We consider a massive black hole in four dimensional AdS space and study the effect of thermal fluctuations on the thermodynamics of the black hole. We consider thermal fluctuations as logarithmic correction terms in the entropy. We analyse the effect of logarithmic correction on thermodynamics potentials like Helmholtz and Gibbs which are found decreasing functions. We study critical points and stability and find that presence of logarithmic correction is necessary to have stable phase and critical point.

In this paper, we would like to obtain quantum gravity effects by using Hořava-Lifshitz black hole. We consider logarithmic corrected thermodynamics quantities and investigate the effects of logarithmic correction term. Logarithmic correction comes from thermal fluctuation and may be interpreted as quantum loop corrections. As black hole is a gravitational system, hence we can investigate quantum gravity effect. We find such effects on the black hole stability and obtain domain of correction coefficient.

BTZ black holes are excellent laboratories for studying black hole thermodynamics which is a bridge between classical general relativity and quantum nature of gravitation. In addition, threedimensional gravity could have equipped us for exploring some of the ideas behind the two dimensional conformal field theory based on the AdS3/CF T2. Considering the significant interests in these regards, we examine charged BTZ black holes. We consider the system contains massive gravity with energy dependent spacetime to enrich the results. In order to make high curvature (energy) BTZ black holes more realistic, we modify the theory by energy dependent constants. We investigate thermodynamic properties of the solutions by calculating heat capacity and free energy. We also analyze thermal stability and study the possibility of Hawking-Page phase transition. At last, we study geometrical thermodynamics of these black holes and compare the results of various approaches.

In this paper we analyse the Bagger-Lambert-Gustavsson (BLG) theory in N = 1 superspace. Furthermore, we will construct the BRST transformations for this theory. These BRST transformations will be integrated out to obtain the finite field dependent version of BRST (FFBRST) transformations. We will also analyse the effect of the FFBRST transformations on the effective action. We will thus show that the FFBRST transformations can be used to relate generating functionals of the BLG theory in two different gauges. *

We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories, in the context of generalized BRST transformations with finite field dependent parameter. In the usual Faddeev-Popov formulation of gauge theories such finite field dependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for a finite transformations. Here we show that FFBRST transformation, with appropriate choice of finite field-dependent parameter, is symmetry of the generating functionals in the Batalin-Vilkovisky formalism. The finite parameter is chosen in such a way that the contribution from the Jacobian of the path integral measure is adjusted with gauge fixed fermions which do not change the generating functionals. Several examples for such a finite parameters are constructed.The field/antifield formulation, alternatively known as Batalin-Vilkovisky (BV) formalism [1][2][3][4], is one of the most powerful techniques to study the gauge field theories.This formulation is developed in Lagrangian framework and extremely useful as it allows us to deal with very general gauge theories including those with open or reducible gauge symmetry algebras. The essential aspects of BV-formalism were originally developed by Zinn-Justin [5] in order to prove the renormalizability of gauge theories. This method provides a convenient way of analyzing the possible violations of symmetries of the action

In this paper, we study the effect of thermal fluctuations on the thermodynamics of a black geometry with hyperscaling violation. These thermal fluctuations in the thermodynamics of this system are produced from quantum corrections of geometry describing this system. We discuss the stability of this system using specific heat and the entire Hessian matrix of the free energy. We will analyze the effects of thermal fluctuations on the stability of this system. We also analyze the effects of thermal fluctuations on the criticality of the hyperscaling-violation background.

We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of both the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples.

Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by f (R) gravity. We compute the corrected N -particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the f (R) correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of f (R) gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an f (R) gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.