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We consider the thermodynamics of a horizon surface from the viewpoint of the vacuum tension $tau =(c^4/4G )$. Numerically, $tau approx 3.026times 10^{43}$ Newton. In order of magnitude, this is the tension that has been proposed for microscopic string models of gravity. However, after decades of hard work on string theory models of gravity, there is no firm scientific evidence that such models of gravity apply empirically. Our purpose is thereby to discuss the gravitational tension in terms of the conventional Einstein general theory of relativity that apparently does explain much and maybe all of presently known experimental gravity data. The central result is that matter on the horizon surface is bound by the entropy-area law by tension in the closely analogous sense that the Wilson action-area law also describes a surface confinement.
The deformation equation of a spacelike submanifold with an arbitrary codimension is given by a general construction without using local frames. In the case of codimension-1, this equation reduces to the evolution equation of the extrinsic curvature
The modified first laws of thermodynamics at the black hole horizon and the cosmological horizon of the Schwarzschild de Sitter black hole and the apparent horizon of the Friedmann-Robertson-Walker cosmology are derived by the surface tensions, respe
We investigate whether the new horizon first law proposed recently still work in $f(R)$ theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the
We present modified cosmological scenarios that arise from the application of the gravity-thermodynamics conjecture, using the Barrow entropy instead of the usual Bekenstein-Hawking one. The former is a modification of the black hole entropy due to q
I generalize the Dray-t Hooft gravitational shockwave to the Kerr-AdS background.