Abstract
We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we derive Einstein's equations from the Clausius relation. Moreover, we show that the gravitational equations of motion for a broad class of diffeomorphism-invariant theories of gravity can be obtained from thermodynamics on the stretched future light cone, provided the Bekenstein-Hawking entropy is replaced by the Wald entropy.
Highlights
In the laws of black hole mechanics [1], the area and surface gravity of a black hole event horizon are associated with entropy and temperature
Taking this idea significantly further, Jacobson [2] attributed thermodynamic properties even to local Rindler horizons, which are essentially just planar patches of certain null congruences passing through arbitrary points in spacetime, and are not event horizons in any global sense
Entropy is a somewhat better-motivated property of our surface than of local Rindler horizons. This is because a future light cone separates its interior from the exterior spacetime; the interior is causally disconnected from the exterior, in the same sense that the interior of a black hole is
Summary
In the laws of black hole mechanics [1], the area and surface gravity of a black hole event horizon are associated with entropy and temperature. Entropy is a somewhat better-motivated property of our surface than of local Rindler horizons This is because a future light cone separates its interior from the exterior spacetime; the interior is causally disconnected from the exterior, in the same sense that the interior of a black hole is. A finite strip of Rindler horizon (unlike an infinite global Rindler horizon) does not separate space into two disconnected regions, and it is not obvious that it should possess an entropy Another appealing feature of our formulation is that the interior of a future light cone resembles that of black holes or de Sitter space in that it admits compact spatial sections. The main goals of this paper are, first, to formulate a definition of the stretched future light cone and, second, to derive the (generalized) Einstein equations from the premise that local holographic thermodynamic properties can be attributed to stretched future light cones
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