Extended Equivalence Principle: Implications for Gravity, Geometry and Thermodynamics

The equivalence principle was formulated by Einstein in an attempt to extend the concept of inertial frames to accelerated frames, thereby bringing in gravity. In recent decades, it has been realised that gravity is linked not only with geometry of space-time but also with thermodynamics especially in connection with black hole horizons, vacuum fluctuations, dark energy, etc. In this work we look at how the equivalence principle manifests itself in these different situations where we have strong gravitational fields. In recent years the generalised uncertainty principle has been invoked to connect gravity and curvature with quantum physics and now we may also need an extended equivalence principle to connect quantum theory with gravity.