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Higher-derivative theories of free higher-spin fields are investigated focusing on their symmetries. Generalizing familiar two-derivative constrained formulations, we first construct less-constrained Einstein-like and Maxwell-like…
In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck…
We show that the introduction of a minimal length in the context of non-commutative spacetime gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a…
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at…
In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic…
We carry out the holographic renormalization of Einstein-Maxwell theory with curvature-squared corrections. In particular, we demonstrate how to construct the generalized Gibbons-Hawking surface term needed to ensure a perturbatively…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity and the eleven-dimensional Horava-Witten model. We show that these effective theories allow a much wider class of solutions…
We construct the higher order terms of curvatures in Lagrangians of the scale factor for the Friedmann-Lemaitre-Robertson-Walker universe, which are linear in the second derivative of the scale factor with respect to cosmic time. It is…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
The method of obtaining of Vlasov-type equations for systems of interacting massive charged particles from the general relativistic Einstein-Hilbert action is considered. An effective approach to synchronizing the proper times of various…
We construct new charged solutions of the Einstein-Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher dimensional Reissner-Nordstr\"{o}m spacetimes. For a negative…
We construct new classes of exact cosmological solutions to five dimensional Einstein-Maxwell-dilaton theory with two coupling constants for the dilaton-Maxwell term and dilaton-cosmological constant term. All the solutions are…
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their…
We study four-dimensional Einstein-Maxwell fields for which any higher-order corrections to the field equations effectively reduces to just a rescaling of the gravitational and the cosmological constant. These configurations are thus…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
Recently interest in using generalized reductions to construct massive supergravity theories has been revived in the context of M-theory and superstring theory. These compactifications produce mass parameters by introducing a linear…