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Register a new userStationary Spacetimes and Self-Adjointness in Klein-Gordon Theory
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We consider the problem of essential self-adjointness of the spatial part of the Klein-Gordon operator in stationary spacetimes. This operator is shown to be a Laplace-Beltrami type operator plus a potential. In globally hyperbolic spacetimes, essential selfadjointness is proven assuming smoothness of the metric components and semi-boundedness of the potential. This extends a recent result for static spacetimes to the stationary case. Furthermore, we generalize the results to certain non-globally hyperbolic spacetimes.
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The FLRW spacetimes can be realized as submanifolds of $mathbb{R}^6$. In this paper we relate the Laplace-Beltrami operator for an homogeneous scalar field $phi$ of $mathbb{R}^6$ to its explicit restriction on FLRW spacetimes. We then make the link between the homogeneous solutions of the equation $square_6 phi = 0$ in $mathbb{R}^6$ and those of the Klein-Gordon equation $(square_{f} - xi R^f + m^2)phi^f=0 $ for the free field $phi^f$ in the FLRW spacetime. We obtain as a byproduct a formula for the Ricci scalar of the FRLW spacetime in terms of the function $f$ defining this spacetime in $mathbb{R}^6$.
We study the influence of stationary axisymmetric spacetimes on Casimir energy. We consider a massive scalar field and analyze its dependence on the apparatus orientation with respect to the dragging direction associated with such spaces. We show that, for an apparatus orientation not considered before in the literature, the Casimir energy can change its sign, producing a repulsive force. As applications, we analyze two specific metrics: one associated with a linear motion of a cylinder and a circular equatorial motion around a gravitational source described by Kerr geometry.
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
We investigate the geodetic precession effect of a parallely transported spin-vector along a circular geodesic in the five-dimensional squashed Kaluza-Klein black hole spacetime. Then we derive the higher-dimensional correction of the precession angle to the general relativity. We find that the correction is proportional to the square of (size of extra dimension)/(gravitational radius of central object).
The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the spectral properties of the Klein-Gordon oscillator, which is closely related to that of the non-relativistic harmonic oscillator in three dimensions. Supersymmetry also enables us to derive a closed-form expression for the energy-dependent Greens function.
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