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The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…
Near a spinning point particle in (2+1)-dimensional gravity (or near an infinitely thin, straight, spinning string in 3+1 dimensions) there is a region of space-time with closed timelike curves. Exact solutions for extended sources with…
Einstein field equations show how matter curve spacetime, but, does curved spacetime creates matter? And if so, can we have geometrical foundations to every matter in the universe? In this note, we suggest an approach to derive non-general…
When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources of the gravitational field, such as neutron stars or black holes. In this paper I discuss another,…
The ADM energy for asymptotically flat spacetimes or its generalizations to asymptotically non-flat spacetimes measure the energy content of a stationary spacetime, such as a single black hole. Such a stationary energy is given as a…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
I take non-locality to be the Michaelson Morley experiment of the 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but emergent from entangled coherent…
Without invoking a perturbative expansion, we define the cosmological curvature perturbation, and consider its behaviour assuming that the universe is smooth over a sufficiently large comoving scale. The equations are simple, resembling…
Interactions with ordinary matter of a flux of high-speed uncharged dark matter particles pervasively present in space are examined. In this model, we find that the property of matter that we designate as mass becomes a measure of the…
In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity"…
We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the…
We define the notion of energy, and compute its values, for gravitational systems involving terms quadratic in curvature. While our construction parallels that of ordinary Einstein gravity, there are significant differences both…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Emergent modified gravity presents a new set of generally covariant gravitational theories in which the space-time metric is not directly given by one of the fundamental fields. A metric compatible with the modified dynamics of gravity is…