Quantum Gravity and String Theory

   

A New Look at Black Holes via Thermal Dimensions and the Complex Coordinates/Temperature Vectors Correspondence

Authors: Carlos Castro

It is shown how the crucial {\bf active diffs} symmetry of General Relativity allows to shift the radial location $ r = 2 G M $ of the horizon associated with the Schwarzschild metric to the $ r = 0^+$ location of a $diffeomorphic$ metric. In doing so, one ends up with a spacetime void surrounding the singularity at $ r = 0$. In order to explore the ``interior" region of this void we introduce complex radial coordinates whose imaginary components have a direct link to the inverse Hawking temperature, and which furnish a path that provides access to interior region. In addition, we show that the black hole entropy $ { A \over 4 } $ (in Planck units) is equal to the $area$ of a rectangular strip in the $complex$ radial-coordinate plane associated to this above path. The gist of the physical interpretation behind this construction is that there is an emergence of thermal dimensions which unfolds as one plunges into the interior void region via the use of complex coordinates. And whose imaginary components capture the span of the thermal dimensions. The filling of the void leads to an $emergent$ internal/thermal dimension via the imaginary part $ \beta_r$ of the complex radial variable $ {\bf r } = r + i \beta_r$.

Comments: 9 Pages.

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Submission history

[v1] 2022-01-21 20:34:11

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