https://doi.org/10.1140/epjc/s10052-021-09714-4
Regular Article - Theoretical Physics
The Raychaudhuri equation for a quantized timelike geodesic congruence
Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, Nadia, India
Received:
28
June
2021
Accepted:
3
October
2021
Published online:
14
October
2021
A recent attempt to arrive at a quantum version of Raychaudhuri’s equation is looked at critically. It is shown that the method, and even the idea, has some inherent problems. The issues are pointed out here. We have also shown that it is possible to salvage the method in some limited domain of applicability. Although no generality can be claimed, a quantum version of the equation should be useful in the context of ascertaining the existence of a singularity in the quantum regime. The equation presented in the present work holds for arbitrary 
dimensions. An important feature of the Hamiltonian in the operator form is that it admits a self-adjoint extension quite generally. Thus, the conservation of probability is ensured.
© The Author(s) 2021
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