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Register a new userTowards Communication in a Curved Spacetime Geometry
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The current race in quantum communication -- endeavouring to establish a global quantum network -- must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti-de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10~radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism can cause a 12.2 % cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information.
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We extend Derricks theorem to the case of a generic irrotational curved spacetime adopting a strategy similar to the original proof. We show that a static relativistic star made of real scalar fields is never possible regardless of the geometrical properties of the (static) spacetimes. The generalised theorem offers a tool that can be used to check the stability of localised solutions of a number of types of scalar fields models as well as of compact objects of theories of gravity with a non-minimally coupled scalar degree of freedom.
We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang-Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensure conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators.
Relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry is considered. The Fermi coordinates adapted to the time-like geodesic are utilized to describe the low-energy physics in the laboratory and to calculate the leading correction due to the curvature of the space-time geometry to the Schrodinger equation. The correction is employed to calculate the probability of excitation for a hydrogen atom that falls in or is scattered by a general Schwarzchild black hole. Since the excited states decay due to spontaneous photon emission, this study provides the theoretical base for detection of small isolated black holes by observing the decay of the excited states as neutral hydrogen atoms in the vacuum are devoured by the black hole.
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation becomes asymmetric for the exchange of the indices, differently from the standard Euclidean one. Its incompressible limit suggests that the viscous term should be represented with the Bochner Laplacian. Moreover the modified Navier-Stokes-Fourier (NSF) equation proposed by Brenner can be considered even in the curved spacetime. To confirm the compatibility with the symmetry principle, SVM is applied to the gauge-invariant Lagrangian of a charged compressible fluid and then the Lorentz force is reproduced as the interaction between the Abelian gauge fields and the viscous charged fluid.
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