Related papers: Positive energy theorem implies constraints on sta…
The positive energy theorems are a fundamental pillar in mathematical general relativity. Originally proved by Schoen-Yau and later Witten, these theorems were established for asymptotically flat manifolds where the metric tends to the…
The Positive Binding Conjecture is a proposed formulation of the Weak Gravity Conjecture appropriate to Anti de-Sitter (AdS) space. It proposes that in a consistent gravitational theory, with a $U(1)$ gauge symmetry, there must exist a…
A generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data is proved. This work is motivated by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the…
Many complex quantum systems can be described by effectively nonlinear dynamics. While such dynamics have many appealing characteristics, they also make the analysis significantly more involved. This is due to the fact that only a few…
In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
The energy in the ghost-free massive gravity theory is calculated via explicitly resolving the initial value constraints for spherically symmetric deformations of flat space. It turns out that the energy is positive in some cases, but in…
We study relativistic stars in the context of scalar tensor theories of gravity that try to account for the observed cosmic acceleration and satisfy the local gravity constraints via the chameleon mechanism. More specifically, we consider…
We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal…
We combine complementary datasets from Cosmic Microwave Background (CMB) anisotropy measurements, high redshift supernovae (SN-Ia) observations and data from local cluster abundances and galaxy clustering (LSS) to constrain the dark energy…
We investigate two simplified non-singular cyclic models with a negative time-varying cosmological constant to represent the non-conventional mechanism of negative cosmological constant expected to address the late-time cosmic acceleration.…
Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We…
The study of energy conditions has many significant applications in general relativistic and cosmological contexts. This paper explores the energy conditions in the framework of the most general scalar-tensor theory with field equations…
Some time ago we have suggested that positive vacuum energy exhibits a finite quantum break time, which can be a signal that a positive cosmological constant is inconsistent. From the requirement that Universe never undergoes through…
It has been shown that in the context of General Relativity (GR) enriched with a new set of discrete symmetry reversal conjugate metrics, negative energy states can be rehabilitated while avoiding the well-known instability issues. We…
We present positive energy theorems in asymptotically translationally invariant spacetimes which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.
We establish adiabatic theorems with and without spectral gap condition for general -- typically dissipative -- linear operators $A(t): D(A(t)) \subset X \to X$ with time-independent domains $D(A(t)) = D$ in some Banach space $X$. Compared…
The positive mass theorem in general relativity states that in an asymptotically flat spacetime, if the momentum--energy tensor is divergence-free and satisfies a dominant energy condition, then a total momentum--energy four-vector can be…
We present a general theory of potentials that support bound states at positive energies (bound states in the continuum). On the theoretical side, we prove that, for systems described by nonlocal potentials of the form $V(r,r')$, bound…