Entanglement Entropy and the Arrow of Time in Wheeler-DeWitt

Abstract: In this talk, I discuss entanglement entropy generation for different models to understand the origin of irreversibility and emergence of arrow of time in quantum cosmology based on the timeless Wheeler-DeWitt equation of canonical quantum gravity using methods from theory of Open Quantum Systems. The Wheeler-DeWitt equation for a quantum Friedmann universe has a potential term which is asymmetric under the sign change of the intrinsic time (logarithm of scale factor of the universe). The structure of the potential term in WDW equation guarantees that there will be entanglement generation between intrinsic time and other degrees of freedom as the universe expands. I discuss construction of analytical solution for a toy model with two scalar fields (system and environment degrees of freedom) in a flat homogeneous and isotropic early uni-verse and how entanglement entropy and arrow of time can be investigated in such a model. We also study this model for symmetric initial condition under a semiclassical approximation to calculate entanglement entropy and develop better understanding of this initial condition for the universe. Along with this we also investigate the case of entanglement entropy generation for quantum fluctuations in the early universe for the Schr ̈odinger equation evolution which can be derived from WDW equation by making the semiclassical approximation. We show in all these models that entropy is very small at the beginning of the universe and increases as the universe expands and the semiclassical time moves forward, which would then form the basis of arrow of time and also the origin of irreversibility in the early universe.

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Generating rotating black hole solutions by using the Cayley-Dickson construction

Abstract: We exploit the power of the Cayley-Dickson algebra to generate stationary rotating black hole solutions in one fell swoop. Specifically, we derive the nine-dimensional Myers-Perry solution with four independent angular momenta by using the Janis-Newman algorithm and Giampieri’s simplification method, exploiting the octonion algebra. A general formula relating the dimension of the Cayley-Dickson algebra with the maximum number of angular momenta in each dimension is derived. Finally, we discuss the cut-off dimension for using the Cayley-Dickson construction along with the Janis-Newman algorithm for producing the rotating solutions. -- Based on: arXiv:2212.09882, 1904.06553, 1708.08969.

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