Lower Dimensional Gravity Research Articles

Taxonomy of brane gravity localisations

Generating an effective theory of lower-dimensional gravity on a submanifold within an original higher-dimensional theory can be achieved even if the reduction space is non-compact. Localisation of gravity on such a lower-dimensional worldvolume can be interpreted in a number of ways. The first scenario, Type I, requires a mathematically consistent Kaluza-Klein style truncation down to a theory in the lower dimension, in which case solutions purely within that reduced theory exist. However, that situation is not a genuine localisation of gravity because all such solutions have higher-dimensional source extensions according to the Kaluza-Klein ansatz. Also, there is no meaningful notion of Newton’s constant for such Type I constructions.Types II and III admit coupling to genuinely localised sources in the higher-dimensional theory, with corresponding solutions involving full sets of higher-dimensional modes. Type II puts no specific boundary conditions near the worldvolume aside from regularity away from sources. In a case where the wave equation separated in the non-compact space transverse to the worldvolume admits a normalisable zero mode, the Type III scenario requires boundary conditions near the worldvolume that permit the inclusion of that zero mode in mode expansions for gravitational wave fluctuations or potentials. In such a case, an effective theory of lower-dimensional gravity can emerge at sufficiently large worldvolume distance scales.This taxonomy of brane gravity localisations is developed in detail for linearised perturbations about a background incorporating the vacuum solution of Salam-Sezgin theory when embedded into ten-dimensional supergravity with a hyperbolic non-compact transverse space. Interpretations of the Newton constant for the corresponding Type III localisation are then analysed.

Conservation and integrability in lower-dimensional gravity

We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.

A class of interior solutions corresponding to a [formula omitted]-dimensional asymptotically anti-de Sitter spacetime

Lower-dimensional gravity has the potential of providing non-trivial and valuable insight into some of the conceptual issues arising in four-dimensional relativistic gravitational analysis. The asymptotically anti-de Sitter ( 2 + 1 )-dimensional spacetime described by Bañados, Teitelboim and Zanelli (BTZ) which admits a black hole solution, has become a source of fascination for theoretical physicists in recent years. By suitably choosing the form of the mass function m ( r ) , we derive a new class of solutions for the interior of an isotropic star corresponding to the exterior ( 2 + 1 ) asymptotically anti-de Sitter BTZ spacetime. The solution obtained satisfies all the regularity conditions and its simple analytical form helps us to study the physical parameters of the configuration in a simple manner.