Gravity as elasticity of spacetime: A paradigm to understand horizon thermodynamics and cosmological constant

Abstract

It is very likely that the quantum description of spacetime is quite di erent from what we perceive at large scales, l (G~=c3)1=2. The long wavelength description of spacetime, based on Einstein's equations, is similar to the description of a continuum solid made of a large number of microscopic degrees of freedom. This paradigm provides a novel interpretation of coordinate transformations as deformations of \spacetime solid" and allows one to obtain Einstein's equations as a consistency condition in the long wave- length limit. The entropy contributed by the microscopic degrees of freedom reduces to a pure surface contribution when Einstein's equations are satis ed. The horizons arises as \defects" in the \spacetime solid" (in the sense of well-de ned singular points) and contributes an entropy which is one quarter of the horizon area. Finally, the response of the microstructure to vacuum energy leads to a near cancellation of the cosmological constant, leaving behind a tiny uctuation which matches with the observed value.