Related papers: Generalized Boundary Conditions for the qBounce Ex…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
I consider an extension of General Relativity by an auxiliary non-dynamical dimension that enables our space-time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…
We discuss possible observational manifestations of static, spherically symmetric solutions of a class of multidimensional theories of gravity, which includes the low energy limits of supergravities and superstring theories as special…
We consider a general five-dimensional sigma-model coupled to gravity, with any number of scalars and general sigma-model metric and potential. We discuss in detail the problem of the boundary conditions for the scalar fluctuations, in the…
With a view toward the problem of computing the linearized cosmological perturbations in Randall-Sundrum cosmological models where a Z2 symmetry has been imposed about a boundary brane, we derive the form of the linearized Israel matching…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
Recent work in the literature has studied a new set of local boundary conditions for the quantized gravitational field, where the spatial components of metric perturbations, and ghost modes, are subject to Robin boundary conditions, whereas…
The consistency of quantum field theories defined on domains with external borders imposes very restrictive constraints on the type of boundary conditions that the fields can satisfy. We analyse the global geometrical and topological…
When spatial boundaries are inserted, SUSY can be broken. We show that in an $\mathcal{N}=2$ supersymmetric theory, all the boundary conditions allowed by self-adjointness of the Hamiltonian break $\mathcal{N}=2$ SUSY while only a few of…
We formulate the most general gravitational models with constant negative curvature ("hyperbolic gravity") on an arbitrary orientable two-dimensional surface of genus $g$ with $b$ circle boundaries in terms of a $\text{PSL}(2,\mathbb…
The recently observed quantum states of neutrons bound in a gravitational field are analyzed in the framework of one-parameter isospectral hamiltonians. Potentials isospectral to the usual Newton potential are explicitly constructed for the…
In this work we introduce Relativistic Quantum Geometry (RQG) on a Modern Kaluza-Klein theory by studying the boundary conditions on a extended Einstein-Hilbert action for a 5D vacuum defined on a 5D (background) Riemannian manifold. We…
Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion…
The one-dimensional Schr\"odinger equation with the point potential in the form of the derivative of Dirac's delta function, $\lambda \delta'(x)$ with $\lambda$ being a coupling constant, is investigated. This equation is known to require…
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…
The laws of thermodynamics in the expanding universe are formulated within the quasi-metric framework. Since the quasi-metric cosmic expansion does not directly influence momenta of material particles, so that the expansion directly cools…
The pure-gravity sector of the minimal Standard-Model Extension is studied in the limit of Riemann spacetime. A method is developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the…
We study the interplay of general relativity, the equivalence principle, and high-precision experiments involving atomic transitions and g factor measurements. In particular, we derive a generalized Dirac Hamiltonian, which describes both…