From Kerr to Heisenberg

Area of Science:

• General Relativity
• Theoretical Physics
• Gravitational Physics

Background:

• The Kerr-Newman solution describes the spacetime of a charged, rotating mass.
• Gravitomagnetism, arising from angular momentum, influences spacetime geometry.
• The Sagnac effect demonstrates spacetime's response to rotation.

Purpose of the Study:

• To analyze the generalized Sagnac effect in Kerr-Newman spacetime.
• To derive the asymmetry in light travel times for counter-rotating beams.
• To investigate the dependence of this asymmetry on source properties and fundamental constants.

Main Methods:

• Exact solution of Einstein's field equations (Kerr-Newman metric).
• Calculation of time-of-flight differences for light beams in the described geometry.
• Analysis of the limit as the circular trajectory shrinks to the origin.

Main Results:

• Explicit formula derived for the right/left asymmetry in light travel times.
• The asymmetry remains finite even as the trajectory radius approaches zero.
• The asymmetry is independent of the source's charge and Newton's constant, depending solely on the gravitomagnetic field.

Conclusions:

• The gravitomagnetic field's symmetry uniquely determines the Sagnac effect asymmetry.
• Introducing fermion spin links this effect to the Heisenberg uncertainty principle's lower limit for energy and time.
• This research provides insights into the interplay of gravity, electromagnetism, and quantum mechanics in extreme spacetime geometries.