Preprint Article Version 1 This version is not peer-reviewed

# Black Hole Entropy from Non-Commutative Geometry and Spontaneous Localisation

Version 1 : Received: 7 November 2019 / Approved: 8 November 2019 / Online: 8 November 2019 (10:54:34 CET)

How to cite: Singh, T.P.; Maithresh, P. Black Hole Entropy from Non-Commutative Geometry and Spontaneous Localisation. Preprints 2019, 2019110096 (doi: 10.20944/preprints201911.0096.v1). Singh, T.P.; Maithresh, P. Black Hole Entropy from Non-Commutative Geometry and Spontaneous Localisation. Preprints 2019, 2019110096 (doi: 10.20944/preprints201911.0096.v1).

## Abstract

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

## Subject Areas

black hole entropy; quantum gravity; non-commutative geometry; spontaneous localisation; trace dynamics