arXiv subjects
Publications and source records attributed to Eren Erberk Erkul.
In this paper, we extend Plebanski's mapping to encode the Einstein equations in ADM form within a bianisotropic electromagnetic medium. We realise this by translating the ADM constraints and evolution equations into dynamical conditions on the medium's constitutive parameters. These transformed equations are then linearised in vacuum to derive gravitational-wave analogues as perturbations of the optical medium.
We identify the relativistic-fluid counterpart of the Unruh effect, in which a comoving probe measures a Thermodynamic Unruh temperature. Frame changes in first-order hydrodynamics are recast as a local, time-dependent hyperbolic rotation in a Rindler-style state space where the instantaneous map between frames is the Thermodynamic Boost and its proper-time variation defines the Thermodynamic Acceleration, which results in an Unruh-like thermal spectrum. To leading order, the Thermodynamic Unruh temperature is frame-independent and universal across out-of-equilibrium relativistic fluid descriptions, from Israel-Stewart to modern theories.
Analogue models of gravity, from Newton to Unruh, have evolved from simple fluid--mechanical models to sophisticated modern experiments. They have shown the robustness of Hawking radiation and highlighted the role of dispersion for quantum fields in curved space. We speculate whether some underlying dispersion may also play a role in explaining the cosmological constant and in resolving the cosmological tensions.
We propose that black holes are \emph{soliton-esque} objects, where gravitational collapse is balanced by quantum vacuum dispersion, modeled via \(R+αR^{2}\) gravity. Classical singularities are replaced by oscillating, finite-radius cores, thereby evading static no-go theorems. The event horizon is replaced by the \textit{Lamarina}, a surface of maximum redshift whose surface geometry yields Hawking-like radiation with corrections. The Raychaudhuri equations impose a Dyson-type ceiling on the maximum radiated power \((P_{\infty} \lesssim c^{5}/G)\), while effective field theory matching dictates a universal minimum Lamarina radius set by the dispersion scale.