Second Order Perturbations of a Macroscopic String; Covariant Approach

Abstract

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessaary for a consistent computation of the energy. We also quantize the perturbations and derive the mass-formula up to second order in perturbations for an observer using world-sheet time $\tau$. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass-spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

New discussion about the quantum mass-spectrum in chapter 4

References in corpus (6)

• Strings, Black Holes and Lorentz Contraction
• Black Holes from Nucleating Strings
• Perturbations of a topological defect as a theory of scalar fields interacting with an external vector potential
• Noether Currents for Bosonic Branes
• String Thermalization at a Black Hole Horizon
• String Spreading on Black Hole Horizon

Cited by in corpus (3)

• Second order perturbations of relativistic membranes in curved spacetime
• Covariant higher order perturbations of branes in curved spacetime
• Pulsating string solution and stability in two parameter $\chi$-deformed background