# Conserved charges in various theories of gravity

The first law of black hole thermodynamics in the presence of a cosmological constant $\Lambda$ can be generalized by introducing a term containing the variation $\delta\Lambda$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc and it has been shown in \cite{1} that the new term has the same structure: $\Lambda$ is a conserved charge associated with a gauge symmetry. In this work, first we propose and prove the generalized Smarr relation in this new paradigm. Then, we reproduce systematically the effective volume" of a black hole which has been introduced before in the literature as the conjugate of pressure. Our construction removes the ambiguity in the definition of volume. Finally, we apply and investigate this formulation of $\Lambda$ as a charge" on a number of solutions to different models of gravity for different spacetime dimensions. Specially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well-defined in principle
 Anisotropic solutions for generalised holography Devecioğlu, Deniz Olgu; Sarıoğlu, Bahtiyar Özgür; Department of Physics (2016) We first find that the four dimensional cosmological Einstein-Yang-Mills theory with $SU(2)$ gauge group admits Lifshitz spacetime as a base solution for the dynamical exponent $z > 1$. Motivated by this, we next demonstrate numerically that the field equations admit black hole solutions which behave regularly on the horizon and at spatial infinity for different horizon topologies. In the second part, using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric back...