermodynamical parameter namely temperature on the horizon is chosen as the recently introduced corrected Hawking temperature. The above thermodynamical analysis is done for homogeneous and isotropic flat FLRW model of the Universe. The restrictions for the validity of GSLT and the TE are presented in tabular form for each gravity theory. Finally, due to complicated expressions, the validity of GSLT and TE are also examined from graphical representation, using three Planck data sets.

The idea of Verlinde that gravity is an entropic force caused by information changes associated with the positions of material bodies, is used in the present work for the FRW model of the Universe. Using modified Hawking temperature, the Friedmann equations are derived on any horizon. For the validity of the first law of thermodynamics (i.e., Clausius relation) it is found that there is modification of Bekenstein entropy on the horizon. However, using equipartition law of energy, Bekenstein entropy is recovered.