Related papers: Time and a physical Hamiltonian for quantum gravit…
Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as first step, we develop the…
The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…
Theories described by non-Hermitian Hamiltonians are known to possess strictly positive energy eigenvalues and exhibit unitary time evolution if the Hamiltonian is symmetric under discrete parity and time (PT) transformation. In this work,…
We develop an algebraic equation to describe the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry from knowledge of the vacuum solution. Starting from a wide class of spherically symmetric…
In this paper, we study a possibility where gravity and time emerge from quantum matter. Within the Hilbert space of matter fields defined on a spatial manifold, we consider a sub-Hilbert space spanned by states which are parameterized by…
We apply the idea of using a matter time gauge in quantum gravity to quantum cosmology. For the Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe with dust and cosmological constant $\Lambda$, we show that the dynamics maps exactly to the…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
It is shown by a straightforward argument that the Hamiltonian generating the time evolution of the Dirac wave function in relativistic quantum mechanics is not hermitian with respect to the covariantly defined inner product whenever the…
In an attempt to re-establish space-time as an essential frame for formulating quantum gravity - rather than an "emergent" one -, we find that exact invariance under scale transformations is an essential new ingredient for such a theory.…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
We study general relativity with pressureless dust in the canonical formulation, with the dust field chosen as a matter-time gauge. The resulting theory has three physical degrees of freedom in the metric field. The linearized canonical…
In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of the Ho\v{r}ava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the…
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
The Hamiltonian formulation of the lowest-order projectable Horava gravity, namely the so-called $\lambda$-$R$ gravity, is studied. Since a preferred foliation has been chosen in projectable Horava gravity, there is no local Hamiltonian…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.