Expanding the black hole thermodynamics from the horizon to achronal Cauchy hypersurface, the general relation between the Einstein equation and thermodynamics is established. Starting from trivial entropy that is generalized by Bekenstein-Hawking entropy, the entropic mass of matter emerges naturally together with Unruh temperature. The key idea is that the cause of mass formation comes down to trivial entropy, and mass density is just the external manifestation of mass. The full Einstein equation with the cosmological constant is derived from the requirement that entropic mass and proper mass are equivalent. This perspective suggests that trivial entropy that causes mass in gravitation may be the best choice for the origin of space-time geometry.
Gravitational Entropy And The Second Law of Thermodynamics for Causal Observers
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究院物理学院）；Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院物理系）
Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass c…
Gravitational Waves and Matter Constraints in Gravity from Entropy
Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院）；Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院空间科学与天体物理研究所）
We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperatu…
在爱因斯坦的引力理论中，视界的熵与其面积成正比。在文献中给出的几个参数表明，在这种情况下，面积和熵都应该用大量子数的等间隔光谱进行量化。但在更一般的理论中（例如，在高斯-博内或兰佐斯-洛夫洛克引力的黑洞解中），视界熵与面积成正比，问题是两者中的哪一个（如果有的话）将具有此属性。\emph{not}。我们给出了一个一般性的论点，即在所有的Lanczos-Lovelock引力理论中，是\emph{entropy}具有等间距的谱。在Gauss-Bonnet引力的情况下，我们使用准简正模频率的渐近形式来明确地证明这一结果。因此，爱因斯坦希尔伯特（EH）引力中面积量子的概念需要在更一般的上下文中被\emph{quantum of entropy}的概念所取代。
We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS$_3$ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute…
We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, space-time foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of space-time, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static space-time region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological …
We study the emergence of entropy in gravitational production of dark matter particles, ultra light scalars minimally coupled to gravity and heavier fermions, from inflation to radiation domination (RD). Initial conditions correspond to dark matter fields in their Bunch-Davies vacua during inflation. The "out" states are correlated particle-antiparticle pairs, and the distribution function is found in both cases. In the adiabatic regime the density matrix features rapid decoherence by dephasing from interference effects in the basis of "out" particle states, effectively reducing it to a diagon…
