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Introduction to the mathematics of general relativity

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Emergence of Friedmann Equation of Cosmology of a Flat Universe from the Time-Energy Uncertainty Principle

Friedmann equation of cosmology is based on the field equations of general relativity. Its derivation is straight-forward once the Einstein’s field equations are given and the derivation is independent of quantum mechanics. In this paper, it is shown that ...

2017

Heat kernel methods for Lifshitz theories

Diego Blas Temino, Mario Herrero Valea

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliat ...

Springer2017

Horava Gravity is Asymptotically Free in 2+1 Dimensions

Sergey Sibiryakov, Diego Blas Temino, Mario Herrero Valea

We compute the beta functions of marginal couplings in projectable Horava gravity in 2 + 1 spacetime dimensions. We show that the renormalization group flow has an asymptotically free fixed point in the ultraviolet (UV), establishing the theory as a UV-com ...

American Physical Society2017

On a Lagrangian Formulation of the Incompressible Euler Equation

Hasan Inci

In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...

Global Science Press2016

Scale-invariant alternatives to general relativity. II. Dilaton properties

Georgios Karananas

In the present paper, we revisit gravitational theories which are invariant under TDiffs-transverse (volume-preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent diffeomorphism-invar ...

Amer Physical Soc2016

Completing Lorentz violating massive gravity at high energies

Sergey Sibiryakov, Diego Blas Temino

Theories with massive gravitons are interesting for a variety of physical applications, ranging from cosmological phenomena to holographic modeling of condensed matter systems. To date, they have been formulated as effective field theories with a cutoff pr ...

Springer Verlag2015

A comment on the construction of the maximal globally hyperbolic Cauchy development

Willie Wai Yeung Wong

Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The con ...

American Institute of Physics2013

A positive mass theorem for two spatial dimensions

Willie Wai Yeung Wong

We observe that an analogue of the Positive Mass Theorem in the time-symmetric case for three-space-time-dimensional general relativity follows trivially from the Gauss-Bonnet theorem. In this case we also have that the spatial slice is diffeomorphic to $\ ...

pre-print2012

Gravitational radiation in Horava gravity

Hillary Sanctuary, Diego Blas Temino

We study the radiation of gravitational waves by self-gravitating binary systems in the low-energy limit of Horava gravity. We find that the predictions for the energy-loss formula of general relativity are modified already for Newtonian sources: the quadr ...

2011

Quasi-static cyclic tests and plastic hinge analysis of RC structural walls

Katrin Beyer, Alessandro Dazio

This paper presents the results of quasi-static cyclic tests on six reinforced concrete (RC) walls performed at the ETH Zurich. These large-scale tests investigate the effect of different vertical reinforcement contents and different reinforcement ductilit ...

Elsevier2009