An introduction to extra dimensions

Constraining extra dimensions using observations of black hole quasi-normal modes

The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass M and the angular momentum J, known as the 'tidal charge' parameter, β . In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through - (a) negative values of β , and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of β correspond to a diminishing imaginary part of the quasi-normal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted values (for a given β ) of the frequency and damping time of the least-damped ℓ = 2 , m = 2 quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, β ≲ - 0.05 , providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.

Bound on Photon Circular Orbits in General Relativity and Beyond

The existence of a photon circular orbit can tell us a lot about the nature of the underlying spacetime, since it plays a pivotal role in the understanding of the characteristic signatures of compact objects, namely the quasi-normal modes and shadow radius. For this purpose, determination of the location of the photon circular orbit is of utmost importance. In this work, we derive bounds on the location of the photon circular orbit around compact objects within the purview of general relativity and beyond. As we have explicitly demonstrated, contrary to the earlier results in the context of general relativity, the bound on the location of the photon circular orbit is not necessarily an upper bound. Depending on the matter content, it is possible to arrive at a lower bound as well. This has interesting implications for the quasi-normal modes and shadow radius, the two key observables related to the strong field tests of gravity. Besides discussing the bound for higher dimensional general relativity, we have also considered how the bound on the photon circular orbits gets modified in the braneworld scenario, for pure Lovelock and general Lovelock theories of gravity. Implications of these results for compact objects were also discussed.

Holographic dark matter and Higgs models

We propose a dark matter candidate within the class of models where electroweak symmetry breaking is triggered by a light composite Higgs boson. In these dual anti-de Sitter/conformal field theory models, the Higgs boson emerges as a holographic pseudo-Goldstone boson, while dark matter can be identified with a stable composite fermion X0. The effective Lagrangian description of the Higgs and X0-multiplets, including higher-dimensional operators, can be tested at future colliders (LHC, ILC) and through astrophysical signals (ultrahigh-energy cosmic rays). The expected mass of X0, mX0 < or approximately 4pif approximately O (TeV), satisfies the bounds extracted from the cosmological relic density, while the experimental searches for dark matter further constrains the possible models.