We investigate the response of the traversable wormholes to the external perturbations through finding their characteristic frequencies and time-domain profiles. The considered solution describes traversable wormholes between the branes in the two brane Randall-Sundrum model and was previously found within Einstein gravity with a conformally coupled scalar field. The evolution of perturbations of a wormhole is similar to that of a black hole and represents damped oscillations (ringing) at intermediately late times, which are suppressed by power law tails (proportional to t −2 for monopole perturbations) at asymptotically late times.

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods

We derive an expression for the quasinormal modes of scalar perturbations in near extreme d-dimensional Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes. We show that, in the near extreme limit, the dynamics of the scalar field is characterized by a Pöschl-Teller effective potential. The results are qualitatively independent of the spacetime dimension and field mass.

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrödinger equation is studied. We prove in particular the following: suppose the Hamiltonian H of a quantum mechanical particle on spacetime R N −1 × R has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the noncommutative versionĤ of H and H have identical spectra.

We investigate the evolution of a scalar field propagating in Reissner-Nordström Anti-de Sitter spacetime. Due to the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object-picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations concerning the wiggle of the imaginary frequencies have been given. The picture of the quasinormal modes depending on the multipole index has also been illustrated.