Flat-space cosmologies (FSCs) are solutions to three-dimensional theories of gravity without cosmological constants that have horizons. A detector located near the timelike singularity spacetime can absorb Hawking modes created horizon. Continuation this process will eventually cause entropy radiation be larger than FSC, which leads information paradox. In paper, we resolve paradox for FSC usin...

The effect of introducing a fifth large-scale space-time dimension to the equations of orbital dynamics was analysed in an earlier paper by the authors. The results showed good agreement with the observed flat rotation curves of galaxies. This analysis did not require the modification of Newtonian dynamics, but rather only their restatement in a five dimensional framework. The same analysis der...

Flat space-time has not heretofore been thought a suitable locus in which to construct model universes because of the presumed necessity of incorporating gravitation in such models and because of the historical lack of a theory of gravitation in flat spacetime. It is here shown that a Lorentz-invariant theory of gravitation can be formulated by incorporating in it the mass-energy relation. Such...

We describe the theory of reciprocal diffusions in flat space. A reciprocal process is a Markov random field on a one dimensional parameter space. Every Markov process is reciprocal but not vice versa. We descibe the first and second order mean differential characteristics of reciprocal diffusions. This includes a new definition of stochastic acceleration. We show that reciprocal diffusions sat...

We point out that aspects of quantum mechanics can be derived from the holographic principle, using only a perturbative limit of classical general relativity. In flat space, the covariant entropy bound reduces to the Bekenstein bound. The latter does not contain Newton’s constant and cannot operate via gravitational backreaction. Instead, it is protected by—and in this sense, predicts—the Heise...

In this paper, we deal with the subdierential concept onHadamard spaces. Flat Hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in Hadamard spaces is nonempty. Proximal subdierentialin Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdierential set is established.